0.07/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.12	% Command  : run_Leo-III %s %d THM
0.12/0.33	% Computer : n019.cluster.edu
0.12/0.33	% Model    : x86_64 x86_64
0.12/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory   : 8042.1875MB
0.12/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit : 1440
0.12/0.33	% WCLimit  : 180
0.12/0.33	% DateTime : Thu Jul  4 07:27:25 EDT 2024
0.12/0.33	% CPUTime  : 
0.96/0.86	% [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
2.11/1.15	% [INFO] 	 Parsing done (287ms). 
2.11/1.16	% [INFO] 	 Running in sequential loop mode. 
2.74/1.37	% [INFO] 	 eprover registered as external prover. 
2.74/1.38	% [INFO] 	 Scanning for conjecture ... 
3.03/1.53	% [INFO] 	 Found a conjecture (or negated_conjecture) and 350 axioms. Running axiom selection ... 
3.36/1.64	% [INFO] 	 Axiom selection finished. Selected 152 axioms (removed 198 axioms). 
4.12/1.78	% [INFO] 	 Problem is higher-order (TPTP THF). 
4.12/1.80	% [INFO] 	 Type checking passed. 
4.12/1.80	% [CONFIG] 	 Using configuration: timeout(180) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
35.14/11.03	% External prover 'e' found a proof!
35.14/11.03	% [INFO] 	 Killing All external provers ... 
35.14/11.03	% Time passed: 10514ms (effective reasoning time: 9873ms)
35.14/11.03	% Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
35.14/11.03	% Axioms used in derivation (152): fact_139_old_Oprod_Oinducts, fact_127_lift__assnI, fact_187_relAPP__def, fact_56_tagged__fun__relD__lhs, fact_209_param__op__nres__ASSERT__bnd, fact_338_fun__rel__id, fact_236_autoref__Let__cong, fact_0_param__bind, fact_29_autoref__Let, fact_168_prod__cases, fact_185_relAPP__def, fact_114_autoref__APP, fact_46_fun__relD2, fact_212_param__op__nres__ASSERT__bnd, fact_182_relAPP__def, fact_205_autoref__RETURN, fact_160_prod__cases, fact_186_relAPP__def, fact_175_surj__pair, fact_26_autoref__Let, fact_294_fun__rel__id__simp, fact_254_autoref__REMOVE__INTERNAL__EQ, fact_159_Pair__inject, fact_157_Pair__inject, fact_25_autoref__Let, fact_95_prod_Oinject, fact_66_tagged__fun__relD__rhs, fact_109_old_Oprod_Oinject, fact_111_autoref__APP, fact_203_autoref__RETURN, fact_195_lift__assn__def, fact_108_old_Oprod_Oinject, fact_206_autoref__RETURN, fact_106_old_Oprod_Oinject, fact_273_Collect__mem__eq, fact_21_autoref__Let, fact_130_old_Oprod_Oinducts, fact_3_param__bind, fact_72_tagged__fun__relD__both, fact_210_param__op__nres__ASSERT__bnd, fact_2_param__bind, fact_263_mem__Collect__eq, fact_272_Collect__mem__eq, fact_219_fun__relE2, fact_12_fun__relI, fact_7_param__bind, fact_107_old_Oprod_Oinject, fact_156_Pair__inject, fact_150_Pair__inject, fact_155_Pair__inject, fact_284_nres__monad2, fact_235_autoref__Let__cong, fact_52_tagged__fun__relD__lhs, fact_264_mem__Collect__eq, fact_261_mem__Collect__eq, fact_169_prod__cases, fact_181_relAPP__def, fact_198_lift__assn__def, fact_275_nres__monad1, fact_118_autoref__APP, fact_105_old_Oprod_Oinject, fact_100_old_Oprod_Oinject, fact_145_old_Oprod_Oexhaust, fact_1_param__bind, fact_242_autoref__Let__cong, fact_28_autoref__Let, fact_115_autoref__APP, fact_250_autoref__REMOVE__INTERNAL__EQ, fact_5_param__bind, fact_117_autoref__APP, fact_148_old_Oprod_Oexhaust, fact_253_autoref__REMOVE__INTERNAL__EQ, fact_91_prod_Oinject, fact_149_old_Oprod_Oexhaust, fact_276_nres__monad1, fact_196_lift__assn__def, fact_126_lift__assnI, fact_8_param__bind, fact_178_surj__pair, fact_86_tagged__fun__relD__none, fact_92_prod_Oinject, fact_207_param__op__nres__ASSERT__bnd, fact_23_autoref__Let, fact_176_surj__pair, fact_280_nres__monad1, fact_136_old_Oprod_Oinducts, fact_274_Collect__mem__eq, fact_283_nres__monad2, fact_6_param__bind, fact_282_nres__monad2, fact_262_mem__Collect__eq, fact_279_nres__monad1, fact_202_autoref__RETURN, fact_113_autoref__APP, fact_116_autoref__APP, fact_270_Collect__mem__eq, fact_188_relAPP__def, fact_281_nres__monad1, fact_82_tagged__fun__relD__none, fact_128_lift__assnI, fact_201_autoref__RETURN, fact_42_fun__relD2, fact_243_autoref__Let__cong, fact_9_param__bind, fact_179_surj__pair, fact_146_old_Oprod_Oexhaust, fact_158_Pair__inject, fact_137_old_Oprod_Oinducts, fact_278_nres__monad1, fact_16_fun__relI, fact_166_prod__cases, fact_147_old_Oprod_Oexhaust, fact_211_param__op__nres__ASSERT__bnd, fact_237_autoref__Let__cong, fact_238_autoref__Let__cong, fact_229_fun__relE1, fact_93_prod_Oinject, fact_125_lift__assnI, fact_170_surj__pair, fact_140_old_Oprod_Oexhaust, fact_32_fun__relD1, fact_177_surj__pair, fact_135_old_Oprod_Oinducts, fact_76_tagged__fun__relD__both, fact_277_nres__monad1, fact_183_relAPP__def, fact_138_old_Oprod_Oinducts, fact_119_autoref__APP, fact_260_mem__Collect__eq, fact_240_autoref__Let__cong, fact_90_prod_Oinject, fact_199_lift__assn__def, fact_129_lift__assnI, fact_251_autoref__REMOVE__INTERNAL__EQ, fact_208_param__op__nres__ASSERT__bnd, fact_184_relAPP__def, fact_271_Collect__mem__eq, fact_197_lift__assn__def, fact_180_relAPP__def, fact_27_autoref__Let, fact_213_param__op__nres__ASSERT__bnd, fact_167_prod__cases, fact_94_prod_Oinject, fact_252_autoref__REMOVE__INTERNAL__EQ, fact_200_autoref__RETURN, fact_189_relAPP__def, fact_204_autoref__RETURN, fact_4_param__bind, fact_36_fun__relD1, fact_62_tagged__fun__relD__rhs, fact_165_prod__cases, fact_239_autoref__Let__cong
35.14/11.03	% No. of inferences in proof: 514
35.14/11.03	% SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10514 ms resp. 9873 ms w/o parsing
36.43/11.21	% SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
36.43/11.21	thf(set_Pr1614046668nres_d_type, type, set_Pr1614046668nres_d: $tType).
36.43/11.21	thf(produc819780758nres_d_type, type, produc819780758nres_d: $tType).
36.43/11.21	thf(set_Pr1712866168nres_d_type, type, set_Pr1712866168nres_d: $tType).
36.43/11.21	thf(set_Pr1710101992nres_d_type, type, set_Pr1710101992nres_d: $tType).
36.43/11.21	thf(produc1834705330nres_d_type, type, produc1834705330nres_d: $tType).
36.43/11.21	thf(set_Pr613277282nres_d_type, type, set_Pr613277282nres_d: $tType).
36.43/11.21	thf(produc809931564nres_d_type, type, produc809931564nres_d: $tType).
36.43/11.21	thf(set_Pr642586912nres_d_type, type, set_Pr642586912nres_d: $tType).
36.43/11.21	thf(set_Pr1436380704nres_b_type, type, set_Pr1436380704nres_b: $tType).
36.43/11.21	thf(set_Pr794589344nres_d_type, type, set_Pr794589344nres_d: $tType).
36.43/11.21	thf(set_Pr1652381728nres_c_type, type, set_Pr1652381728nres_c: $tType).
36.43/11.21	thf(set_Pr1245537056nres_c_type, type, set_Pr1245537056nres_c: $tType).
36.43/11.21	thf(set_Pr24800800nres_d_type, type, set_Pr24800800nres_d: $tType).
36.43/11.21	thf(set_Pr2039330848nres_a_type, type, set_Pr2039330848nres_a: $tType).
36.43/11.21	thf(set_Pr818594592nres_b_type, type, set_Pr818594592nres_b: $tType).
36.43/11.21	thf(set_Pr882593184nres_c_type, type, set_Pr882593184nres_c: $tType).
36.43/11.21	thf(set_Pr1824526846nres_d_type, type, set_Pr1824526846nres_d: $tType).
36.43/11.21	thf(produc235099114nres_d_type, type, produc235099114nres_d: $tType).
36.43/11.21	thf(produc1869490410nres_b_type, type, produc1869490410nres_b: $tType).
36.43/11.21	thf(produc2007659370nres_d_type, type, produc2007659370nres_d: $tType).
36.43/11.21	thf(produc1545802474nres_c_type, type, produc1545802474nres_c: $tType).
36.43/11.21	thf(produc1811455466nres_c_type, type, produc1811455466nres_c: $tType).
36.43/11.21	thf(produc2043357418nres_d_type, type, produc2043357418nres_d: $tType).
36.43/11.21	thf(produc1298363114nres_a_type, type, produc1298363114nres_a: $tType).
36.43/11.21	thf(produc1530265066nres_b_type, type, produc1530265066nres_b: $tType).
36.43/11.21	thf(produc1581500522nres_c_type, type, produc1581500522nres_c: $tType).
36.43/11.21	thf(set_Pr1125433775_nat_o_type, type, set_Pr1125433775_nat_o: $tType).
36.43/11.21	thf(produc416848975_nat_o_type, type, produc416848975_nat_o: $tType).
36.43/11.21	thf(set_Pr1413987240nres_d_type, type, set_Pr1413987240nres_d: $tType).
36.43/11.21	thf(set_Pr584391464nres_c_type, type, set_Pr584391464nres_c: $tType).
36.43/11.21	thf(set_Pr2080238504nres_d_type, type, set_Pr2080238504nres_d: $tType).
36.43/11.21	thf(set_Pr1358127528nres_b_type, type, set_Pr1358127528nres_b: $tType).
36.43/11.21	thf(set_Pr1250642728nres_c_type, type, set_Pr1250642728nres_c: $tType).
36.43/11.21	thf(produc1479083634nres_d_type, type, produc1479083634nres_d: $tType).
36.43/11.21	thf(produc1716397554nres_c_type, type, produc1716397554nres_c: $tType).
36.43/11.21	thf(produc1677145714nres_d_type, type, produc1677145714nres_d: $tType).
36.43/11.21	thf(produc96971890nres_b_type, type, produc96971890nres_b: $tType).
36.43/11.21	thf(produc1914459634nres_c_type, type, produc1914459634nres_c: $tType).
36.43/11.21	thf(set_Pr1146978466nres_d_type, type, set_Pr1146978466nres_d: $tType).
36.43/11.21	thf(set_Pr1402127136nres_b_type, type, set_Pr1402127136nres_b: $tType).
36.43/11.21	thf(set_Pr451158306nres_d_type, type, set_Pr451158306nres_d: $tType).
36.43/11.21	thf(set_Pr57594146nres_c_type, type, set_Pr57594146nres_c: $tType).
36.43/11.21	thf(set_Pr181592673nres_c_type, type, set_Pr181592673nres_c: $tType).
36.43/11.21	thf(set_Pr797615136nres_d_type, type, set_Pr797615136nres_d: $tType).
36.43/11.21	thf(set_Pr436741343nres_a_type, type, set_Pr436741343nres_a: $tType).
36.43/11.21	thf(set_Pr1052763806nres_b_type, type, set_Pr1052763806nres_b: $tType).
36.43/11.21	thf(set_Pr404050976nres_c_type, type, set_Pr404050976nres_c: $tType).
36.43/11.21	thf(set_Pr1602564423_nat_o_type, type, set_Pr1602564423_nat_o: $tType).
36.43/11.21	thf(produc1757587562nres_d_type, type, produc1757587562nres_d: $tType).
36.43/11.21	thf(set_Pr1537816964nres_d_type, type, set_Pr1537816964nres_d: $tType).
36.43/11.21	thf(set_Pr1351316363_int_o_type, type, set_Pr1351316363_int_o: $tType).
36.43/11.21	thf(produc1616993579_int_o_type, type, produc1616993579_int_o: $tType).
36.43/11.21	thf(set_Pr766923865_nat_o_type, type, set_Pr766923865_nat_o: $tType).
36.43/11.21	thf(set_Pr1435428853_int_o_type, type, set_Pr1435428853_int_o: $tType).
36.43/11.21	thf(set_Pr42712642nres_b_type, type, set_Pr42712642nres_b: $tType).
36.43/11.21	thf(set_Pr119249666nres_d_type, type, set_Pr119249666nres_d: $tType).
36.43/11.21	thf(set_Pr1345535106nres_b_type, type, set_Pr1345535106nres_b: $tType).
36.43/11.21	thf(set_Pr1812169344nres_c_type, type, set_Pr1812169344nres_c: $tType).
36.43/11.21	thf(set_Pr890971136nres_a_type, type, set_Pr890971136nres_a: $tType).
36.43/11.21	thf(set_Pr1434142398nres_d_type, type, set_Pr1434142398nres_d: $tType).
36.43/11.21	thf(set_Pr512944190nres_b_type, type, set_Pr512944190nres_b: $tType).
36.43/11.21	thf(set_Pr979578428nres_c_type, type, set_Pr979578428nres_c: $tType).
36.43/11.21	thf(set_Pr409172028nres_c_type, type, set_Pr409172028nres_c: $tType).
36.43/11.21	thf(set_Pr589481214nres_d_type, type, set_Pr589481214nres_d: $tType).
36.43/11.21	thf(set_Pr1635457468nres_a_type, type, set_Pr1635457468nres_a: $tType).
36.43/11.21	thf(set_Pr1815766654nres_b_type, type, set_Pr1815766654nres_b: $tType).
36.43/11.21	thf(set_Pr134917244nres_c_type, type, set_Pr134917244nres_c: $tType).
36.43/11.21	thf(set_Pr1361202684nres_a_type, type, set_Pr1361202684nres_a: $tType).
36.43/11.21	thf(produc1314004473_nat_o_type, type, produc1314004473_nat_o: $tType).
36.43/11.21	thf(set_Pr524661639_nat_o_type, type, set_Pr524661639_nat_o: $tType).
36.43/11.21	thf(set_Pr1774281699_o_o_o_type, type, set_Pr1774281699_o_o_o: $tType).
36.43/11.21	thf(set_Pr37069423_o_c_c_type, type, set_Pr37069423_o_c_c: $tType).
36.43/11.21	thf(produc13679884nres_b_type, type, produc13679884nres_b: $tType).
36.43/11.21	thf(produc2052210762nres_c_type, type, produc2052210762nres_c: $tType).
36.43/11.21	thf(produc1484956106nres_a_type, type, produc1484956106nres_a: $tType).
36.43/11.21	thf(produc1943257992nres_d_type, type, produc1943257992nres_d: $tType).
36.43/11.21	thf(produc1376003336nres_b_type, type, produc1376003336nres_b: $tType).
36.43/11.21	thf(produc1106446854nres_c_type, type, produc1106446854nres_c: $tType).
36.43/11.21	thf(produc2103861704nres_d_type, type, produc2103861704nres_d: $tType).
36.43/11.21	thf(produc1536607048nres_b_type, type, produc1536607048nres_b: $tType).
36.43/11.21	thf(produc1267050566nres_c_type, type, produc1267050566nres_c: $tType).
36.43/11.21	thf(produc699795910nres_a_type, type, produc699795910nres_a: $tType).
36.43/11.21	thf(produc1174115751_nat_o_type, type, produc1174115751_nat_o: $tType).
36.43/11.21	thf(set_Pr1920786322nres_d_type, type, set_Pr1920786322nres_d: $tType).
36.43/11.21	thf(set_Pr1176961680nres_b_type, type, set_Pr1176961680nres_b: $tType).
36.43/11.21	thf(set_Pr1408729042nres_c_type, type, set_Pr1408729042nres_c: $tType).
36.43/11.21	thf(set_Pr664904400nres_a_type, type, set_Pr664904400nres_a: $tType).
36.43/11.21	thf(set_Pr1640496404nres_d_type, type, set_Pr1640496404nres_d: $tType).
36.43/11.21	thf(set_Pr194842259nres_c_type, type, set_Pr194842259nres_c: $tType).
36.43/11.21	thf(set_Pr896671762nres_b_type, type, set_Pr896671762nres_b: $tType).
36.43/11.21	thf(set_Pr1598501265nres_a_type, type, set_Pr1598501265nres_a: $tType).
36.43/11.21	thf(set_Pr426609621nres_d_type, type, set_Pr426609621nres_d: $tType).
36.43/11.21	thf(set_Pr1128439124nres_c_type, type, set_Pr1128439124nres_c: $tType).
36.43/11.21	thf(set_Pr1830268627nres_b_type, type, set_Pr1830268627nres_b: $tType).
36.43/11.21	thf(set_Pr384614482nres_a_type, type, set_Pr384614482nres_a: $tType).
36.43/11.21	thf(set_Pr1524520971nt_o_o_type, type, set_Pr1524520971nt_o_o: $tType).
36.43/11.21	thf(set_Pr1371175689_o_o_o_type, type, set_Pr1371175689_o_o_o: $tType).
36.43/11.21	thf(set_Pr68707591_o_o_o_type, type, set_Pr68707591_o_o_o: $tType).
36.43/11.21	thf(produc1410942426nres_b_type, type, produc1410942426nres_b: $tType).
36.43/11.21	thf(produc1565049884nres_c_type, type, produc1565049884nres_c: $tType).
36.43/11.21	thf(produc1433404954nres_a_type, type, produc1433404954nres_a: $tType).
36.43/11.21	thf(produc1719157342nres_d_type, type, produc1719157342nres_d: $tType).
36.43/11.21	thf(produc1587512412nres_b_type, type, produc1587512412nres_b: $tType).
36.43/11.21	thf(produc1741619870nres_c_type, type, produc1741619870nres_c: $tType).
36.43/11.21	thf(produc1609974940nres_a_type, type, produc1609974940nres_a: $tType).
36.43/11.21	thf(produc496448427nt_o_o_type, type, produc496448427nt_o_o: $tType).
36.43/11.21	thf(set_Pr807116335_c_c_c_type, type, set_Pr807116335_c_c_c: $tType).
36.43/11.21	thf(set_Pr1659864199_nat_o_type, type, set_Pr1659864199_nat_o: $tType).
36.43/11.21	thf(set_Pr1320171143_int_o_type, type, set_Pr1320171143_int_o: $tType).
36.43/11.21	thf(produc1039600167_o_o_o_type, type, produc1039600167_o_o_o: $tType).
36.43/11.21	thf(set_Pr46530663_o_c_c_type, type, set_Pr46530663_o_c_c: $tType).
36.43/11.21	thf(refine116648739nres_d_type, type, refine116648739nres_d: $tType).
36.43/11.21	thf(refine1696877731nres_b_type, type, refine1696877731nres_b: $tType).
36.43/11.21	thf(set_Pr2088790547_o_o_o_type, type, set_Pr2088790547_o_o_o: $tType).
36.43/11.21	thf(produc724473255_nat_o_type, type, produc724473255_nat_o: $tType).
36.43/11.21	thf(produc480790439_int_o_type, type, produc480790439_int_o: $tType).
36.43/11.21	thf(set_Pr2058424041at_o_o_type, type, set_Pr2058424041at_o_o: $tType).
36.43/11.21	thf(set_Pr1006121889nt_o_o_type, type, set_Pr1006121889nt_o_o: $tType).
36.43/11.21	thf(set_Pr1495585653nt_o_o_type, type, set_Pr1495585653nt_o_o: $tType).
36.43/11.21	thf(set_Pr1673989513_c_c_c_type, type, set_Pr1673989513_c_c_c: $tType).
36.43/11.21	thf(set_Pr1357842111at_nat_type, type, set_Pr1357842111at_nat: $tType).
36.43/11.21	thf(set_Pr1749533559at_int_type, type, set_Pr1749533559at_int: $tType).
36.43/11.21	thf(set_Pr1719254903nt_nat_type, type, set_Pr1719254903nt_nat: $tType).
36.43/11.21	thf(set_Pr2110946351nt_int_type, type, set_Pr2110946351nt_int: $tType).
36.43/11.21	thf(produc1839156403_o_o_o_type, type, produc1839156403_o_o_o: $tType).
36.43/11.21	thf(set_Pr1933985801_c_o_o_type, type, set_Pr1933985801_c_o_o: $tType).
36.43/11.21	thf(set_Pr1955643401_o_o_c_type, type, set_Pr1955643401_o_o_c: $tType).
36.43/11.21	thf(produc482595465at_o_o_type, type, produc482595465at_o_o: $tType).
36.43/11.21	thf(produc426758977nt_o_o_type, type, produc426758977nt_o_o: $tType).
36.43/11.21	thf(set_Pr618353415_o_o_o_type, type, set_Pr618353415_o_o_o: $tType).
36.43/11.21	thf(set_Pr933902153_nat_c_type, type, set_Pr933902153_nat_c: $tType).
36.43/11.21	thf(set_Pr1575377993_int_c_type, type, set_Pr1575377993_int_c: $tType).
36.43/11.21	thf(produc1281043295at_nat_type, type, produc1281043295at_nat: $tType).
36.43/11.21	thf(produc610583575at_int_type, type, produc610583575at_int: $tType).
36.43/11.21	thf(produc1389674519nt_nat_type, type, produc1389674519nt_nat: $tType).
36.43/11.21	thf(produc719214799nt_int_type, type, produc719214799nt_int: $tType).
36.43/11.21	thf(set_Pr310822599_nat_o_type, type, set_Pr310822599_nat_o: $tType).
36.43/11.21	thf(set_Pr94755271_int_o_type, type, set_Pr94755271_int_o: $tType).
36.43/11.21	thf(set_Pr343524935_o_nat_type, type, set_Pr343524935_o_nat: $tType).
36.43/11.21	thf(set_Pr1437791047_o_int_type, type, set_Pr1437791047_o_int: $tType).
36.43/11.21	thf(produc1838469673_c_o_o_type, type, produc1838469673_c_o_o: $tType).
36.43/11.21	thf(produc2056997417_o_o_c_type, type, produc2056997417_o_o_c: $tType).
36.43/11.21	thf(produc46704423_o_o_o_type, type, produc46704423_o_o_o: $tType).
36.43/11.21	thf(set_Pr1234209675_a_c_c_type, type, set_Pr1234209675_a_c_c: $tType).
36.43/11.21	thf(produc1144174441_nat_c_type, type, produc1144174441_nat_c: $tType).
36.43/11.21	thf(produc1769036905_int_c_type, type, produc1769036905_int_c: $tType).
36.43/11.21	thf(set_Pr709440729_a_o_c_type, type, set_Pr709440729_a_o_c: $tType).
36.43/11.21	thf(produc878596327_nat_o_type, type, produc878596327_nat_o: $tType).
36.43/11.21	thf(produc1620501479_int_o_type, type, produc1620501479_int_o: $tType).
36.43/11.21	thf(produc1991839847_o_nat_type, type, produc1991839847_o_nat: $tType).
36.43/11.21	thf(produc922271079_o_int_type, type, produc922271079_o_int: $tType).
36.43/11.21	thf(set_Pr934623755_o_o_o_type, type, set_Pr934623755_o_o_o: $tType).
36.43/11.21	thf(set_Pr1986765409at_nat_type, type, set_Pr1986765409at_nat: $tType).
36.43/11.21	thf(set_Pr1858794777nt_int_type, type, set_Pr1858794777nt_int: $tType).
36.43/11.21	thf(product_prod_a_a_c_c_type, type, product_prod_a_a_c_c: $tType).
36.43/11.21	thf(product_prod_o_a_o_c_type, type, product_prod_o_a_o_c: $tType).
36.43/11.21	thf(product_prod_o_o_o_o_type, type, product_prod_o_o_o_o: $tType).
36.43/11.21	thf(refine449204144nres_d_type, type, refine449204144nres_d: $tType).
36.43/11.21	thf(refine440942639nres_c_type, type, refine440942639nres_c: $tType).
36.43/11.21	thf(refine432681134nres_b_type, type, refine432681134nres_b: $tType).
36.43/11.21	thf(refine424419629nres_a_type, type, refine424419629nres_a: $tType).
36.43/11.21	thf(set_Product_prod_d_d_type, type, set_Product_prod_d_d: $tType).
36.43/11.21	thf(set_Product_prod_d_b_type, type, set_Product_prod_d_b: $tType).
36.43/11.21	thf(set_Product_prod_c_c_type, type, set_Product_prod_c_c: $tType).
36.43/11.21	thf(set_Product_prod_c_a_type, type, set_Product_prod_c_a: $tType).
36.43/11.21	thf(set_Product_prod_b_d_type, type, set_Product_prod_b_d: $tType).
36.43/11.21	thf(set_Product_prod_b_c_type, type, set_Product_prod_b_c: $tType).
36.43/11.21	thf(set_Product_prod_b_b_type, type, set_Product_prod_b_b: $tType).
36.43/11.21	thf(set_Product_prod_b_a_type, type, set_Product_prod_b_a: $tType).
36.43/11.21	thf(set_Product_prod_a_d_type, type, set_Product_prod_a_d: $tType).
36.43/11.21	thf(set_Product_prod_a_c_type, type, set_Product_prod_a_c: $tType).
36.43/11.21	thf(set_Product_prod_a_b_type, type, set_Product_prod_a_b: $tType).
36.43/11.21	thf(set_Product_prod_a_a_type, type, set_Product_prod_a_a: $tType).
36.43/11.21	thf(product_prod_nat_nat_type, type, product_prod_nat_nat: $tType).
36.43/11.21	thf(product_prod_int_int_type, type, product_prod_int_int: $tType).
36.43/11.21	thf(set_Product_prod_o_o_type, type, set_Product_prod_o_o: $tType).
36.43/11.21	thf(product_prod_b_d_type, type, product_prod_b_d: $tType).
36.43/11.21	thf(product_prod_a_c_type, type, product_prod_a_c: $tType).
36.43/11.21	thf(product_prod_a_a_type, type, product_prod_a_a: $tType).
36.43/11.21	thf(product_prod_o_o_type, type, product_prod_o_o: $tType).
36.43/11.21	thf(autoref_annot_type, type, autoref_annot: $tType).
36.43/11.21	thf(nat_type, type, nat: $tType).
36.43/11.21	thf(int_type, type, int: $tType).
36.43/11.21	thf(d_type, type, d: $tType).
36.43/11.21	thf(c_type, type, c: $tType).
36.43/11.21	thf(b_type, type, b: $tType).
36.43/11.21	thf(a_type, type, a: $tType).
36.43/11.21	thf(autore867490625_o_c_c_type, type, autore867490625_o_c_c: ((($o > $o) > ((($o > $o) > c) > c)) > (autoref_annot > (($o > $o) > ((($o > $o) > c) > c))))).
36.43/11.21	thf(autore1290907938nres_b_type, type, autore1290907938nres_b: ((a > ((a > refine432681134nres_b) > refine432681134nres_b)) > (autoref_annot > (a > ((a > refine432681134nres_b) > refine432681134nres_b))))).
36.43/11.21	thf(autore1757597947_o_o_o_type, type, autore1757597947_o_o_o: ((c > ((c > ($o > $o)) > ($o > $o))) > (autoref_annot > (c > ((c > ($o > $o)) > ($o > $o)))))).
36.43/11.21	thf(autore956520418nres_c_type, type, autore956520418nres_c: ((c > ((c > refine440942639nres_c) > refine440942639nres_c)) > (autoref_annot > (c > ((c > refine440942639nres_c) > refine440942639nres_c))))).
36.43/11.21	thf(autore241567778nres_d_type, type, autore241567778nres_d: ((c > ((c > refine449204144nres_d) > refine449204144nres_d)) > (autoref_annot > (c > ((c > refine449204144nres_d) > refine449204144nres_d))))).
36.43/11.21	thf(autore1422848225_c_c_c_type, type, autore1422848225_c_c_c: ((c > ((c > c) > c)) > (autoref_annot > (c > ((c > c) > c))))).
36.43/11.21	thf(autore73061154nres_c_type, type, autore73061154nres_c: ((d > ((d > refine440942639nres_c) > refine440942639nres_c)) > (autoref_annot > (d > ((d > refine440942639nres_c) > refine440942639nres_c))))).
36.43/11.21	thf(autore1505592162nres_d_type, type, autore1505592162nres_d: ((d > ((d > refine449204144nres_d) > refine449204144nres_d)) > (autoref_annot > (d > ((d > refine449204144nres_d) > refine449204144nres_d))))).
36.43/11.21	thf(autoref_APP_o_o_c_c_type, type, autoref_APP_o_o_c_c: (((($o > $o) > c) > c) > ((($o > $o) > c) > c))).
36.43/11.21	thf(autore1733926270_o_c_c_type, type, autore1733926270_o_c_c: ((($o > $o) > ((($o > $o) > c) > c)) > (($o > $o) > ((($o > $o) > c) > c)))).
36.43/11.21	thf(autoref_APP_o_o_a_type, type, autoref_APP_o_o_a: ((($o > $o) > a) > (($o > $o) > a))).
36.43/11.21	thf(autoref_APP_o_o_c_type, type, autoref_APP_o_o_c: ((($o > $o) > c) > (($o > $o) > c))).
36.43/11.21	thf(autore956252284nres_b_type, type, autore956252284nres_b: (((a > refine432681134nres_b) > refine432681134nres_b) > ((a > refine432681134nres_b) > refine432681134nres_b))).
36.43/11.21	thf(autore821920247_o_o_o_type, type, autore821920247_o_o_o: (((c > ($o > $o)) > ($o > $o)) > ((c > ($o > $o)) > ($o > $o)))).
36.43/11.21	thf(autore2084714426nres_c_type, type, autore2084714426nres_c: (((c > refine440942639nres_c) > refine440942639nres_c) > ((c > refine440942639nres_c) > refine440942639nres_c))).
36.43/11.22	thf(autore1159379066nres_d_type, type, autore1159379066nres_d: (((c > refine449204144nres_d) > refine449204144nres_d) > ((c > refine449204144nres_d) > refine449204144nres_d))).
36.43/11.22	thf(autoref_APP_c_c_c_type, type, autoref_APP_c_c_c: (((c > c) > c) > ((c > c) > c))).
36.43/11.22	thf(autore964129529nres_c_type, type, autore964129529nres_c: (((d > refine440942639nres_c) > refine440942639nres_c) > ((d > refine440942639nres_c) > refine440942639nres_c))).
36.43/11.22	thf(autore38794169nres_d_type, type, autore38794169nres_d: (((d > refine449204144nres_d) > refine449204144nres_d) > ((d > refine449204144nres_d) > refine449204144nres_d))).
36.43/11.22	thf(autore781669463nres_b_type, type, autore781669463nres_b: ((a > ((a > refine432681134nres_b) > refine432681134nres_b)) > (a > ((a > refine432681134nres_b) > refine432681134nres_b)))).
36.43/11.22	thf(autoref_APP_a_o_o_type, type, autoref_APP_a_o_o: ((a > ($o > $o)) > (a > ($o > $o)))).
36.43/11.22	thf(autore1382402919nres_a_type, type, autore1382402919nres_a: ((a > refine424419629nres_a) > (a > refine424419629nres_a))).
36.43/11.22	thf(autore1390664424nres_b_type, type, autore1390664424nres_b: ((a > refine432681134nres_b) > (a > refine432681134nres_b))).
36.43/11.22	thf(autoref_APP_a_a_type, type, autoref_APP_a_a: ((a > a) > (a > a))).
36.43/11.22	thf(autore1669652584nres_a_type, type, autore1669652584nres_a: ((b > refine424419629nres_a) > (b > refine424419629nres_a))).
36.43/11.22	thf(autore1677914089nres_b_type, type, autore1677914089nres_b: ((b > refine432681134nres_b) > (b > refine432681134nres_b))).
36.43/11.22	thf(autore1554881264_o_o_o_type, type, autore1554881264_o_o_o: ((c > ((c > ($o > $o)) > ($o > $o))) > (c > ((c > ($o > $o)) > ($o > $o))))).
36.43/11.22	thf(autore224164375nres_c_type, type, autore224164375nres_c: ((c > ((c > refine440942639nres_c) > refine440942639nres_c)) > (c > ((c > refine440942639nres_c) > refine440942639nres_c)))).
36.43/11.22	thf(autore430131799nres_d_type, type, autore430131799nres_d: ((c > ((c > refine449204144nres_d) > refine449204144nres_d)) > (c > ((c > refine449204144nres_d) > refine449204144nres_d)))).
36.43/11.22	thf(autoref_APP_c_c_c_c_type, type, autoref_APP_c_c_c_c: ((c > ((c > c) > c)) > (c > ((c > c) > c)))).
36.43/11.22	thf(autoref_APP_c_o_o_type, type, autoref_APP_c_o_o: ((c > ($o > $o)) > (c > ($o > $o)))).
36.43/11.22	thf(autore1973425259nres_c_type, type, autore1973425259nres_c: ((c > refine440942639nres_c) > (c > refine440942639nres_c))).
36.43/11.22	thf(autore1981686764nres_d_type, type, autore1981686764nres_d: ((c > refine449204144nres_d) > (c > refine449204144nres_d))).
36.43/11.22	thf(autoref_APP_c_c_type, type, autoref_APP_c_c: ((c > c) > (c > c))).
36.43/11.22	thf(autore1989911767nres_c_type, type, autore1989911767nres_c: ((d > ((d > refine440942639nres_c) > refine440942639nres_c)) > (d > ((d > refine440942639nres_c) > refine440942639nres_c)))).
36.43/11.22	thf(autore48395543nres_d_type, type, autore48395543nres_d: ((d > ((d > refine449204144nres_d) > refine449204144nres_d)) > (d > ((d > refine449204144nres_d) > refine449204144nres_d)))).
36.43/11.22	thf(autore113191276nres_c_type, type, autore113191276nres_c: ((d > refine440942639nres_c) > (d > refine440942639nres_c))).
36.43/11.22	thf(autore121452781nres_d_type, type, autore121452781nres_d: ((d > refine449204144nres_d) > (d > refine449204144nres_d))).
36.43/11.22	thf(autore971224502_o_c_c_type, type, autore971224502_o_c_c: ((($o > $o) > ((($o > $o) > c) > c)) > (($o > $o) > ((($o > $o) > c) > c)))).
36.43/11.22	thf(autore906565869nres_b_type, type, autore906565869nres_b: ((a > ((a > refine432681134nres_b) > refine432681134nres_b)) > (a > ((a > refine432681134nres_b) > refine432681134nres_b)))).
36.43/11.22	thf(autore1861331824_o_o_o_type, type, autore1861331824_o_o_o: ((c > ((c > ($o > $o)) > ($o > $o))) > (c > ((c > ($o > $o)) > ($o > $o))))).
36.43/11.22	thf(autore572178349nres_c_type, type, autore572178349nres_c: ((c > ((c > refine440942639nres_c) > refine440942639nres_c)) > (c > ((c > refine440942639nres_c) > refine440942639nres_c)))).
36.43/11.22	thf(autore2004709357nres_d_type, type, autore2004709357nres_d: ((c > ((c > refine449204144nres_d) > refine449204144nres_d)) > (c > ((c > refine449204144nres_d) > refine449204144nres_d)))).
36.43/11.22	thf(autoref_OP_c_c_c_c_type, type, autoref_OP_c_c_c_c: ((c > ((c > c) > c)) > (c > ((c > c) > c)))).
36.43/11.22	thf(autore1836202733nres_c_type, type, autore1836202733nres_c: ((d > ((d > refine440942639nres_c) > refine440942639nres_c)) > (d > ((d > refine440942639nres_c) > refine440942639nres_c)))).
36.43/11.22	thf(autore1121250093nres_d_type, type, autore1121250093nres_d: ((d > ((d > refine449204144nres_d) > refine449204144nres_d)) > (d > ((d > refine449204144nres_d) > refine449204144nres_d)))).
36.43/11.22	thf(autore821969498_o_c_c_type, type, autore821969498_o_c_c: (set_Pr37069423_o_c_c > autoref_annot)).
36.43/11.22	thf(autore1424734926_o_o_o_type, type, autore1424734926_o_o_o: (set_Pr1774281699_o_o_o > autoref_annot)).
36.43/11.22	thf(autore1545784985nres_c_type, type, autore1545784985nres_c: (set_Pr1250642728nres_c > autoref_annot)).
36.43/11.22	thf(autore16598297nres_b_type, type, autore16598297nres_b: (set_Pr1358127528nres_b > autoref_annot)).
36.43/11.22	thf(autore349294361nres_d_type, type, autore349294361nres_d: (set_Pr2080238504nres_d > autoref_annot)).
36.43/11.22	thf(autore464253722_c_c_c_type, type, autore464253722_c_c_c: (set_Pr807116335_c_c_c > autoref_annot)).
36.43/11.22	thf(autore1683160729nres_c_type, type, autore1683160729nres_c: (set_Pr584391464nres_c > autoref_annot)).
36.43/11.22	thf(autore486670105nres_d_type, type, autore486670105nres_d: (set_Pr1413987240nres_d > autoref_annot)).
36.43/11.22	thf(autore1113312320RNAL_o_type, type, autore1113312320RNAL_o: ($o > $o)).
36.43/11.22	thf(autore233619284nres_b_type, type, autore233619284nres_b: (((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)) > (((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)) > $o))).
36.43/11.22	thf(autore1360171649nres_b_type, type, autore1360171649nres_b: (((a > refine432681134nres_b) > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > $o))).
36.43/11.22	thf(autore1318775848nres_b_type, type, autore1318775848nres_b: ((a > ((a > refine432681134nres_b) > refine432681134nres_b)) > ((a > ((a > refine432681134nres_b) > refine432681134nres_b)) > $o))).
36.43/11.22	thf(autore519998265nres_b_type, type, autore519998265nres_b: ((a > refine432681134nres_b) > ((a > refine432681134nres_b) > $o))).
36.43/11.22	thf(autore1904863386L_EQ_a_type, type, autore1904863386L_EQ_a: (a > (a > $o))).
36.43/11.22	thf(produc2068274457_o_o_c_type, type, produc2068274457_o_o_c: ((($o > $o) > a) > ((($o > $o) > c) > produc2056997417_o_o_c))).
36.43/11.22	thf(produc1910095910nres_d_type, type, produc1910095910nres_d: (((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)) > (((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d)) > produc809931564nres_d))).
36.43/11.22	thf(produc2075136412nres_d_type, type, produc2075136412nres_d: (((a > refine432681134nres_b) > refine432681134nres_b) > (((c > refine449204144nres_d) > refine449204144nres_d) > produc1757587562nres_d))).
36.43/11.22	thf(product_Pair_o_o_o_o_type, type, product_Pair_o_o_o_o: (($o > $o) > (($o > $o) > product_prod_o_o_o_o))).
36.43/11.22	thf(produc973126316nres_d_type, type, produc973126316nres_d: ((refine1696877731nres_b > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)) > ((refine116648739nres_d > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d)) > produc1834705330nres_d))).
36.43/11.22	thf(produc912866704nres_d_type, type, produc912866704nres_d: ((refine424419629nres_a > ((refine424419629nres_a > ((a > refine432681134nres_b) > refine432681134nres_b)) > ((a > refine432681134nres_b) > refine432681134nres_b))) > ((refine440942639nres_c > ((refine440942639nres_c > ((c > refine449204144nres_d) > refine449204144nres_d)) > ((c > refine449204144nres_d) > refine449204144nres_d))) > produc819780758nres_d))).
36.43/11.22	thf(produc2073916516nres_c_type, type, produc2073916516nres_c: ((refine424419629nres_a > ((a > refine424419629nres_a) > refine424419629nres_a)) > ((refine440942639nres_c > ((c > refine440942639nres_c) > refine440942639nres_c)) > produc1581500522nres_c))).
36.43/11.22	thf(produc1992182244nres_b_type, type, produc1992182244nres_b: ((refine424419629nres_a > ((a > refine432681134nres_b) > refine432681134nres_b)) > ((refine424419629nres_a > ((a > refine432681134nres_b) > refine432681134nres_b)) > produc1530265066nres_b))).
36.43/11.22	thf(produc1066811108nres_a_type, type, produc1066811108nres_a: ((refine424419629nres_a > ((a > refine432681134nres_b) > refine432681134nres_b)) > ((refine432681134nres_b > ((b > refine424419629nres_a) > refine424419629nres_a)) > produc1298363114nres_a))).
36.43/11.22	thf(produc1576596708nres_d_type, type, produc1576596708nres_d: ((refine424419629nres_a > ((a > refine432681134nres_b) > refine432681134nres_b)) > ((refine440942639nres_c > ((c > refine449204144nres_d) > refine449204144nres_d)) > produc2043357418nres_d))).
36.43/11.22	thf(produc651225572nres_c_type, type, produc651225572nres_c: ((refine424419629nres_a > ((a > refine432681134nres_b) > refine432681134nres_b)) > ((refine449204144nres_d > ((d > refine440942639nres_c) > refine440942639nres_c)) > produc1811455466nres_c))).
36.43/11.22	thf(produc385572580nres_c_type, type, produc385572580nres_c: ((refine432681134nres_b > ((b > refine424419629nres_a) > refine424419629nres_a)) > ((refine449204144nres_d > ((d > refine440942639nres_c) > refine440942639nres_c)) > produc1545802474nres_c))).
36.43/11.22	thf(produc2035736420nres_d_type, type, produc2035736420nres_d: ((refine432681134nres_b > ((b > refine432681134nres_b) > refine432681134nres_b)) > ((refine449204144nres_d > ((d > refine449204144nres_d) > refine449204144nres_d)) > produc2007659370nres_d))).
36.43/11.22	thf(produc183923940nres_b_type, type, produc183923940nres_b: ((refine440942639nres_c > ((c > refine449204144nres_d) > refine449204144nres_d)) > ((refine424419629nres_a > ((a > refine432681134nres_b) > refine432681134nres_b)) > produc1869490410nres_b))).
36.43/11.22	thf(produc1915822052nres_d_type, type, produc1915822052nres_d: ((refine440942639nres_c > ((c > refine449204144nres_d) > refine449204144nres_d)) > ((refine440942639nres_c > ((c > refine449204144nres_d) > refine449204144nres_d)) > produc235099114nres_d))).
36.43/11.22	thf(produc1824358636nres_c_type, type, produc1824358636nres_c: ((a > ((a > refine424419629nres_a) > refine424419629nres_a)) > ((c > ((c > refine440942639nres_c) > refine440942639nres_c)) > produc1914459634nres_c))).
36.43/11.22	thf(produc295171948nres_b_type, type, produc295171948nres_b: ((a > ((a > refine432681134nres_b) > refine432681134nres_b)) > ((a > ((a > refine432681134nres_b) > refine432681134nres_b)) > produc96971890nres_b))).
36.43/11.22	thf(produc627868012nres_d_type, type, produc627868012nres_d: ((a > ((a > refine432681134nres_b) > refine432681134nres_b)) > ((c > ((c > refine449204144nres_d) > refine449204144nres_d)) > produc1677145714nres_d))).
36.43/11.22	thf(produc1393542937_c_o_o_type, type, produc1393542937_c_o_o: ((a > ($o > $o)) > ((c > ($o > $o)) > produc1838469673_c_o_o))).
36.43/11.22	thf(produc278407104nres_a_type, type, produc278407104nres_a: ((a > refine424419629nres_a) > ((a > refine424419629nres_a) > produc699795910nres_a))).
36.43/11.22	thf(produc1827604032nres_c_type, type, produc1827604032nres_c: ((a > refine424419629nres_a) > ((c > refine440942639nres_c) > produc1267050566nres_c))).
36.43/11.22	thf(produc809128386nres_b_type, type, produc809128386nres_b: ((a > refine432681134nres_b) > ((a > refine432681134nres_b) > produc1536607048nres_b))).
36.43/11.22	thf(produc210841666nres_d_type, type, produc210841666nres_d: ((a > refine432681134nres_b) > ((c > refine449204144nres_d) > produc2103861704nres_d))).
36.43/11.22	thf(product_Pair_a_a_c_c_type, type, product_Pair_a_a_c_c: ((a > a) > ((c > c) > product_prod_a_a_c_c))).
36.43/11.22	thf(produc1961734380nres_c_type, type, produc1961734380nres_c: ((b > ((b > refine424419629nres_a) > refine424419629nres_a)) > ((d > ((d > refine440942639nres_c) > refine440942639nres_c)) > produc1716397554nres_c))).
36.43/11.22	thf(produc765243756nres_d_type, type, produc765243756nres_d: ((b > ((b > refine432681134nres_b) > refine432681134nres_b)) > ((d > ((d > refine449204144nres_d) > refine449204144nres_d)) > produc1479083634nres_d))).
36.43/11.22	thf(produc316577664nres_c_type, type, produc316577664nres_c: ((b > refine424419629nres_a) > ((d > refine440942639nres_c) > produc1106446854nres_c))).
36.43/11.22	thf(produc1445585666nres_b_type, type, produc1445585666nres_b: ((b > refine432681134nres_b) > ((b > refine432681134nres_b) > produc1376003336nres_b))).
36.43/11.22	thf(produc847298946nres_d_type, type, produc847298946nres_d: ((b > refine432681134nres_b) > ((d > refine449204144nres_d) > produc1943257992nres_d))).
36.43/11.22	thf(produc1063567300nres_a_type, type, produc1063567300nres_a: ((c > refine440942639nres_c) > ((a > refine424419629nres_a) > produc1484956106nres_a))).
36.43/11.22	thf(produc465280580nres_c_type, type, produc465280580nres_c: ((c > refine440942639nres_c) > ((c > refine440942639nres_c) > produc2052210762nres_c))).
36.43/11.22	thf(produc83262214nres_b_type, type, produc83262214nres_b: ((d > refine449204144nres_d) > ((b > refine432681134nres_b) > produc13679884nres_b))).
36.43/11.22	thf(produc1136923598nres_a_type, type, produc1136923598nres_a: (refine424419629nres_a > (refine424419629nres_a > produc1609974940nres_a))).
36.43/11.22	thf(produc1153446608nres_c_type, type, produc1153446608nres_c: (refine424419629nres_a > (refine440942639nres_c > produc1741619870nres_c))).
36.43/11.22	thf(produc2130641934nres_b_type, type, produc2130641934nres_b: (refine432681134nres_b > (refine432681134nres_b > produc1587512412nres_b))).
36.43/11.22	thf(produc2147164944nres_d_type, type, produc2147164944nres_d: (refine432681134nres_b > (refine449204144nres_d > produc1719157342nres_d))).
36.43/11.22	thf(produc960353612nres_a_type, type, produc960353612nres_a: (refine440942639nres_c > (refine424419629nres_a > produc1433404954nres_a))).
36.43/11.22	thf(produc976876622nres_c_type, type, produc976876622nres_c: (refine440942639nres_c > (refine440942639nres_c > produc1565049884nres_c))).
36.43/11.22	thf(produc1954071948nres_b_type, type, produc1954071948nres_b: (refine449204144nres_d > (refine432681134nres_b > produc1410942426nres_b))).
36.43/11.22	thf(product_Pair_a_a_type, type, product_Pair_a_a: (a > (a > product_prod_a_a))).
36.43/11.22	thf(product_Pair_a_c_type, type, product_Pair_a_c: (a > (c > product_prod_a_c))).
36.43/11.22	thf(product_Pair_b_d_type, type, product_Pair_b_d: (b > (d > product_prod_b_d))).
36.43/11.22	thf(refine2063221604TURN_a_type, type, refine2063221604TURN_a: (a > refine424419629nres_a)).
36.43/11.22	thf(refine2063221605TURN_b_type, type, refine2063221605TURN_b: (b > refine432681134nres_b)).
36.43/11.22	thf(refine2063221606TURN_c_type, type, refine2063221606TURN_c: (c > refine440942639nres_c)).
36.43/11.22	thf(refine2063221607TURN_d_type, type, refine2063221607TURN_d: (d > refine449204144nres_d)).
36.43/11.22	thf(refine1985319227es_b_b_type, type, refine1985319227es_b_b: (refine1696877731nres_b > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b))).
36.43/11.22	thf(refine1129534141es_d_d_type, type, refine1129534141es_d_d: (refine116648739nres_d > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d))).
36.43/11.22	thf(refine436832838nd_a_a_type, type, refine436832838nd_a_a: (refine424419629nres_a > ((a > refine424419629nres_a) > refine424419629nres_a))).
36.43/11.22	thf(refine436832839nd_a_b_type, type, refine436832839nd_a_b: (refine424419629nres_a > ((a > refine432681134nres_b) > refine432681134nres_b))).
36.43/11.22	thf(refine1264602245nd_b_a_type, type, refine1264602245nd_b_a: (refine432681134nres_b > ((b > refine424419629nres_a) > refine424419629nres_a))).
36.43/11.22	thf(refine1264602246nd_b_b_type, type, refine1264602246nd_b_b: (refine432681134nres_b > ((b > refine432681134nres_b) > refine432681134nres_b))).
36.43/11.22	thf(refine2092371654nd_c_c_type, type, refine2092371654nd_c_c: (refine440942639nres_c > ((c > refine440942639nres_c) > refine440942639nres_c))).
36.43/11.22	thf(refine2092371655nd_c_d_type, type, refine2092371655nd_c_d: (refine440942639nres_c > ((c > refine449204144nres_d) > refine449204144nres_d))).
36.43/11.22	thf(refine772657413nd_d_c_type, type, refine772657413nd_d_c: (refine449204144nres_d > ((d > refine440942639nres_c) > refine440942639nres_c))).
36.43/11.22	thf(refine772657414nd_d_d_type, type, refine772657414nd_d_d: (refine449204144nres_d > ((d > refine449204144nres_d) > refine449204144nres_d))).
36.43/11.22	thf(refine1711024813nres_d_type, type, refine1711024813nres_d: (set_Pr613277282nres_d > ((((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d)) > $o) > (((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)) > $o)))).
36.43/11.22	thf(refine1958703523nres_d_type, type, refine1958703523nres_d: (set_Pr797615136nres_d > ((((c > refine449204144nres_d) > refine449204144nres_d) > $o) > (((a > refine432681134nres_b) > refine432681134nres_b) > $o)))).
36.43/11.22	thf(refine408412177nres_d_type, type, refine408412177nres_d: (set_Pr2080238504nres_d > (((c > ((c > refine449204144nres_d) > refine449204144nres_d)) > $o) > ((a > ((a > refine432681134nres_b) > refine432681134nres_b)) > $o)))).
36.43/11.22	thf(refine746536475nres_d_type, type, refine746536475nres_d: (set_Pr589481214nres_d > (((c > refine449204144nres_d) > $o) > ((a > refine432681134nres_b) > $o)))).
36.43/11.22	thf(refine321891363sn_a_c_type, type, refine321891363sn_a_c: (set_Product_prod_a_c > ((c > $o) > (a > $o)))).
36.43/11.22	thf(refine1535302424nres_d_type, type, refine1535302424nres_d: (set_Pr589481214nres_d > set_Pr1537816964nres_d)).
36.43/11.22	thf(refine737062558el_a_a_type, type, refine737062558el_a_a: (set_Product_prod_a_a > set_Pr384614482nres_a)).
36.43/11.22	thf(refine737062559el_a_b_type, type, refine737062559el_a_b: (set_Product_prod_a_b > set_Pr1830268627nres_b)).
36.43/11.22	thf(refine737062560el_a_c_type, type, refine737062560el_a_c: (set_Product_prod_a_c > set_Pr1128439124nres_c)).
36.43/11.22	thf(refine737062561el_a_d_type, type, refine737062561el_a_d: (set_Product_prod_a_d > set_Pr426609621nres_d)).
36.43/11.22	thf(refine1564831965el_b_a_type, type, refine1564831965el_b_a: (set_Product_prod_b_a > set_Pr1598501265nres_a)).
36.43/11.22	thf(refine1564831966el_b_b_type, type, refine1564831966el_b_b: (set_Product_prod_b_b > set_Pr896671762nres_b)).
36.43/11.22	thf(refine1564831967el_b_c_type, type, refine1564831967el_b_c: (set_Product_prod_b_c > set_Pr194842259nres_c)).
36.43/11.22	thf(refine1564831968el_b_d_type, type, refine1564831968el_b_d: (set_Product_prod_b_d > set_Pr1640496404nres_d)).
36.43/11.22	thf(refine245117724el_c_a_type, type, refine245117724el_c_a: (set_Product_prod_c_a > set_Pr664904400nres_a)).
36.43/11.22	thf(refine245117726el_c_c_type, type, refine245117726el_c_c: (set_Product_prod_c_c > set_Pr1408729042nres_c)).
36.43/11.22	thf(refine1072887132el_d_b_type, type, refine1072887132el_d_b: (set_Product_prod_d_b > set_Pr1176961680nres_b)).
36.43/11.22	thf(refine1072887134el_d_d_type, type, refine1072887134el_d_d: (set_Product_prod_d_d > set_Pr1920786322nres_d)).
36.43/11.22	thf(refine1437029927_bnd_a_type, type, refine1437029927_bnd_a: ($o > (refine424419629nres_a > refine424419629nres_a))).
36.43/11.22	thf(refine1437029928_bnd_b_type, type, refine1437029928_bnd_b: ($o > (refine432681134nres_b > refine432681134nres_b))).
36.43/11.22	thf(refine1437029929_bnd_c_type, type, refine1437029929_bnd_c: ($o > (refine440942639nres_c > refine440942639nres_c))).
36.43/11.22	thf(refine1437029930_bnd_d_type, type, refine1437029930_bnd_d: ($o > (refine449204144nres_d > refine449204144nres_d))).
36.43/11.22	thf(id_a_R351071993nres_b_type, type, id_a_R351071993nres_b: set_Pr1815766654nres_b).
36.43/11.22	thf(id_Ref1256934482nres_b_type, type, id_Ref1256934482nres_b: set_Pr896671762nres_b).
36.43/11.22	thf(id_a_type, type, id_a: set_Product_prod_a_a).
36.43/11.22	thf(fun_re1859931662_c_a_c_type, type, fun_re1859931662_c_a_c: (set_Pr1955643401_o_o_c > (set_Product_prod_a_c > set_Pr46530663_o_c_c))).
36.43/11.22	thf(fun_re2071856555nres_d_type, type, fun_re2071856555nres_d: (set_Pr797615136nres_d > (set_Pr1640496404nres_d > set_Pr1824526846nres_d))).
36.43/11.22	thf(fun_re1144975870_o_c_c_type, type, fun_re1144975870_o_c_c: (set_Pr934623755_o_o_o > (set_Pr46530663_o_c_c > set_Pr37069423_o_c_c))).
36.43/11.22	thf(fun_rel_o_o_o_o_a_c_type, type, fun_rel_o_o_o_o_a_c: (set_Pr934623755_o_o_o > (set_Product_prod_a_c > set_Pr1955643401_o_o_c))).
36.43/11.22	thf(fun_re692194867nres_d_type, type, fun_re692194867nres_d: (set_Pr24800800nres_d > (set_Pr797615136nres_d > set_Pr1712866168nres_d))).
36.43/11.22	thf(fun_re2021699288_o_o_o_type, type, fun_re2021699288_o_o_o: (set_Pr1933985801_c_o_o > (set_Pr934623755_o_o_o > set_Pr1371175689_o_o_o))).
36.43/11.22	thf(fun_re1877185935nres_c_type, type, fun_re1877185935nres_c: (set_Pr134917244nres_c > (set_Pr1128439124nres_c > set_Pr404050976nres_c))).
36.43/11.22	thf(fun_re1579405647nres_b_type, type, fun_re1579405647nres_b: (set_Pr1815766654nres_b > (set_Pr896671762nres_b > set_Pr1052763806nres_b))).
36.43/11.22	thf(fun_re1140323340nres_a_type, type, fun_re1140323340nres_a: (set_Pr1635457468nres_a > (set_Pr1598501265nres_a > set_Pr436741343nres_a))).
36.43/11.22	thf(fun_re1306413669nres_d_type, type, fun_re1306413669nres_d: (set_Pr589481214nres_d > (set_Pr1824526846nres_d > set_Pr613277282nres_d))).
36.43/11.22	thf(fun_re1394577105nres_d_type, type, fun_re1394577105nres_d: (set_Pr589481214nres_d > (set_Pr1640496404nres_d > set_Pr797615136nres_d))).
36.43/11.22	thf(fun_re955494798nres_c_type, type, fun_re955494798nres_c: (set_Pr409172028nres_c > (set_Pr194842259nres_c > set_Pr181592673nres_c))).
36.43/11.22	thf(fun_rel_a_a_c_c_a_c_type, type, fun_rel_a_a_c_c_a_c: (set_Pr1234209675_a_c_c > (set_Product_prod_a_c > set_Pr1673989513_c_c_c))).
36.43/11.22	thf(fun_re1366722255nres_c_type, type, fun_re1366722255nres_c: (set_Pr979578428nres_c > (set_Pr1128439124nres_c > set_Pr57594146nres_c))).
36.43/11.22	thf(fun_re884113425nres_d_type, type, fun_re884113425nres_d: (set_Pr1434142398nres_d > (set_Pr1640496404nres_d > set_Pr451158306nres_d))).
36.43/11.22	thf(fun_re1925572817nres_b_type, type, fun_re1925572817nres_b: (set_Pr1345535106nres_b > (set_Pr1176961680nres_b > set_Pr1402127136nres_b))).
36.43/11.22	thf(fun_re1740744275nres_d_type, type, fun_re1740744275nres_d: (set_Pr119249666nres_d > (set_Pr1920786322nres_d > set_Pr1146978466nres_d))).
36.43/11.22	thf(fun_re1732033515nres_d_type, type, fun_re1732033515nres_d: (set_Pr1537816964nres_d > (set_Pr1824526846nres_d > set_Pr1710101992nres_d))).
36.43/11.22	thf(fun_re2045802267nres_b_type, type, fun_re2045802267nres_b: (set_Pr384614482nres_a > (set_Pr1052763806nres_b > set_Pr818594592nres_b))).
36.43/11.22	thf(fun_re1904331357nres_a_type, type, fun_re1904331357nres_a: (set_Pr1830268627nres_b > (set_Pr436741343nres_a > set_Pr2039330848nres_a))).
36.43/11.22	thf(fun_re1190106143nres_d_type, type, fun_re1190106143nres_d: (set_Pr1128439124nres_c > (set_Pr1712866168nres_d > set_Pr1614046668nres_d))).
36.43/11.22	thf(fun_re1915547295nres_c_type, type, fun_re1915547295nres_c: (set_Pr1128439124nres_c > (set_Pr404050976nres_c > set_Pr882593184nres_c))).
36.43/11.22	thf(fun_re439246495nres_d_type, type, fun_re439246495nres_d: (set_Pr1128439124nres_c > (set_Pr797615136nres_d > set_Pr24800800nres_d))).
36.43/11.22	thf(fun_re297775585nres_c_type, type, fun_re297775585nres_c: (set_Pr426609621nres_d > (set_Pr181592673nres_c > set_Pr1245537056nres_c))).
36.43/11.22	thf(fun_re816936095nres_c_type, type, fun_re816936095nres_c: (set_Pr1640496404nres_d > (set_Pr57594146nres_c > set_Pr1652381728nres_c))).
36.43/11.22	thf(fun_re1488118943nres_d_type, type, fun_re1488118943nres_d: (set_Pr1640496404nres_d > (set_Pr451158306nres_d > set_Pr794589344nres_d))).
36.43/11.22	thf(fun_re650017687nres_b_type, type, fun_re650017687nres_b: (set_Pr664904400nres_a > (set_Pr1402127136nres_b > set_Pr1436380704nres_b))).
36.43/11.22	thf(fun_re1190945563nres_d_type, type, fun_re1190945563nres_d: (set_Pr1408729042nres_c > (set_Pr1146978466nres_d > set_Pr642586912nres_d))).
36.43/11.22	thf(fun_re1165441639nres_b_type, type, fun_re1165441639nres_b: (set_Product_prod_a_a > (set_Pr1052763806nres_b > set_Pr1358127528nres_b))).
36.43/11.22	thf(fun_re843975451nres_a_type, type, fun_re843975451nres_a: (set_Product_prod_a_a > (set_Pr384614482nres_a > set_Pr1361202684nres_a))).
36.43/11.22	thf(fun_re1837693787nres_b_type, type, fun_re1837693787nres_b: (set_Product_prod_a_a > (set_Pr896671762nres_b > set_Pr1815766654nres_b))).
36.43/11.22	thf(fun_re708847385nres_a_type, type, fun_re708847385nres_a: (set_Product_prod_a_b > (set_Pr1598501265nres_a > set_Pr1635457468nres_a))).
36.43/11.22	thf(fun_re362844942_o_o_o_type, type, fun_re362844942_o_o_o: (set_Product_prod_a_c > (set_Pr1371175689_o_o_o > set_Pr1774281699_o_o_o))).
36.43/11.22	thf(fun_re418666087nres_c_type, type, fun_re418666087nres_c: (set_Product_prod_a_c > (set_Pr404050976nres_c > set_Pr1250642728nres_c))).
36.43/11.22	thf(fun_re1089848935nres_d_type, type, fun_re1089848935nres_d: (set_Product_prod_a_c > (set_Pr797615136nres_d > set_Pr2080238504nres_d))).
36.43/11.22	thf(fun_re836380558_c_c_c_type, type, fun_re836380558_c_c_c: (set_Product_prod_a_c > (set_Pr1673989513_c_c_c > set_Pr807116335_c_c_c))).
36.43/11.22	thf(fun_rel_a_c_o_o_o_o_type, type, fun_rel_a_c_o_o_o_o: (set_Product_prod_a_c > (set_Pr934623755_o_o_o > set_Pr1933985801_c_o_o))).
36.43/11.22	thf(fun_re766812315nres_c_type, type, fun_re766812315nres_c: (set_Product_prod_a_c > (set_Pr1128439124nres_c > set_Pr134917244nres_c))).
36.43/11.22	thf(fun_re1760530651nres_d_type, type, fun_re1760530651nres_d: (set_Product_prod_a_c > (set_Pr1640496404nres_d > set_Pr589481214nres_d))).
36.43/11.22	thf(fun_rel_a_c_a_c_type, type, fun_rel_a_c_a_c: (set_Product_prod_a_c > (set_Product_prod_a_c > set_Pr1234209675_a_c_c))).
36.43/11.22	thf(fun_re631684249nres_c_type, type, fun_re631684249nres_c: (set_Product_prod_a_d > (set_Pr194842259nres_c > set_Pr409172028nres_c))).
36.43/11.22	thf(fun_re132614427nres_b_type, type, fun_re132614427nres_b: (set_Product_prod_b_b > (set_Pr896671762nres_b > set_Pr512944190nres_b))).
36.43/11.22	thf(fun_re430551721nres_c_type, type, fun_re430551721nres_c: (set_Product_prod_b_d > (set_Pr57594146nres_c > set_Pr584391464nres_c))).
36.43/11.22	thf(fun_re1101734569nres_d_type, type, fun_re1101734569nres_d: (set_Product_prod_b_d > (set_Pr451158306nres_d > set_Pr1413987240nres_d))).
36.43/11.22	thf(fun_re1209216603nres_c_type, type, fun_re1209216603nres_c: (set_Product_prod_b_d > (set_Pr1128439124nres_c > set_Pr979578428nres_c))).
36.43/11.22	thf(fun_re55451291nres_d_type, type, fun_re55451291nres_d: (set_Product_prod_b_d > (set_Pr1640496404nres_d > set_Pr1434142398nres_d))).
36.43/11.22	thf(fun_re1645900187nres_a_type, type, fun_re1645900187nres_a: (set_Product_prod_c_a > (set_Pr664904400nres_a > set_Pr890971136nres_a))).
36.43/11.22	thf(fun_re492134875nres_b_type, type, fun_re492134875nres_b: (set_Product_prod_c_a > (set_Pr1176961680nres_b > set_Pr1345535106nres_b))).
36.43/11.22	thf(fun_re1568737051nres_c_type, type, fun_re1568737051nres_c: (set_Product_prod_c_c > (set_Pr1408729042nres_c > set_Pr1812169344nres_c))).
36.43/11.22	thf(fun_re414971739nres_d_type, type, fun_re414971739nres_d: (set_Product_prod_c_c > (set_Pr1920786322nres_d > set_Pr119249666nres_d))).
36.43/11.22	thf(fun_re934539163nres_b_type, type, fun_re934539163nres_b: (set_Product_prod_d_b > (set_Pr1176961680nres_b > set_Pr42712642nres_b))).
36.43/11.22	thf(relAPP1562327022_o_c_c_type, type, relAPP1562327022_o_c_c: ((set_Pr46530663_o_c_c > set_Pr37069423_o_c_c) > (set_Pr46530663_o_c_c > set_Pr37069423_o_c_c))).
36.43/11.22	thf(relAPP1388319497nres_d_type, type, relAPP1388319497nres_d: ((set_Pr1824526846nres_d > set_Pr613277282nres_d) > (set_Pr1824526846nres_d > set_Pr613277282nres_d))).
36.43/11.22	thf(relAPP745136137nres_d_type, type, relAPP745136137nres_d: ((set_Pr1824526846nres_d > set_Pr1710101992nres_d) > (set_Pr1824526846nres_d > set_Pr1710101992nres_d))).
36.43/11.22	thf(relAPP412764446_o_c_c_type, type, relAPP412764446_o_c_c: ((set_Pr1955643401_o_o_c > (set_Product_prod_a_c > set_Pr46530663_o_c_c)) > (set_Pr1955643401_o_o_c > (set_Product_prod_a_c > set_Pr46530663_o_c_c)))).
36.43/11.22	thf(relAPP1095654971nres_d_type, type, relAPP1095654971nres_d: ((set_Pr1712866168nres_d > set_Pr1614046668nres_d) > (set_Pr1712866168nres_d > set_Pr1614046668nres_d))).
36.43/11.22	thf(relAPP1723270664_o_o_o_type, type, relAPP1723270664_o_o_o: ((set_Pr1371175689_o_o_o > set_Pr1774281699_o_o_o) > (set_Pr1371175689_o_o_o > set_Pr1774281699_o_o_o))).
36.43/11.22	thf(relAPP765626983nres_c_type, type, relAPP765626983nres_c: ((set_Pr404050976nres_c > set_Pr882593184nres_c) > (set_Pr404050976nres_c > set_Pr882593184nres_c))).
36.43/11.22	thf(relAPP998488211nres_c_type, type, relAPP998488211nres_c: ((set_Pr404050976nres_c > set_Pr1250642728nres_c) > (set_Pr404050976nres_c > set_Pr1250642728nres_c))).
36.43/11.22	thf(relAPP869047273nres_b_type, type, relAPP869047273nres_b: ((set_Pr1052763806nres_b > set_Pr818594592nres_b) > (set_Pr1052763806nres_b > set_Pr818594592nres_b))).
36.43/11.22	thf(relAPP91071253nres_b_type, type, relAPP91071253nres_b: ((set_Pr1052763806nres_b > set_Pr1358127528nres_b) > (set_Pr1052763806nres_b > set_Pr1358127528nres_b))).
36.43/11.22	thf(relAPP1102334824nres_a_type, type, relAPP1102334824nres_a: ((set_Pr436741343nres_a > set_Pr2039330848nres_a) > (set_Pr436741343nres_a > set_Pr2039330848nres_a))).
36.43/11.22	thf(relAPP1953591565nres_d_type, type, relAPP1953591565nres_d: ((set_Pr797615136nres_d > (set_Pr1640496404nres_d > set_Pr1824526846nres_d)) > (set_Pr797615136nres_d > (set_Pr1640496404nres_d > set_Pr1824526846nres_d)))).
36.43/11.22	thf(relAPP1659518317nres_d_type, type, relAPP1659518317nres_d: ((set_Pr797615136nres_d > set_Pr1712866168nres_d) > (set_Pr797615136nres_d > set_Pr1712866168nres_d))).
36.43/11.22	thf(relAPP511982311nres_d_type, type, relAPP511982311nres_d: ((set_Pr797615136nres_d > set_Pr24800800nres_d) > (set_Pr797615136nres_d > set_Pr24800800nres_d))).
36.43/11.22	thf(relAPP1354295571nres_d_type, type, relAPP1354295571nres_d: ((set_Pr797615136nres_d > set_Pr2080238504nres_d) > (set_Pr797615136nres_d > set_Pr2080238504nres_d))).
36.43/11.22	thf(relAPP745269862nres_c_type, type, relAPP745269862nres_c: ((set_Pr181592673nres_c > set_Pr1245537056nres_c) > (set_Pr181592673nres_c > set_Pr1245537056nres_c))).
36.43/11.22	thf(relAPP1804623572_c_c_c_type, type, relAPP1804623572_c_c_c: ((set_Pr1673989513_c_c_c > set_Pr807116335_c_c_c) > (set_Pr1673989513_c_c_c > set_Pr807116335_c_c_c))).
36.43/11.22	thf(relAPP944912869nres_c_type, type, relAPP944912869nres_c: ((set_Pr57594146nres_c > set_Pr1652381728nres_c) > (set_Pr57594146nres_c > set_Pr1652381728nres_c))).
36.43/11.22	thf(relAPP131141393nres_c_type, type, relAPP131141393nres_c: ((set_Pr57594146nres_c > set_Pr584391464nres_c) > (set_Pr57594146nres_c > set_Pr584391464nres_c))).
36.43/11.22	thf(relAPP691268197nres_d_type, type, relAPP691268197nres_d: ((set_Pr451158306nres_d > set_Pr794589344nres_d) > (set_Pr451158306nres_d > set_Pr794589344nres_d))).
36.43/11.22	thf(relAPP486948753nres_d_type, type, relAPP486948753nres_d: ((set_Pr451158306nres_d > set_Pr1413987240nres_d) > (set_Pr451158306nres_d > set_Pr1413987240nres_d))).
36.43/11.22	thf(relAPP1077394663nres_b_type, type, relAPP1077394663nres_b: ((set_Pr1402127136nres_b > set_Pr1436380704nres_b) > (set_Pr1402127136nres_b > set_Pr1436380704nres_b))).
36.43/11.22	thf(relAPP720329701nres_d_type, type, relAPP720329701nres_d: ((set_Pr1146978466nres_d > set_Pr642586912nres_d) > (set_Pr1146978466nres_d > set_Pr642586912nres_d))).
36.43/11.22	thf(relAPP2129980178_o_c_c_type, type, relAPP2129980178_o_c_c: ((set_Pr934623755_o_o_o > (set_Pr46530663_o_c_c > set_Pr37069423_o_c_c)) > (set_Pr934623755_o_o_o > (set_Pr46530663_o_c_c > set_Pr37069423_o_c_c)))).
36.43/11.22	thf(relAPP1750172554_o_o_c_type, type, relAPP1750172554_o_o_c: ((set_Pr934623755_o_o_o > (set_Product_prod_a_c > set_Pr1955643401_o_o_c)) > (set_Pr934623755_o_o_o > (set_Product_prod_a_c > set_Pr1955643401_o_o_c)))).
36.43/11.22	thf(relAPP829628004_o_o_o_type, type, relAPP829628004_o_o_o: ((set_Pr934623755_o_o_o > set_Pr1371175689_o_o_o) > (set_Pr934623755_o_o_o > set_Pr1371175689_o_o_o))).
36.43/11.22	thf(relAPP1525934692_c_o_o_type, type, relAPP1525934692_c_o_o: ((set_Pr934623755_o_o_o > set_Pr1933985801_c_o_o) > (set_Pr934623755_o_o_o > set_Pr1933985801_c_o_o))).
36.43/11.22	thf(relAPP759382665nres_d_type, type, relAPP759382665nres_d: ((set_Pr24800800nres_d > (set_Pr797615136nres_d > set_Pr1712866168nres_d)) > (set_Pr24800800nres_d > (set_Pr797615136nres_d > set_Pr1712866168nres_d)))).
36.43/11.22	thf(relAPP1210499902_o_o_o_type, type, relAPP1210499902_o_o_o: ((set_Pr1933985801_c_o_o > (set_Pr934623755_o_o_o > set_Pr1371175689_o_o_o)) > (set_Pr1933985801_c_o_o > (set_Pr934623755_o_o_o > set_Pr1371175689_o_o_o)))).
36.43/11.22	thf(relAPP483050597nres_c_type, type, relAPP483050597nres_c: ((set_Pr134917244nres_c > (set_Pr1128439124nres_c > set_Pr404050976nres_c)) > (set_Pr134917244nres_c > (set_Pr1128439124nres_c > set_Pr404050976nres_c)))).
36.43/11.22	thf(relAPP1293188647nres_b_type, type, relAPP1293188647nres_b: ((set_Pr1815766654nres_b > (set_Pr896671762nres_b > set_Pr1052763806nres_b)) > (set_Pr1815766654nres_b > (set_Pr896671762nres_b > set_Pr1052763806nres_b)))).
36.43/11.22	thf(relAPP811277159nres_a_type, type, relAPP811277159nres_a: ((set_Pr1635457468nres_a > (set_Pr1598501265nres_a > set_Pr436741343nres_a)) > (set_Pr1635457468nres_a > (set_Pr1598501265nres_a > set_Pr436741343nres_a)))).
36.43/11.22	thf(relAPP1716516381nres_d_type, type, relAPP1716516381nres_d: ((set_Pr589481214nres_d > (set_Pr1824526846nres_d > set_Pr613277282nres_d)) > (set_Pr589481214nres_d > (set_Pr1824526846nres_d > set_Pr613277282nres_d)))).
36.43/11.22	thf(relAPP98076839nres_d_type, type, relAPP98076839nres_d: ((set_Pr589481214nres_d > (set_Pr1640496404nres_d > set_Pr797615136nres_d)) > (set_Pr589481214nres_d > (set_Pr1640496404nres_d > set_Pr797615136nres_d)))).
36.43/11.22	thf(relAPP1482036727nres_d_type, type, relAPP1482036727nres_d: ((set_Pr589481214nres_d > set_Pr1537816964nres_d) > (set_Pr589481214nres_d > set_Pr1537816964nres_d))).
36.43/11.22	thf(relAPP1763648999nres_c_type, type, relAPP1763648999nres_c: ((set_Pr409172028nres_c > (set_Pr194842259nres_c > set_Pr181592673nres_c)) > (set_Pr409172028nres_c > (set_Pr194842259nres_c > set_Pr181592673nres_c)))).
36.43/11.22	thf(relAPP981449866_c_c_c_type, type, relAPP981449866_c_c_c: ((set_Pr1234209675_a_c_c > (set_Product_prod_a_c > set_Pr1673989513_c_c_c)) > (set_Pr1234209675_a_c_c > (set_Product_prod_a_c > set_Pr1673989513_c_c_c)))).
36.43/11.22	thf(relAPP1790450405nres_c_type, type, relAPP1790450405nres_c: ((set_Pr979578428nres_c > (set_Pr1128439124nres_c > set_Pr57594146nres_c)) > (set_Pr979578428nres_c > (set_Pr1128439124nres_c > set_Pr57594146nres_c)))).
36.43/11.22	thf(relAPP1405476647nres_d_type, type, relAPP1405476647nres_d: ((set_Pr1434142398nres_d > (set_Pr1640496404nres_d > set_Pr451158306nres_d)) > (set_Pr1434142398nres_d > (set_Pr1640496404nres_d > set_Pr451158306nres_d)))).
36.43/11.22	thf(relAPP38185259nres_b_type, type, relAPP38185259nres_b: ((set_Pr1345535106nres_b > (set_Pr1176961680nres_b > set_Pr1402127136nres_b)) > (set_Pr1345535106nres_b > (set_Pr1176961680nres_b > set_Pr1402127136nres_b)))).
36.43/11.22	thf(relAPP990557099nres_d_type, type, relAPP990557099nres_d: ((set_Pr119249666nres_d > (set_Pr1920786322nres_d > set_Pr1146978466nres_d)) > (set_Pr119249666nres_d > (set_Pr1920786322nres_d > set_Pr1146978466nres_d)))).
36.43/11.22	thf(relAPP1787540131nres_d_type, type, relAPP1787540131nres_d: ((set_Pr1537816964nres_d > (set_Pr1824526846nres_d > set_Pr1710101992nres_d)) > (set_Pr1537816964nres_d > (set_Pr1824526846nres_d > set_Pr1710101992nres_d)))).
36.43/11.22	thf(relAPP1111247343nres_b_type, type, relAPP1111247343nres_b: ((set_Pr384614482nres_a > (set_Pr1052763806nres_b > set_Pr818594592nres_b)) > (set_Pr384614482nres_a > (set_Pr1052763806nres_b > set_Pr818594592nres_b)))).
36.43/11.22	thf(relAPP907138281nres_a_type, type, relAPP907138281nres_a: ((set_Pr384614482nres_a > set_Pr1361202684nres_a) > (set_Pr384614482nres_a > set_Pr1361202684nres_a))).
36.43/11.22	thf(relAPP1042385007nres_a_type, type, relAPP1042385007nres_a: ((set_Pr1830268627nres_b > (set_Pr436741343nres_a > set_Pr2039330848nres_a)) > (set_Pr1830268627nres_b > (set_Pr436741343nres_a > set_Pr2039330848nres_a)))).
36.43/11.22	thf(relAPP422583323nres_d_type, type, relAPP422583323nres_d: ((set_Pr1128439124nres_c > (set_Pr1712866168nres_d > set_Pr1614046668nres_d)) > (set_Pr1128439124nres_c > (set_Pr1712866168nres_d > set_Pr1614046668nres_d)))).
36.43/11.22	thf(relAPP177337967nres_c_type, type, relAPP177337967nres_c: ((set_Pr1128439124nres_c > (set_Pr404050976nres_c > set_Pr882593184nres_c)) > (set_Pr1128439124nres_c > (set_Pr404050976nres_c > set_Pr882593184nres_c)))).
36.43/11.22	thf(relAPP1396672239nres_d_type, type, relAPP1396672239nres_d: ((set_Pr1128439124nres_c > (set_Pr797615136nres_d > set_Pr24800800nres_d)) > (set_Pr1128439124nres_c > (set_Pr797615136nres_d > set_Pr24800800nres_d)))).
36.43/11.22	thf(relAPP1774615993nres_c_type, type, relAPP1774615993nres_c: ((set_Pr1128439124nres_c > set_Pr404050976nres_c) > (set_Pr1128439124nres_c > set_Pr404050976nres_c))).
36.43/11.22	thf(relAPP489595641nres_c_type, type, relAPP489595641nres_c: ((set_Pr1128439124nres_c > set_Pr57594146nres_c) > (set_Pr1128439124nres_c > set_Pr57594146nres_c))).
36.43/11.22	thf(relAPP2018433511nres_c_type, type, relAPP2018433511nres_c: ((set_Pr1128439124nres_c > set_Pr134917244nres_c) > (set_Pr1128439124nres_c > set_Pr134917244nres_c))).
36.43/11.22	thf(relAPP1564590053nres_c_type, type, relAPP1564590053nres_c: ((set_Pr1128439124nres_c > set_Pr979578428nres_c) > (set_Pr1128439124nres_c > set_Pr979578428nres_c))).
36.43/11.22	thf(relAPP1327809903nres_c_type, type, relAPP1327809903nres_c: ((set_Pr426609621nres_d > (set_Pr181592673nres_c > set_Pr1245537056nres_c)) > (set_Pr426609621nres_d > (set_Pr181592673nres_c > set_Pr1245537056nres_c)))).
36.43/11.22	thf(relAPP919190011nres_a_type, type, relAPP919190011nres_a: ((set_Pr1598501265nres_a > set_Pr436741343nres_a) > (set_Pr1598501265nres_a > set_Pr436741343nres_a))).
36.43/11.22	thf(relAPP587861290nres_a_type, type, relAPP587861290nres_a: ((set_Pr1598501265nres_a > set_Pr1635457468nres_a) > (set_Pr1598501265nres_a > set_Pr1635457468nres_a))).
36.43/11.22	thf(relAPP2095637113nres_b_type, type, relAPP2095637113nres_b: ((set_Pr896671762nres_b > set_Pr1052763806nres_b) > (set_Pr896671762nres_b > set_Pr1052763806nres_b))).
36.43/11.22	thf(relAPP1936960811nres_b_type, type, relAPP1936960811nres_b: ((set_Pr896671762nres_b > set_Pr1815766654nres_b) > (set_Pr896671762nres_b > set_Pr1815766654nres_b))).
36.43/11.22	thf(relAPP1483117353nres_b_type, type, relAPP1483117353nres_b: ((set_Pr896671762nres_b > set_Pr512944190nres_b) > (set_Pr896671762nres_b > set_Pr512944190nres_b))).
36.43/11.22	thf(relAPP1784890619nres_c_type, type, relAPP1784890619nres_c: ((set_Pr194842259nres_c > set_Pr181592673nres_c) > (set_Pr194842259nres_c > set_Pr181592673nres_c))).
36.43/11.22	thf(relAPP1699156520nres_c_type, type, relAPP1699156520nres_c: ((set_Pr194842259nres_c > set_Pr409172028nres_c) > (set_Pr194842259nres_c > set_Pr409172028nres_c))).
36.43/11.22	thf(relAPP492592111nres_c_type, type, relAPP492592111nres_c: ((set_Pr1640496404nres_d > (set_Pr57594146nres_c > set_Pr1652381728nres_c)) > (set_Pr1640496404nres_d > (set_Pr57594146nres_c > set_Pr1652381728nres_c)))).
36.43/11.22	thf(relAPP1711926383nres_d_type, type, relAPP1711926383nres_d: ((set_Pr1640496404nres_d > (set_Pr451158306nres_d > set_Pr794589344nres_d)) > (set_Pr1640496404nres_d > (set_Pr451158306nres_d > set_Pr794589344nres_d)))).
36.43/11.22	thf(relAPP1552964229nres_d_type, type, relAPP1552964229nres_d: ((set_Pr1640496404nres_d > set_Pr1824526846nres_d) > (set_Pr1640496404nres_d > set_Pr1824526846nres_d))).
36.43/11.22	thf(relAPP813854073nres_d_type, type, relAPP813854073nres_d: ((set_Pr1640496404nres_d > set_Pr797615136nres_d) > (set_Pr1640496404nres_d > set_Pr797615136nres_d))).
36.43/11.22	thf(relAPP1676317369nres_d_type, type, relAPP1676317369nres_d: ((set_Pr1640496404nres_d > set_Pr451158306nres_d) > (set_Pr1640496404nres_d > set_Pr451158306nres_d))).
36.43/11.22	thf(relAPP900772393nres_d_type, type, relAPP900772393nres_d: ((set_Pr1640496404nres_d > set_Pr589481214nres_d) > (set_Pr1640496404nres_d > set_Pr589481214nres_d))).
36.43/11.22	thf(relAPP446928935nres_d_type, type, relAPP446928935nres_d: ((set_Pr1640496404nres_d > set_Pr1434142398nres_d) > (set_Pr1640496404nres_d > set_Pr1434142398nres_d))).
36.43/11.22	thf(relAPP1747515631nres_b_type, type, relAPP1747515631nres_b: ((set_Pr664904400nres_a > (set_Pr1402127136nres_b > set_Pr1436380704nres_b)) > (set_Pr664904400nres_a > (set_Pr1402127136nres_b > set_Pr1436380704nres_b)))).
36.43/11.22	thf(relAPP947801195nres_a_type, type, relAPP947801195nres_a: ((set_Pr664904400nres_a > set_Pr890971136nres_a) > (set_Pr664904400nres_a > set_Pr890971136nres_a))).
36.43/11.22	thf(relAPP2032940527nres_d_type, type, relAPP2032940527nres_d: ((set_Pr1408729042nres_c > (set_Pr1146978466nres_d > set_Pr642586912nres_d)) > (set_Pr1408729042nres_c > (set_Pr1146978466nres_d > set_Pr642586912nres_d)))).
36.43/11.22	thf(relAPP2059096425nres_c_type, type, relAPP2059096425nres_c: ((set_Pr1408729042nres_c > set_Pr1812169344nres_c) > (set_Pr1408729042nres_c > set_Pr1812169344nres_c))).
36.43/11.22	thf(relAPP1033339257nres_b_type, type, relAPP1033339257nres_b: ((set_Pr1176961680nres_b > set_Pr1402127136nres_b) > (set_Pr1176961680nres_b > set_Pr1402127136nres_b))).
36.43/11.22	thf(relAPP1977623725nres_b_type, type, relAPP1977623725nres_b: ((set_Pr1176961680nres_b > set_Pr1345535106nres_b) > (set_Pr1176961680nres_b > set_Pr1345535106nres_b))).
36.43/11.22	thf(relAPP1523780267nres_b_type, type, relAPP1523780267nres_b: ((set_Pr1176961680nres_b > set_Pr42712642nres_b) > (set_Pr1176961680nres_b > set_Pr42712642nres_b))).
36.43/11.22	thf(relAPP1899039865nres_d_type, type, relAPP1899039865nres_d: ((set_Pr1920786322nres_d > set_Pr1146978466nres_d) > (set_Pr1920786322nres_d > set_Pr1146978466nres_d))).
36.43/11.22	thf(relAPP941435307nres_d_type, type, relAPP941435307nres_d: ((set_Pr1920786322nres_d > set_Pr119249666nres_d) > (set_Pr1920786322nres_d > set_Pr119249666nres_d))).
36.43/11.22	thf(relAPP1740535279nres_b_type, type, relAPP1740535279nres_b: ((set_Product_prod_a_a > (set_Pr1052763806nres_b > set_Pr1358127528nres_b)) > (set_Product_prod_a_a > (set_Pr1052763806nres_b > set_Pr1358127528nres_b)))).
36.43/11.22	thf(relAPP439940547nres_a_type, type, relAPP439940547nres_a: ((set_Product_prod_a_a > (set_Pr384614482nres_a > set_Pr1361202684nres_a)) > (set_Product_prod_a_a > (set_Pr384614482nres_a > set_Pr1361202684nres_a)))).
36.43/11.22	thf(relAPP1536875909nres_b_type, type, relAPP1536875909nres_b: ((set_Product_prod_a_a > (set_Pr896671762nres_b > set_Pr1815766654nres_b)) > (set_Product_prod_a_a > (set_Pr896671762nres_b > set_Pr1815766654nres_b)))).
36.43/11.22	thf(relAPP1642956907nres_a_type, type, relAPP1642956907nres_a: ((set_Product_prod_a_a > set_Pr384614482nres_a) > (set_Product_prod_a_a > set_Pr384614482nres_a))).
36.43/11.22	thf(relAPP456341443nres_a_type, type, relAPP456341443nres_a: ((set_Product_prod_a_b > (set_Pr1598501265nres_a > set_Pr1635457468nres_a)) > (set_Product_prod_a_b > (set_Pr1598501265nres_a > set_Pr1635457468nres_a)))).
36.43/11.22	thf(relAPP11374829nres_b_type, type, relAPP11374829nres_b: ((set_Product_prod_a_b > set_Pr1830268627nres_b) > (set_Product_prod_a_b > set_Pr1830268627nres_b))).
36.43/11.22	thf(relAPP913737114_o_o_o_type, type, relAPP913737114_o_o_o: ((set_Product_prod_a_c > (set_Pr1371175689_o_o_o > set_Pr1774281699_o_o_o)) > (set_Product_prod_a_c > (set_Pr1371175689_o_o_o > set_Pr1774281699_o_o_o)))).
36.43/11.22	thf(relAPP1155943915nres_c_type, type, relAPP1155943915nres_c: ((set_Product_prod_a_c > (set_Pr404050976nres_c > set_Pr1250642728nres_c)) > (set_Product_prod_a_c > (set_Pr404050976nres_c > set_Pr1250642728nres_c)))).
36.43/11.22	thf(relAPP1135042155nres_d_type, type, relAPP1135042155nres_d: ((set_Product_prod_a_c > (set_Pr797615136nres_d > set_Pr2080238504nres_d)) > (set_Product_prod_a_c > (set_Pr797615136nres_d > set_Pr2080238504nres_d)))).
36.43/11.22	thf(relAPP1889825126_c_c_c_type, type, relAPP1889825126_c_c_c: ((set_Product_prod_a_c > (set_Pr1673989513_c_c_c > set_Pr807116335_c_c_c)) > (set_Product_prod_a_c > (set_Pr1673989513_c_c_c > set_Pr807116335_c_c_c)))).
36.43/11.22	thf(relAPP589338430_c_o_o_type, type, relAPP589338430_c_o_o: ((set_Product_prod_a_c > (set_Pr934623755_o_o_o > set_Pr1933985801_c_o_o)) > (set_Product_prod_a_c > (set_Pr934623755_o_o_o > set_Pr1933985801_c_o_o)))).
36.43/11.22	thf(relAPP173519167nres_c_type, type, relAPP173519167nres_c: ((set_Product_prod_a_c > (set_Pr1128439124nres_c > set_Pr134917244nres_c)) > (set_Product_prod_a_c > (set_Pr1128439124nres_c > set_Pr134917244nres_c)))).
36.43/11.22	thf(relAPP1270454529nres_d_type, type, relAPP1270454529nres_d: ((set_Product_prod_a_c > (set_Pr1640496404nres_d > set_Pr589481214nres_d)) > (set_Product_prod_a_c > (set_Pr1640496404nres_d > set_Pr589481214nres_d)))).
36.43/11.22	thf(relAPP887115074_a_c_c_type, type, relAPP887115074_a_c_c: ((set_Product_prod_a_c > (set_Product_prod_a_c > set_Pr1234209675_a_c_c)) > (set_Product_prod_a_c > (set_Product_prod_a_c > set_Pr1234209675_a_c_c)))).
36.43/11.22	thf(relAPP1774770060_o_c_c_type, type, relAPP1774770060_o_c_c: ((set_Product_prod_a_c > set_Pr46530663_o_c_c) > (set_Product_prod_a_c > set_Pr46530663_o_c_c))).
36.43/11.22	thf(relAPP970620078_o_o_c_type, type, relAPP970620078_o_o_c: ((set_Product_prod_a_c > set_Pr1955643401_o_o_c) > (set_Product_prod_a_c > set_Pr1955643401_o_o_c))).
36.43/11.22	thf(relAPP1311785006_c_c_c_type, type, relAPP1311785006_c_c_c: ((set_Product_prod_a_c > set_Pr1673989513_c_c_c) > (set_Product_prod_a_c > set_Pr1673989513_c_c_c))).
36.43/11.22	thf(relAPP237429680_a_c_c_type, type, relAPP237429680_a_c_c: ((set_Product_prod_a_c > set_Pr1234209675_a_c_c) > (set_Product_prod_a_c > set_Pr1234209675_a_c_c))).
36.43/11.22	thf(relAPP527276399nres_c_type, type, relAPP527276399nres_c: ((set_Product_prod_a_c > set_Pr1128439124nres_c) > (set_Product_prod_a_c > set_Pr1128439124nres_c))).
36.43/11.22	thf(relAPP189920063nres_c_type, type, relAPP189920063nres_c: ((set_Product_prod_a_d > (set_Pr194842259nres_c > set_Pr409172028nres_c)) > (set_Product_prod_a_d > (set_Pr194842259nres_c > set_Pr409172028nres_c)))).
36.43/11.22	thf(relAPP1043177969nres_d_type, type, relAPP1043177969nres_d: ((set_Product_prod_a_d > set_Pr426609621nres_d) > (set_Product_prod_a_d > set_Pr426609621nres_d))).
36.43/11.22	thf(relAPP1912873449nres_a_type, type, relAPP1912873449nres_a: ((set_Product_prod_b_a > set_Pr1598501265nres_a) > (set_Product_prod_b_a > set_Pr1598501265nres_a))).
36.43/11.22	thf(relAPP2073227843nres_b_type, type, relAPP2073227843nres_b: ((set_Product_prod_b_b > (set_Pr896671762nres_b > set_Pr512944190nres_b)) > (set_Product_prod_b_b > (set_Pr896671762nres_b > set_Pr512944190nres_b)))).
36.43/11.22	thf(relAPP281291371nres_b_type, type, relAPP281291371nres_b: ((set_Product_prod_b_b > set_Pr896671762nres_b) > (set_Product_prod_b_b > set_Pr896671762nres_b))).
36.43/11.22	thf(relAPP797192941nres_c_type, type, relAPP797192941nres_c: ((set_Product_prod_b_c > set_Pr194842259nres_c) > (set_Product_prod_b_c > set_Pr194842259nres_c))).
36.43/11.22	thf(relAPP2017502121nres_c_type, type, relAPP2017502121nres_c: ((set_Product_prod_b_d > (set_Pr57594146nres_c > set_Pr584391464nres_c)) > (set_Product_prod_b_d > (set_Pr57594146nres_c > set_Pr584391464nres_c)))).
36.43/11.22	thf(relAPP1996600361nres_d_type, type, relAPP1996600361nres_d: ((set_Product_prod_b_d > (set_Pr451158306nres_d > set_Pr1413987240nres_d)) > (set_Product_prod_b_d > (set_Pr451158306nres_d > set_Pr1413987240nres_d)))).
36.43/11.22	thf(relAPP709871101nres_c_type, type, relAPP709871101nres_c: ((set_Product_prod_b_d > (set_Pr1128439124nres_c > set_Pr979578428nres_c)) > (set_Product_prod_b_d > (set_Pr1128439124nres_c > set_Pr979578428nres_c)))).
36.43/11.22	thf(relAPP1806806463nres_d_type, type, relAPP1806806463nres_d: ((set_Product_prod_b_d > (set_Pr1640496404nres_d > set_Pr1434142398nres_d)) > (set_Product_prod_b_d > (set_Pr1640496404nres_d > set_Pr1434142398nres_d)))).
36.43/11.22	thf(relAPP1313094511nres_d_type, type, relAPP1313094511nres_d: ((set_Product_prod_b_d > set_Pr1640496404nres_d) > (set_Product_prod_b_d > set_Pr1640496404nres_d))).
36.43/11.22	thf(relAPP1825452871nres_a_type, type, relAPP1825452871nres_a: ((set_Product_prod_c_a > (set_Pr664904400nres_a > set_Pr890971136nres_a)) > (set_Product_prod_c_a > (set_Pr664904400nres_a > set_Pr890971136nres_a)))).
36.43/11.22	thf(relAPP774904585nres_b_type, type, relAPP774904585nres_b: ((set_Product_prod_c_a > (set_Pr1176961680nres_b > set_Pr1345535106nres_b)) > (set_Product_prod_c_a > (set_Pr1176961680nres_b > set_Pr1345535106nres_b)))).
36.43/11.22	thf(relAPP35306343nres_a_type, type, relAPP35306343nres_a: ((set_Product_prod_c_a > set_Pr664904400nres_a) > (set_Product_prod_c_a > set_Pr664904400nres_a))).
36.43/11.22	thf(relAPP1559031491nres_c_type, type, relAPP1559031491nres_c: ((set_Product_prod_c_c > (set_Pr1408729042nres_c > set_Pr1812169344nres_c)) > (set_Product_prod_c_c > (set_Pr1408729042nres_c > set_Pr1812169344nres_c)))).
36.43/11.22	thf(relAPP508483205nres_d_type, type, relAPP508483205nres_d: ((set_Product_prod_c_c > (set_Pr1920786322nres_d > set_Pr119249666nres_d)) > (set_Product_prod_c_c > (set_Pr1920786322nres_d > set_Pr119249666nres_d)))).
36.43/11.22	thf(relAPP1067109483nres_c_type, type, relAPP1067109483nres_c: ((set_Product_prod_c_c > set_Pr1408729042nres_c) > (set_Product_prod_c_c > set_Pr1408729042nres_c))).
36.43/11.22	thf(relAPP1311256519nres_b_type, type, relAPP1311256519nres_b: ((set_Product_prod_d_b > (set_Pr1176961680nres_b > set_Pr42712642nres_b)) > (set_Product_prod_d_b > (set_Pr1176961680nres_b > set_Pr42712642nres_b)))).
36.43/11.22	thf(relAPP821124455nres_b_type, type, relAPP821124455nres_b: ((set_Product_prod_d_b > set_Pr1176961680nres_b) > (set_Product_prod_d_b > set_Pr1176961680nres_b))).
36.43/11.22	thf(relAPP1852927595nres_d_type, type, relAPP1852927595nres_d: ((set_Product_prod_d_d > set_Pr1920786322nres_d) > (set_Product_prod_d_d > set_Pr1920786322nres_d))).
36.43/11.22	thf(collec1321668993nres_d_type, type, collec1321668993nres_d: ((produc809931564nres_d > $o) > set_Pr613277282nres_d)).
36.43/11.22	thf(collec1671161663nres_d_type, type, collec1671161663nres_d: ((produc1757587562nres_d > $o) > set_Pr797615136nres_d)).
36.43/11.22	thf(collec554837959nres_d_type, type, collec554837959nres_d: ((produc1677145714nres_d > $o) > set_Pr2080238504nres_d)).
36.43/11.22	thf(collec1639315997nres_d_type, type, collec1639315997nres_d: ((produc2103861704nres_d > $o) > set_Pr589481214nres_d)).
36.43/11.22	thf(collec662378644od_a_c_type, type, collec662378644od_a_c: ((product_prod_a_c > $o) > set_Product_prod_a_c)).
36.43/11.22	thf(member1270020946_o_o_c_type, type, member1270020946_o_o_c: (produc2056997417_o_o_c > (set_Pr1955643401_o_o_c > $o))).
36.43/11.22	thf(member660096835nres_d_type, type, member660096835nres_d: (produc809931564nres_d > (set_Pr613277282nres_d > $o))).
36.43/11.22	thf(member461830657nres_d_type, type, member461830657nres_d: (produc1757587562nres_d > (set_Pr797615136nres_d > $o))).
36.43/11.22	thf(member250723412_o_o_o_type, type, member250723412_o_o_o: (product_prod_o_o_o_o > (set_Pr934623755_o_o_o > $o))).
36.43/11.22	thf(member449974729nres_d_type, type, member449974729nres_d: (produc1834705330nres_d > (set_Pr1710101992nres_d > $o))).
36.43/11.22	thf(member508530605nres_d_type, type, member508530605nres_d: (produc819780758nres_d > (set_Pr1614046668nres_d > $o))).
36.43/11.22	thf(member1751415169nres_c_type, type, member1751415169nres_c: (produc1581500522nres_c > (set_Pr882593184nres_c > $o))).
36.43/11.22	thf(member1700179713nres_b_type, type, member1700179713nres_b: (produc1530265066nres_b > (set_Pr818594592nres_b > $o))).
36.43/11.22	thf(member1468277761nres_a_type, type, member1468277761nres_a: (produc1298363114nres_a > (set_Pr2039330848nres_a > $o))).
36.43/11.22	thf(member65788417nres_d_type, type, member65788417nres_d: (produc2043357418nres_d > (set_Pr24800800nres_d > $o))).
36.43/11.22	thf(member1981370113nres_c_type, type, member1981370113nres_c: (produc1811455466nres_c > (set_Pr1245537056nres_c > $o))).
36.43/11.22	thf(member1715717121nres_c_type, type, member1715717121nres_c: (produc1545802474nres_c > (set_Pr1652381728nres_c > $o))).
36.43/11.22	thf(member30090369nres_d_type, type, member30090369nres_d: (produc2007659370nres_d > (set_Pr794589344nres_d > $o))).
36.43/11.22	thf(member2039405057nres_b_type, type, member2039405057nres_b: (produc1869490410nres_b > (set_Pr1436380704nres_b > $o))).
36.43/11.22	thf(member405013761nres_d_type, type, member405013761nres_d: (produc235099114nres_d > (set_Pr642586912nres_d > $o))).
36.43/11.22	thf(member427035401nres_c_type, type, member427035401nres_c: (produc1914459634nres_c > (set_Pr1250642728nres_c > $o))).
36.43/11.22	thf(member757031305nres_b_type, type, member757031305nres_b: (produc96971890nres_b > (set_Pr1358127528nres_b > $o))).
36.43/11.22	thf(member189721481nres_d_type, type, member189721481nres_d: (produc1677145714nres_d > (set_Pr2080238504nres_d > $o))).
36.43/11.22	thf(member1051493202_c_o_o_type, type, member1051493202_c_o_o: (produc1838469673_c_o_o > (set_Pr1933985801_c_o_o > $o))).
36.43/11.22	thf(member1680325597nres_a_type, type, member1680325597nres_a: (produc699795910nres_a > (set_Pr1361202684nres_a > $o))).
36.43/11.22	thf(member100096605nres_c_type, type, member100096605nres_c: (produc1267050566nres_c > (set_Pr134917244nres_c > $o))).
36.43/11.22	thf(member369653087nres_b_type, type, member369653087nres_b: (produc1536607048nres_b > (set_Pr1815766654nres_b > $o))).
36.43/11.22	thf(member936907743nres_d_type, type, member936907743nres_d: (produc2103861704nres_d > (set_Pr589481214nres_d > $o))).
36.43/11.22	thf(member1010099668_a_c_c_type, type, member1010099668_a_c_c: (product_prod_a_a_c_c > (set_Pr1234209675_a_c_c > $o))).
36.43/11.22	thf(member228973321nres_c_type, type, member228973321nres_c: (produc1716397554nres_c > (set_Pr584391464nres_c > $o))).
36.43/11.22	thf(member2139143049nres_d_type, type, member2139143049nres_d: (produc1479083634nres_d > (set_Pr1413987240nres_d > $o))).
36.43/11.22	thf(member2086976541nres_c_type, type, member2086976541nres_c: (produc1106446854nres_c > (set_Pr979578428nres_c > $o))).
36.43/11.22	thf(member209049375nres_b_type, type, member209049375nres_b: (produc1376003336nres_b > (set_Pr512944190nres_b > $o))).
36.43/11.22	thf(member776304031nres_d_type, type, member776304031nres_d: (produc1943257992nres_d > (set_Pr1434142398nres_d > $o))).
36.43/11.22	thf(member318002145nres_a_type, type, member318002145nres_a: (produc1484956106nres_a > (set_Pr890971136nres_a > $o))).
36.43/11.22	thf(member885256801nres_c_type, type, member885256801nres_c: (produc2052210762nres_c > (set_Pr1812169344nres_c > $o))).
36.43/11.22	thf(member994209571nres_b_type, type, member994209571nres_b: (produc13679884nres_b > (set_Pr42712642nres_b > $o))).
36.43/11.22	thf(member1468928819nres_a_type, type, member1468928819nres_a: (produc1609974940nres_a > (set_Pr384614482nres_a > $o))).
36.43/11.22	thf(member1600573749nres_c_type, type, member1600573749nres_c: (produc1741619870nres_c > (set_Pr1128439124nres_c > $o))).
36.43/11.22	thf(member1446466291nres_b_type, type, member1446466291nres_b: (produc1587512412nres_b > (set_Pr896671762nres_b > $o))).
36.43/11.22	thf(member1578111221nres_d_type, type, member1578111221nres_d: (produc1719157342nres_d > (set_Pr1640496404nres_d > $o))).
36.43/11.22	thf(member1292358833nres_a_type, type, member1292358833nres_a: (produc1433404954nres_a > (set_Pr664904400nres_a > $o))).
36.43/11.22	thf(member1424003763nres_c_type, type, member1424003763nres_c: (produc1565049884nres_c > (set_Pr1408729042nres_c > $o))).
36.43/11.22	thf(member1269896305nres_b_type, type, member1269896305nres_b: (produc1410942426nres_b > (set_Pr1176961680nres_b > $o))).
36.43/11.22	thf(member449909584od_a_a_type, type, member449909584od_a_a: (product_prod_a_a > (set_Product_prod_a_a > $o))).
36.43/11.22	thf(member466432594od_a_c_type, type, member466432594od_a_c: (product_prod_a_c > (set_Product_prod_a_c > $o))).
36.43/11.22	thf(member1302463506od_b_d_type, type, member1302463506od_b_d: (product_prod_b_d > (set_Product_prod_b_d > $o))).
36.43/11.22	thf(r1_type, type, r1: set_Product_prod_a_c).
36.43/11.22	thf(r2_type, type, r2: set_Product_prod_b_d).
36.43/11.22	thf(sk1_type, type, sk1: (product_prod_o_o_o_o > ($o > $o))).
36.43/11.22	thf(sk2_type, type, sk2: (product_prod_o_o_o_o > ($o > $o))).
36.43/11.22	thf(sk109_type, type, sk109: $o).
36.43/11.22	thf(sk110_type, type, sk110: $o).
36.43/11.22	thf(sk111_type, type, sk111: $o).
36.43/11.22	thf(sk112_type, type, sk112: $o).
36.43/11.22	thf(sk113_type, type, sk113: $o).
36.43/11.22	thf(89,axiom,((! [A:$o,B:$o,C:refine424419629nres_a,D:refine424419629nres_a,E:set_Product_prod_a_a]: (((B) <= (A)) => ((member1468928819nres_a @ (produc1136923598nres_a @ (refine1437029927_bnd_a @ B @ C) @ (refine1437029927_bnd_a @ A @ D)) @ (relAPP1642956907nres_a @ refine737062558el_a_a @ E)) <= (((B) => (member1468928819nres_a @ (produc1136923598nres_a @ C @ D) @ (relAPP1642956907nres_a @ refine737062558el_a_a @ E))) <= (A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_param__op__nres__ASSERT__bnd)).
36.43/11.22	thf(3021,plain,((! [A:$o,B:$o,C:refine424419629nres_a,D:refine424419629nres_a,E:set_Product_prod_a_a]: (((B) | ~ (A)) => ((member1468928819nres_a @ (produc1136923598nres_a @ (refine1437029927_bnd_a @ B @ C) @ (refine1437029927_bnd_a @ A @ D)) @ (relAPP1642956907nres_a @ (refine737062558el_a_a) @ E)) | ~ (((B) => (member1468928819nres_a @ (produc1136923598nres_a @ C @ D) @ (relAPP1642956907nres_a @ (refine737062558el_a_a) @ E))) | ~ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])).
36.43/11.22	thf(6,axiom,((! [A:($o > $o),B:($o > $o),C:($o > $o),D:($o > $o)]: ((~ ((A = C) => (B != D))) <= ((product_Pair_o_o_o_o @ A @ B) = (product_Pair_o_o_o_o @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_Pair__inject)).
36.43/11.22	thf(169,plain,((! [A:($o > $o),B:($o > $o),C:($o > $o),D:($o > $o)]: (~ (((A) = (C)) => (~ ((B) = (D)))) | ~ ((product_Pair_o_o_o_o @ (A) @ (B)) = (product_Pair_o_o_o_o @ (C) @ (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
36.43/11.22	thf(479,plain,((~ (((^ [A:$o]: (A)) = (^ [A:$o]: (($false)))) => (~ (((~)) = (^ [A:$o]: (A))))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ ((~))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(540,plain,((((~)) = (^ [A:$o]: (A))) | (~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ ((~))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A)))))),inference(cnf,[status(esa)],[479])).
36.43/11.22	thf(1167,plain,((((~)) = (^ [A:$o]: (A))) | ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ ((~))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A))))),inference(lifteq,[status(thm)],[540])).
36.43/11.22	thf(1168,plain,(((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ ((~))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A))))),inference(simp,[status(thm)],[1167])).
36.43/11.22	thf(85,axiom,((! [A:produc809931564nres_d]: ~ (! [B:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)),C:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d))]: (A != (produc1910095910nres_d @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_old_Oprod_Oexhaust)).
36.43/11.22	thf(3008,plain,((! [A:produc809931564nres_d]: ~ (! [B:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)),C:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d))]: ~ (A = (produc1910095910nres_d @ (B) @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])).
36.43/11.22	thf(44,axiom,((! [A:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)),B:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d)),C:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)),D:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d))]: (((produc1910095910nres_d @ A @ B) = (produc1910095910nres_d @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_old_Oprod_Oinject)).
36.43/11.22	thf(2778,plain,((! [A:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)),B:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d)),C:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)),D:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d))]: (((produc1910095910nres_d @ (A) @ (B)) = (produc1910095910nres_d @ (C) @ (D))) = (((A) = (C)) & ((B) = (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])).
36.43/11.22	thf(102,axiom,((! [A:product_prod_a_c]: ? [B:a,C:c]: (A = (product_Pair_a_c @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_surj__pair)).
36.43/11.22	thf(3072,plain,((! [A:product_prod_a_c]: ? [B:a,C:c]: (A = (product_Pair_a_c @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])).
36.43/11.22	thf(7,axiom,((! [A:(product_prod_o_o_o_o > $o),B:product_prod_o_o_o_o]: ((A @ B) <= (! [C:($o > $o),D:($o > $o)]: (A @ (product_Pair_o_o_o_o @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_prod__cases)).
36.43/11.22	thf(1406,plain,((! [A:(product_prod_o_o_o_o > $o),B:product_prod_o_o_o_o]: ((A @ B) | ~ (! [C:($o > $o),D:($o > $o)]: (A @ (product_Pair_o_o_o_o @ (C) @ (D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
36.43/11.22	thf(152,axiom,((! [A:(a > refine432681134nres_b),B:(c > refine449204144nres_d),C:set_Product_prod_a_c,D:set_Pr1640496404nres_d,E:a,F:c]: (((member466432594od_a_c @ (product_Pair_a_c @ E @ F) @ C) => (member1578111221nres_d @ (produc2147164944nres_d @ (A @ E) @ (B @ F)) @ D)) <= (member936907743nres_d @ (produc210841666nres_d @ A @ B) @ (relAPP900772393nres_d @ (relAPP1270454529nres_d @ fun_re1760530651nres_d @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_tagged__fun__relD__none)).
36.43/11.22	thf(3230,plain,((! [A:(a > refine432681134nres_b),B:(c > refine449204144nres_d),C:set_Product_prod_a_c,D:set_Pr1640496404nres_d,E:a,F:c]: (((member466432594od_a_c @ (product_Pair_a_c @ E @ F) @ C) => (member1578111221nres_d @ (produc2147164944nres_d @ (A @ E) @ (B @ F)) @ D)) | ~ (member936907743nres_d @ (produc210841666nres_d @ (A) @ (B)) @ (relAPP900772393nres_d @ (relAPP1270454529nres_d @ fun_re1760530651nres_d @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])).
36.43/11.22	thf(74,axiom,((! [A:$o,B:$o,C:refine449204144nres_d,D:refine432681134nres_b,E:set_Product_prod_d_b]: (((member1269896305nres_b @ (produc1954071948nres_b @ (refine1437029930_bnd_d @ B @ C) @ (refine1437029928_bnd_b @ A @ D)) @ (relAPP821124455nres_b @ refine1072887132el_d_b @ E)) <= (((B) => (member1269896305nres_b @ (produc1954071948nres_b @ C @ D) @ (relAPP821124455nres_b @ refine1072887132el_d_b @ E))) <= (A))) <= ((A) => (B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_param__op__nres__ASSERT__bnd)).
36.43/11.22	thf(2953,plain,((! [A:$o,B:$o,C:refine449204144nres_d,D:refine432681134nres_b,E:set_Product_prod_d_b]: ((member1269896305nres_b @ (produc1954071948nres_b @ (refine1437029930_bnd_d @ B @ C) @ (refine1437029928_bnd_b @ A @ D)) @ (relAPP821124455nres_b @ (refine1072887132el_d_b) @ E)) | ~ (((B) => (member1269896305nres_b @ (produc1954071948nres_b @ C @ D) @ (relAPP821124455nres_b @ (refine1072887132el_d_b) @ E))) | ~ (A)) | ~ ((A) => (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])).
36.43/11.22	thf(11,axiom,((! [A:($o > $o),B:($o > $o),C:($o > $o),D:($o > $o)]: (((product_Pair_o_o_o_o @ A @ B) = (product_Pair_o_o_o_o @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_prod_Oinject)).
36.43/11.22	thf(1419,plain,((! [A:($o > $o),B:($o > $o),C:($o > $o),D:($o > $o)]: (((product_Pair_o_o_o_o @ (A) @ (B)) = (product_Pair_o_o_o_o @ (C) @ (D))) = (((A) = (C)) & ((B) = (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
36.43/11.22	thf(1600,plain,((((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true))))) = (((^ [A:$o]: (A)) = (^ [A:$o]: (A))) & ((^ [A:$o]: (A)) = (^ [A:$o]: (($true))))))),inference(instance,[status(thm)],[1419])).
36.43/11.22	thf(1601,plain,((((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true))))) = ((^ [A:$o]: (A)) = (^ [A:$o]: (($true)))))),inference(simp,[status(thm)],[1600])).
36.43/11.22	thf(1826,plain,((((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true))))) = ((^ [A:$o]: (A)) = (^ [A:$o]: (($true)))))),inference(lifteq,[status(thm)],[1601])).
36.43/11.22	thf(3451,plain,(((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true))))) | (~ ((^ [A:$o]: (A)) = (^ [A:$o]: (($true)))))),inference(bool_ext,[status(thm)],[1826])).
36.43/11.22	thf(3457,plain,(((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true))))) | ((^ [A:$o]: (A)) != (^ [A:$o]: (($true))))),inference(lifteq,[status(thm)],[3451])).
36.43/11.22	thf(3460,plain,(~ (sk109) | ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true)))))),inference(func_ext,[status(esa)],[3457])).
36.43/11.22	thf(18,axiom,((! [A:produc2103861704nres_d,B:(produc2103861704nres_d > $o)]: ((member936907743nres_d @ A @ (collec1639315997nres_d @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_mem__Collect__eq)).
36.43/11.22	thf(2676,plain,((! [A:produc2103861704nres_d,B:(produc2103861704nres_d > $o)]: ((member936907743nres_d @ A @ (collec1639315997nres_d @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])).
36.43/11.22	thf(86,axiom,((! [A:set_Product_prod_a_c]: ((collec662378644od_a_c @ (^ [B:product_prod_a_c]: (member466432594od_a_c @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_Collect__mem__eq)).
36.43/11.22	thf(3012,plain,((! [A:set_Product_prod_a_c]: ((collec662378644od_a_c @ (^ [B:product_prod_a_c]: (member466432594od_a_c @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])).
36.43/11.22	thf(307,plain,((~ ((((~)) = (^ [A:$o]: (A))) => (~ ((^ [A:$o]: (($true))) = (^ [A:$o]: (A))))) | ~ ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (($true)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(630,plain,((((~)) = (^ [A:$o]: (A))) | (~ ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (($true)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))))),inference(cnf,[status(esa)],[307])).
36.43/11.22	thf(1040,plain,((((~)) = (^ [A:$o]: (A))) | ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (($true)))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))))),inference(lifteq,[status(thm)],[630])).
36.43/11.22	thf(1041,plain,(((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (($true)))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))))),inference(simp,[status(thm)],[1040])).
36.43/11.22	thf(113,axiom,((relAPP1135042155nres_d = (^ [A:(set_Product_prod_a_c > (set_Pr797615136nres_d > set_Pr2080238504nres_d))]: (A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_relAPP__def)).
36.43/11.22	thf(3102,plain,(((relAPP1135042155nres_d) = (^ [A:(set_Product_prod_a_c > (set_Pr797615136nres_d > set_Pr2080238504nres_d))]: (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])).
36.43/11.22	thf(3103,plain,(((relAPP1135042155nres_d) = (^ [A:(set_Product_prod_a_c > (set_Pr797615136nres_d > set_Pr2080238504nres_d))]: (A)))),inference(lifteq,[status(thm)],[3102])).
36.43/11.22	thf(28,axiom,((! [A:(a > a),B:(c > c),C:set_Product_prod_a_c,D:set_Product_prod_a_c,E:a,F:c]: ((member1010099668_a_c_c @ (product_Pair_a_a_c_c @ A @ B) @ (relAPP237429680_a_c_c @ (relAPP887115074_a_c_c @ fun_rel_a_c_a_c @ C) @ D)) => ((member466432594od_a_c @ (product_Pair_a_c @ E @ F) @ C) => (member466432594od_a_c @ (product_Pair_a_c @ (autoref_APP_a_a @ A @ E) @ (autoref_APP_c_c @ B @ F)) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_autoref__APP)).
36.43/11.22	thf(2723,plain,((! [A:(a > a),B:(c > c),C:set_Product_prod_a_c,D:set_Product_prod_a_c,E:a,F:c]: ((member1010099668_a_c_c @ (product_Pair_a_a_c_c @ (A) @ (B)) @ (relAPP237429680_a_c_c @ (relAPP887115074_a_c_c @ fun_rel_a_c_a_c @ C) @ D)) => ((member466432594od_a_c @ (product_Pair_a_c @ E @ F) @ C) => (member466432594od_a_c @ (product_Pair_a_c @ (autoref_APP_a_a @ (A) @ E) @ (autoref_APP_c_c @ (B) @ F)) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])).
36.43/11.22	thf(79,axiom,((refine1958703523nres_d = (^ [A:set_Pr797615136nres_d,B:(((c > refine449204144nres_d) > refine449204144nres_d) > $o),C:((a > refine432681134nres_b) > refine432681134nres_b)]: ? [D:((c > refine449204144nres_d) > refine449204144nres_d)]: ((B @ D) & (member461830657nres_d @ (produc2075136412nres_d @ C @ D) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_lift__assn__def)).
36.43/11.22	thf(2985,plain,(((refine1958703523nres_d) = (^ [A:set_Pr797615136nres_d,B:(((c > refine449204144nres_d) > refine449204144nres_d) > $o),C:((a > refine432681134nres_b) > refine432681134nres_b)]: ? [D:((c > refine449204144nres_d) > refine449204144nres_d)]: ((B @ D) & (member461830657nres_d @ (produc2075136412nres_d @ C @ D) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])).
36.43/11.22	thf(57,axiom,((! [A:set_Product_prod_c_a]: (member318002145nres_a @ (produc1063567300nres_a @ refine2063221606TURN_c @ refine2063221604TURN_a) @ (relAPP947801195nres_a @ (relAPP1825452871nres_a @ fun_re1645900187nres_a @ A) @ (relAPP35306343nres_a @ refine245117724el_c_a @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_autoref__RETURN)).
36.43/11.22	thf(2819,plain,((! [A:set_Product_prod_c_a]: (member318002145nres_a @ (produc1063567300nres_a @ (refine2063221606TURN_c) @ (refine2063221604TURN_a)) @ (relAPP947801195nres_a @ (relAPP1825452871nres_a @ fun_re1645900187nres_a @ A) @ (relAPP35306343nres_a @ (refine245117724el_c_a) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])).
36.43/11.22	thf(302,plain,((~ (((^ [A:$o]: (($true))) = (^ [A:$o]: (A))) => (~ ((^ [A:$o]: (A)) = ((~))))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ ((~)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(653,plain,(((^ [A:$o]: (A)) = ((~))) | (~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ ((~)))))),inference(cnf,[status(esa)],[302])).
36.43/11.22	thf(1227,plain,((((~)) = (^ [A:$o]: (A))) | ((product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ ((~))))),inference(lifteq,[status(thm)],[653])).
36.43/11.22	thf(1228,plain,(((product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ ((~))))),inference(simp,[status(thm)],[1227])).
36.43/11.22	thf(31,axiom,((! [A:product_prod_a_c]: ~ (! [B:a,C:c]: (A != (product_Pair_a_c @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_old_Oprod_Oexhaust)).
36.43/11.22	thf(2735,plain,((! [A:product_prod_a_c]: ~ (! [B:a,C:c]: ~ (A = (product_Pair_a_c @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])).
36.43/11.22	thf(98,axiom,((! [A:product_prod_a_c,B:(product_prod_a_c > $o)]: ((member466432594od_a_c @ A @ (collec662378644od_a_c @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_mem__Collect__eq)).
36.43/11.22	thf(3061,plain,((! [A:product_prod_a_c,B:(product_prod_a_c > $o)]: ((member466432594od_a_c @ A @ (collec662378644od_a_c @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])).
36.43/11.22	thf(23,axiom,((! [A:set_Pr589481214nres_d]: ((collec1639315997nres_d @ (^ [B:produc2103861704nres_d]: (member936907743nres_d @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_Collect__mem__eq)).
36.43/11.22	thf(2708,plain,((! [A:set_Pr589481214nres_d]: ((collec1639315997nres_d @ (^ [B:produc2103861704nres_d]: (member936907743nres_d @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])).
36.43/11.22	thf(127,axiom,((! [A:set_Product_prod_a_d,B:set_Product_prod_b_c]: (member1981370113nres_c @ (produc651225572nres_c @ refine436832839nd_a_b @ refine772657413nd_d_c) @ (relAPP745269862nres_c @ (relAPP1327809903nres_c @ fun_re297775585nres_c @ (relAPP1043177969nres_d @ refine737062561el_a_d @ A)) @ (relAPP1784890619nres_c @ (relAPP1763648999nres_c @ fun_re955494798nres_c @ (relAPP1699156520nres_c @ (relAPP189920063nres_c @ fun_re631684249nres_c @ A) @ (relAPP797192941nres_c @ refine1564831967el_b_c @ B))) @ (relAPP797192941nres_c @ refine1564831967el_b_c @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_param__bind)).
36.43/11.22	thf(3148,plain,((! [A:set_Product_prod_a_d,B:set_Product_prod_b_c]: (member1981370113nres_c @ (produc651225572nres_c @ (refine436832839nd_a_b) @ (refine772657413nd_d_c)) @ (relAPP745269862nres_c @ (relAPP1327809903nres_c @ fun_re297775585nres_c @ (relAPP1043177969nres_d @ refine737062561el_a_d @ A)) @ (relAPP1784890619nres_c @ (relAPP1763648999nres_c @ fun_re955494798nres_c @ (relAPP1699156520nres_c @ (relAPP189920063nres_c @ fun_re631684249nres_c @ A) @ (relAPP797192941nres_c @ refine1564831967el_b_c @ B))) @ (relAPP797192941nres_c @ (refine1564831967el_b_c) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])).
36.43/11.22	thf(501,plain,((~ (((^ [A:$o]: (A)) = (^ [A:$o]: (($false)))) => (~ ((^ [A:$o]: (($false))) = (^ [A:$o]: (($true)))))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (($true))))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(893,plain,(((^ [A:$o]: (($false))) = (^ [A:$o]: (($true)))) | (~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (($true))))))),inference(cnf,[status(esa)],[501])).
36.43/11.22	thf(916,plain,(((^ [A:$o]: (($false))) = (^ [A:$o]: (($true)))) | ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (($true)))))),inference(lifteq,[status(thm)],[893])).
36.43/11.22	thf(917,plain,(((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (($true)))))),inference(simp,[status(thm)],[916])).
36.43/11.22	thf(108,axiom,(((relAPP1936960811nres_b @ (relAPP1536875909nres_b @ fun_re1837693787nres_b @ id_a) @ id_Ref1256934482nres_b) = id_a_R351071993nres_b)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_fun__rel__id__simp)).
36.43/11.22	thf(3089,plain,(((relAPP1936960811nres_b @ (relAPP1536875909nres_b @ fun_re1837693787nres_b @ id_a) @ id_Ref1256934482nres_b) = id_a_R351071993nres_b)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])).
36.43/11.22	thf(364,plain,((~ (((^ [A:$o]: (($false))) = (^ [A:$o]: (A))) => (~ ((^ [A:$o]: (A)) = (^ [A:$o]: (A))))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(365,plain,((((^ [A:$o]: (($false))) = (^ [A:$o]: (A))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))))),inference(simp,[status(thm)],[364])).
36.43/11.22	thf(538,plain,(((^ [A:$o]: (($false))) = (^ [A:$o]: (A))) | (~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))))),inference(cnf,[status(esa)],[365])).
36.43/11.22	thf(949,plain,(((^ [A:$o]: (($false))) = (^ [A:$o]: (A))) | ((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))))),inference(lifteq,[status(thm)],[538])).
36.43/11.22	thf(21,axiom,((! [A:produc1757587562nres_d,B:(produc1757587562nres_d > $o)]: ((member461830657nres_d @ A @ (collec1671161663nres_d @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_mem__Collect__eq)).
36.43/11.22	thf(2703,plain,((! [A:produc1757587562nres_d,B:(produc1757587562nres_d > $o)]: ((member461830657nres_d @ A @ (collec1671161663nres_d @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])).
36.43/11.22	thf(515,plain,((~ (((^ [A:$o]: (($false))) = ((~))) => (~ ((^ [A:$o]: (A)) = ((~))))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ ((~)) @ ((~)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(710,plain,(((^ [A:$o]: (A)) = ((~))) | (~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ ((~)) @ ((~)))))),inference(cnf,[status(esa)],[515])).
36.43/11.22	thf(1054,plain,((((~)) = (^ [A:$o]: (A))) | ((product_Pair_o_o_o_o @ ((~)) @ ((~))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A))))),inference(lifteq,[status(thm)],[710])).
36.43/11.22	thf(1055,plain,(((product_Pair_o_o_o_o @ ((~)) @ ((~))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A))))),inference(simp,[status(thm)],[1054])).
36.43/11.22	thf(8,axiom,((! [A:(($o > $o) > a),B:(($o > $o) > c),C:set_Pr934623755_o_o_o,D:set_Product_prod_a_c,E:($o > $o),F:($o > $o)]: ((member1270020946_o_o_c @ (produc2068274457_o_o_c @ A @ B) @ (relAPP970620078_o_o_c @ (relAPP1750172554_o_o_c @ fun_rel_o_o_o_o_a_c @ C) @ D)) => ((member250723412_o_o_o @ (product_Pair_o_o_o_o @ E @ F) @ C) => (member466432594od_a_c @ (product_Pair_a_c @ (autoref_APP_o_o_a @ A @ E) @ (autoref_APP_o_o_c @ B @ F)) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_autoref__APP)).
36.43/11.22	thf(1409,plain,((! [A:(($o > $o) > a),B:(($o > $o) > c),C:set_Pr934623755_o_o_o,D:set_Product_prod_a_c,E:($o > $o),F:($o > $o)]: ((member1270020946_o_o_c @ (produc2068274457_o_o_c @ (A) @ (B)) @ (relAPP970620078_o_o_c @ (relAPP1750172554_o_o_c @ fun_rel_o_o_o_o_a_c @ C) @ D)) => ((member250723412_o_o_o @ (product_Pair_o_o_o_o @ (E) @ (F)) @ C) => (member466432594od_a_c @ (product_Pair_a_c @ (autoref_APP_o_o_a @ (A) @ (E)) @ (autoref_APP_o_o_c @ (B) @ (F))) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
36.43/11.22	thf(118,axiom,((relAPP527276399nres_c = (^ [A:(set_Product_prod_a_c > set_Pr1128439124nres_c)]: (A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_relAPP__def)).
36.43/11.22	thf(3124,plain,(((relAPP527276399nres_c) = (^ [A:(set_Product_prod_a_c > set_Pr1128439124nres_c)]: (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])).
36.43/11.22	thf(3125,plain,(((relAPP527276399nres_c) = (^ [A:(set_Product_prod_a_c > set_Pr1128439124nres_c)]: (A)))),inference(lifteq,[status(thm)],[3124])).
36.43/11.22	thf(112,axiom,((! [A:(produc2103861704nres_d > $o),B:produc2103861704nres_d]: ((A @ B) <= (! [C:(a > refine432681134nres_b),D:(c > refine449204144nres_d)]: (A @ (produc210841666nres_d @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_prod__cases)).
36.43/11.22	thf(3099,plain,((! [A:(produc2103861704nres_d > $o),B:produc2103861704nres_d]: ((A @ B) | ~ (! [C:(a > refine432681134nres_b),D:(c > refine449204144nres_d)]: (A @ (produc210841666nres_d @ (C) @ (D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])).
36.43/11.22	thf(460,plain,((~ ((((~)) = (^ [A:$o]: (A))) => (~ ((^ [A:$o]: (($false))) = (^ [A:$o]: (A))))) | ~ ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (($false)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(587,plain,((((~)) = (^ [A:$o]: (A))) | (~ ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (($false)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))))),inference(cnf,[status(esa)],[460])).
36.43/11.22	thf(968,plain,((((~)) = (^ [A:$o]: (A))) | ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (($false)))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))))),inference(lifteq,[status(thm)],[587])).
36.43/11.22	thf(969,plain,(((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (($false)))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))))),inference(simp,[status(thm)],[968])).
36.43/11.22	thf(106,axiom,((! [A:a,B:c,C:a,D:c]: (((product_Pair_a_c @ A @ B) = (product_Pair_a_c @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_old_Oprod_Oinject)).
36.43/11.22	thf(3084,plain,((! [A:a,B:c,C:a,D:c]: (((product_Pair_a_c @ A @ B) = (product_Pair_a_c @ C @ D)) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])).
36.43/11.22	thf(444,plain,((~ (((^ [A:$o]: (($false))) = ((~))) => (~ (((~)) = (^ [A:$o]: (A))))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ ((~))) = (product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(738,plain,((((~)) = (^ [A:$o]: (A))) | (~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ ((~))) = (product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A)))))),inference(cnf,[status(esa)],[444])).
36.43/11.22	thf(1099,plain,((((~)) = (^ [A:$o]: (A))) | ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ ((~))))),inference(lifteq,[status(thm)],[738])).
36.43/11.22	thf(1100,plain,(((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ ((~))))),inference(simp,[status(thm)],[1099])).
36.43/11.22	thf(61,axiom,((! [A:(a > refine432681134nres_b),B:(c > refine449204144nres_d),C:(a > refine432681134nres_b),D:(c > refine449204144nres_d)]: ((~ ((B != D) <= (A = C))) <= ((produc210841666nres_d @ A @ B) = (produc210841666nres_d @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_Pair__inject)).
36.43/11.22	thf(2829,plain,((! [A:(a > refine432681134nres_b),B:(c > refine449204144nres_d),C:(a > refine432681134nres_b),D:(c > refine449204144nres_d)]: (~ (~ ((B) = (D)) | ~ ((A) = (C))) | ~ ((produc210841666nres_d @ (A) @ (B)) = (produc210841666nres_d @ (C) @ (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])).
36.43/11.22	thf(1731,plain,((((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))) = (((^ [A:$o]: (($false))) = (^ [A:$o]: (A))) & ((^ [A:$o]: (A)) = (^ [A:$o]: (A)))))),inference(instance,[status(thm)],[1419])).
36.43/11.22	thf(1732,plain,((((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))) = ((^ [A:$o]: (($false))) = (^ [A:$o]: (A))))),inference(simp,[status(thm)],[1731])).
36.43/11.22	thf(1922,plain,((((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))) = ((^ [A:$o]: (($false))) = (^ [A:$o]: (A))))),inference(lifteq,[status(thm)],[1732])).
36.43/11.22	thf(20,axiom,((! [A:$o,B:$o,C:refine432681134nres_b,D:refine432681134nres_b,E:set_Product_prod_b_b]: (((B) <= (A)) => (((A) => ((B) => (member1446466291nres_b @ (produc2130641934nres_b @ C @ D) @ (relAPP281291371nres_b @ refine1564831966el_b_b @ E)))) => (member1446466291nres_b @ (produc2130641934nres_b @ (refine1437029928_bnd_b @ B @ C) @ (refine1437029928_bnd_b @ A @ D)) @ (relAPP281291371nres_b @ refine1564831966el_b_b @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_param__op__nres__ASSERT__bnd)).
36.43/11.22	thf(2691,plain,((! [A:$o,B:$o,C:refine432681134nres_b,D:refine432681134nres_b,E:set_Product_prod_b_b]: (((B) | ~ (A)) => (((A) => ((B) => (member1446466291nres_b @ (produc2130641934nres_b @ C @ D) @ (relAPP281291371nres_b @ (refine1564831966el_b_b) @ E)))) => (member1446466291nres_b @ (produc2130641934nres_b @ (refine1437029928_bnd_b @ B @ C) @ (refine1437029928_bnd_b @ A @ D)) @ (relAPP281291371nres_b @ (refine1564831966el_b_b) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])).
36.43/11.22	thf(5,axiom,((! [A:(a > refine432681134nres_b),B:(a > refine432681134nres_b),C:set_Pr896671762nres_b,D:refine432681134nres_b,E:a]: (((D = (A @ E)) => (member1446466291nres_b @ (produc2130641934nres_b @ D @ (B @ E)) @ C)) <= (member369653087nres_b @ (produc809128386nres_b @ A @ B) @ (relAPP1936960811nres_b @ (relAPP1536875909nres_b @ fun_re1837693787nres_b @ id_a) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_fun__relE2)).
36.43/11.22	thf(164,plain,((! [A:(a > refine432681134nres_b),B:(a > refine432681134nres_b),C:set_Pr896671762nres_b,D:refine432681134nres_b,E:a]: (((D = (A @ E)) => (member1446466291nres_b @ (produc2130641934nres_b @ D @ (B @ E)) @ C)) | ~ (member369653087nres_b @ (produc809128386nres_b @ (A) @ (B)) @ (relAPP1936960811nres_b @ (relAPP1536875909nres_b @ fun_re1837693787nres_b @ id_a) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
36.43/11.22	thf(103,axiom,((! [A:(produc2103861704nres_d > $o),B:produc2103861704nres_d]: ((! [C:(a > refine432681134nres_b),D:(c > refine449204144nres_d)]: (A @ (produc210841666nres_d @ C @ D))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_old_Oprod_Oinducts)).
36.43/11.22	thf(3075,plain,((! [A:(produc2103861704nres_d > $o),B:produc2103861704nres_d]: ((! [C:(a > refine432681134nres_b),D:(c > refine449204144nres_d)]: (A @ (produc210841666nres_d @ (C) @ (D)))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])).
36.43/11.22	thf(66,axiom,((! [A:a,B:c,C:set_Product_prod_a_c,D:(a > ($o > $o)),E:(c > ($o > $o)),F:set_Pr934623755_o_o_o]: ((member466432594od_a_c @ (product_Pair_a_c @ A @ B) @ C) => ((! [G:c]: ((autore1113312320RNAL_o @ (B = G)) => (! [H:a]: ((member466432594od_a_c @ (product_Pair_a_c @ H @ G) @ C) => (member250723412_o_o_o @ (product_Pair_o_o_o_o @ (D @ H) @ (autoref_APP_c_o_o @ E @ G)) @ F))))) => (member250723412_o_o_o @ (product_Pair_o_o_o_o @ (D @ A) @ (autore821920247_o_o_o @ (autore1554881264_o_o_o @ (autore1757597947_o_o_o @ (autore1861331824_o_o_o @ (^ [G:c,H:(c > ($o > $o))]: (H @ G))) @ (autore1424734926_o_o_o @ (relAPP1723270664_o_o_o @ (relAPP913737114_o_o_o @ fun_re362844942_o_o_o @ C) @ (relAPP829628004_o_o_o @ (relAPP1210499902_o_o_o @ fun_re2021699288_o_o_o @ (relAPP1525934692_c_o_o @ (relAPP589338430_c_o_o @ fun_rel_a_c_o_o_o_o @ C) @ F)) @ F)))) @ B) @ E)) @ F))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_autoref__Let__cong)).
36.43/11.22	thf(2925,plain,((! [A:a,B:c,C:set_Product_prod_a_c,D:(a > ($o > $o)),E:(c > ($o > $o)),F:set_Pr934623755_o_o_o]: ((member466432594od_a_c @ (product_Pair_a_c @ A @ B) @ C) => ((! [G:c]: ((autore1113312320RNAL_o @ (B = G)) => (! [H:a]: ((member466432594od_a_c @ (product_Pair_a_c @ H @ G) @ C) => (member250723412_o_o_o @ (product_Pair_o_o_o_o @ (D @ H) @ (autoref_APP_c_o_o @ E @ G)) @ F))))) => (member250723412_o_o_o @ (product_Pair_o_o_o_o @ (D @ A) @ (autore821920247_o_o_o @ (autore1554881264_o_o_o @ (autore1757597947_o_o_o @ (autore1861331824_o_o_o @ (^ [G:c,H:(c > ($o > $o))]: (H @ G))) @ (autore1424734926_o_o_o @ (relAPP1723270664_o_o_o @ (relAPP913737114_o_o_o @ fun_re362844942_o_o_o @ C) @ (relAPP829628004_o_o_o @ (relAPP1210499902_o_o_o @ fun_re2021699288_o_o_o @ (relAPP1525934692_c_o_o @ (relAPP589338430_c_o_o @ fun_rel_a_c_o_o_o_o @ C) @ F)) @ F)))) @ B) @ E)) @ F))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])).
36.43/11.22	thf(110,axiom,((! [A:(produc809931564nres_d > $o),B:produc809931564nres_d]: ((! [C:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)),D:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d))]: (A @ (produc1910095910nres_d @ C @ D))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_prod__cases)).
36.43/11.22	thf(3093,plain,((! [A:(produc809931564nres_d > $o),B:produc809931564nres_d]: ((! [C:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)),D:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d))]: (A @ (produc1910095910nres_d @ (C) @ (D)))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])).
36.43/11.22	thf(73,axiom,((! [A:(a > refine432681134nres_b),B:(c > refine449204144nres_d),C:set_Pr589481214nres_d,D:(a > refine432681134nres_b)]: (((member936907743nres_d @ (produc210841666nres_d @ D @ B) @ C) <= (autore519998265nres_b @ A @ D)) <= (member936907743nres_d @ (produc210841666nres_d @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_autoref__REMOVE__INTERNAL__EQ)).
36.43/11.22	thf(2950,plain,((! [A:(a > refine432681134nres_b),B:(c > refine449204144nres_d),C:set_Pr589481214nres_d,D:(a > refine432681134nres_b)]: ((member936907743nres_d @ (produc210841666nres_d @ (D) @ (B)) @ C) | ~ (autore519998265nres_b @ (A) @ (D)) | ~ (member936907743nres_d @ (produc210841666nres_d @ (A) @ (B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])).
36.43/11.22	thf(10,axiom,((! [A:product_prod_o_o_o_o]: ~ (! [B:($o > $o),C:($o > $o)]: (A != (product_Pair_o_o_o_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_old_Oprod_Oexhaust)).
36.43/11.22	thf(1415,plain,((! [A:product_prod_o_o_o_o]: ~ (! [B:($o > $o),C:($o > $o)]: ~ (A = (product_Pair_o_o_o_o @ (B) @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
36.43/11.22	thf(283,plain,((~ (((^ [A:$o]: (A)) = (^ [A:$o]: (($false)))) => (~ ((^ [A:$o]: (A)) = ((~))))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ ((~)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(881,plain,(((^ [A:$o]: (A)) = ((~))) | (~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ ((~)))))),inference(cnf,[status(esa)],[283])).
36.43/11.22	thf(980,plain,((((~)) = (^ [A:$o]: (A))) | ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ ((~))))),inference(lifteq,[status(thm)],[881])).
36.43/11.22	thf(981,plain,(((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ ((~))))),inference(simp,[status(thm)],[980])).
36.43/11.22	thf(91,axiom,((! [A:(a > refine432681134nres_b),B:(c > refine449204144nres_d),C:(a > refine432681134nres_b),D:(c > refine449204144nres_d)]: (((produc210841666nres_d @ A @ B) = (produc210841666nres_d @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_old_Oprod_Oinject)).
36.43/11.22	thf(3036,plain,((! [A:(a > refine432681134nres_b),B:(c > refine449204144nres_d),C:(a > refine432681134nres_b),D:(c > refine449204144nres_d)]: (((produc210841666nres_d @ (A) @ (B)) = (produc210841666nres_d @ (C) @ (D))) = (((B) = (D)) & ((A) = (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])).
36.43/11.22	thf(150,axiom,((! [A:set_Product_prod_a_b,B:set_Product_prod_b_a]: (member1468277761nres_a @ (produc1066811108nres_a @ refine436832839nd_a_b @ refine1264602245nd_b_a) @ (relAPP1102334824nres_a @ (relAPP1042385007nres_a @ fun_re1904331357nres_a @ (relAPP11374829nres_b @ refine737062559el_a_b @ A)) @ (relAPP919190011nres_a @ (relAPP811277159nres_a @ fun_re1140323340nres_a @ (relAPP587861290nres_a @ (relAPP456341443nres_a @ fun_re708847385nres_a @ A) @ (relAPP1912873449nres_a @ refine1564831965el_b_a @ B))) @ (relAPP1912873449nres_a @ refine1564831965el_b_a @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_param__bind)).
36.43/11.22	thf(3226,plain,((! [A:set_Product_prod_a_b,B:set_Product_prod_b_a]: (member1468277761nres_a @ (produc1066811108nres_a @ (refine436832839nd_a_b) @ (refine1264602245nd_b_a)) @ (relAPP1102334824nres_a @ (relAPP1042385007nres_a @ fun_re1904331357nres_a @ (relAPP11374829nres_b @ refine737062559el_a_b @ A)) @ (relAPP919190011nres_a @ (relAPP811277159nres_a @ fun_re1140323340nres_a @ (relAPP587861290nres_a @ (relAPP456341443nres_a @ fun_re708847385nres_a @ A) @ (relAPP1912873449nres_a @ refine1564831965el_b_a @ B))) @ (relAPP1912873449nres_a @ (refine1564831965el_b_a) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])).
36.43/11.22	thf(42,axiom,((! [A:(produc1757587562nres_d > $o),B:produc1757587562nres_d]: ((A @ B) <= (! [C:((a > refine432681134nres_b) > refine432681134nres_b),D:((c > refine449204144nres_d) > refine449204144nres_d)]: (A @ (produc2075136412nres_d @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_old_Oprod_Oinducts)).
36.43/11.22	thf(2772,plain,((! [A:(produc1757587562nres_d > $o),B:produc1757587562nres_d]: ((A @ B) | ~ (! [C:((a > refine432681134nres_b) > refine432681134nres_b),D:((c > refine449204144nres_d) > refine449204144nres_d)]: (A @ (produc2075136412nres_d @ (C) @ (D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])).
36.43/11.22	thf(130,axiom,((! [A:set_Pr589481214nres_d,B:set_Product_prod_b_d]: (member449974729nres_d @ (produc973126316nres_d @ refine1985319227es_b_b @ refine1129534141es_d_d) @ (relAPP745136137nres_d @ (relAPP1787540131nres_d @ fun_re1732033515nres_d @ (relAPP1482036727nres_d @ refine1535302424nres_d @ A)) @ (relAPP1552964229nres_d @ (relAPP1953591565nres_d @ fun_re2071856555nres_d @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ A) @ (relAPP1313094511nres_d @ refine1564831968el_b_d @ B))) @ (relAPP1313094511nres_d @ refine1564831968el_b_d @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_param__bind)).
36.43/11.22	thf(3157,plain,((! [A:set_Pr589481214nres_d,B:set_Product_prod_b_d]: (member449974729nres_d @ (produc973126316nres_d @ (refine1985319227es_b_b) @ (refine1129534141es_d_d)) @ (relAPP745136137nres_d @ (relAPP1787540131nres_d @ fun_re1732033515nres_d @ (relAPP1482036727nres_d @ refine1535302424nres_d @ A)) @ (relAPP1552964229nres_d @ (relAPP1953591565nres_d @ fun_re2071856555nres_d @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ A) @ (relAPP1313094511nres_d @ refine1564831968el_b_d @ B))) @ (relAPP1313094511nres_d @ (refine1564831968el_b_d) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])).
36.43/11.22	thf(473,plain,((~ ((((~)) = (^ [A:$o]: (A))) => (~ ((^ [A:$o]: (($true))) = (^ [A:$o]: (($false)))))) | ~ ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (($true)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false))))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(789,plain,((((~)) = (^ [A:$o]: (A))) | (~ ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (($true)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false))))))),inference(cnf,[status(esa)],[473])).
36.43/11.22	thf(987,plain,((((~)) = (^ [A:$o]: (A))) | ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (($true)))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))))),inference(lifteq,[status(thm)],[789])).
36.43/11.22	thf(988,plain,(((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (($true)))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))))),inference(simp,[status(thm)],[987])).
36.43/11.22	thf(50,axiom,((refine746536475nres_d = (^ [A:set_Pr589481214nres_d,B:((c > refine449204144nres_d) > $o),C:(a > refine432681134nres_b)]: ? [D:(c > refine449204144nres_d)]: ((B @ D) & (member936907743nres_d @ (produc210841666nres_d @ C @ D) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_lift__assn__def)).
36.43/11.22	thf(2799,plain,(((refine746536475nres_d) = (^ [A:set_Pr589481214nres_d,B:((c > refine449204144nres_d) > $o),C:(a > refine432681134nres_b)]: ? [D:(c > refine449204144nres_d)]: ((B @ D) & (member936907743nres_d @ (produc210841666nres_d @ C @ D) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])).
36.43/11.22	thf(52,axiom,((! [A:produc809931564nres_d]: ? [B:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)),C:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d))]: (A = (produc1910095910nres_d @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_surj__pair)).
36.43/11.22	thf(2804,plain,((! [A:produc809931564nres_d]: ? [B:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)),C:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d))]: (A = (produc1910095910nres_d @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])).
36.43/11.22	thf(75,axiom,((! [A:set_Product_prod_a_c,B:set_Pr1128439124nres_c]: (member427035401nres_c @ (produc1824358636nres_c @ (^ [C:a,D:(a > refine424419629nres_a)]: (D @ C)) @ (^ [C:c,D:(c > refine440942639nres_c)]: (D @ C))) @ (relAPP998488211nres_c @ (relAPP1155943915nres_c @ fun_re418666087nres_c @ A) @ (relAPP1774615993nres_c @ (relAPP483050597nres_c @ fun_re1877185935nres_c @ (relAPP2018433511nres_c @ (relAPP173519167nres_c @ fun_re766812315nres_c @ A) @ B)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_autoref__Let)).
36.43/11.22	thf(2965,plain,((! [A:set_Product_prod_a_c,B:set_Pr1128439124nres_c]: (member427035401nres_c @ (produc1824358636nres_c @ (^ [C:a,D:(a > refine424419629nres_a)]: (D @ C)) @ (^ [C:c,D:(c > refine440942639nres_c)]: (D @ C))) @ (relAPP998488211nres_c @ (relAPP1155943915nres_c @ fun_re418666087nres_c @ A) @ (relAPP1774615993nres_c @ (relAPP483050597nres_c @ fun_re1877185935nres_c @ (relAPP2018433511nres_c @ (relAPP173519167nres_c @ fun_re766812315nres_c @ A) @ B)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])).
36.43/11.22	thf(65,axiom,((! [A:((a > refine432681134nres_b) > refine432681134nres_b),B:((c > refine449204144nres_d) > refine449204144nres_d),C:set_Pr797615136nres_d,D:(((c > refine449204144nres_d) > refine449204144nres_d) > $o)]: (((refine1958703523nres_d @ C @ D @ A) <= (D @ B)) <= (member461830657nres_d @ (produc2075136412nres_d @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_lift__assnI)).
36.43/11.22	thf(2922,plain,((! [A:((a > refine432681134nres_b) > refine432681134nres_b),B:((c > refine449204144nres_d) > refine449204144nres_d),C:set_Pr797615136nres_d,D:(((c > refine449204144nres_d) > refine449204144nres_d) > $o)]: ((refine1958703523nres_d @ C @ (D) @ (A)) | ~ (D @ (B)) | ~ (member461830657nres_d @ (produc2075136412nres_d @ (A) @ (B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])).
36.43/11.22	thf(205,plain,((~ ((((~)) = (^ [A:$o]: (A))) => (~ ((^ [A:$o]: (A)) = (^ [A:$o]: (A))))) | ~ ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(206,plain,(((((~)) = (^ [A:$o]: (A))) | ~ ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))))),inference(simp,[status(thm)],[205])).
36.43/11.22	thf(626,plain,((((~)) = (^ [A:$o]: (A))) | (~ ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))))),inference(cnf,[status(esa)],[206])).
36.43/11.22	thf(1205,plain,((((~)) = (^ [A:$o]: (A))) | ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))))),inference(lifteq,[status(thm)],[626])).
36.43/11.22	thf(1206,plain,(((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))))),inference(simp,[status(thm)],[1205])).
36.43/11.22	thf(138,axiom,((! [A:((a > refine432681134nres_b) > refine432681134nres_b),B:((c > refine449204144nres_d) > refine449204144nres_d),C:set_Pr589481214nres_d,D:set_Pr1640496404nres_d,E:(c > refine449204144nres_d),F:refine449204144nres_d]: (((! [G:(a > refine432681134nres_b)]: ((member1578111221nres_d @ (produc2147164944nres_d @ (A @ G) @ F) @ D) <= (member936907743nres_d @ (produc210841666nres_d @ G @ E) @ C))) <= ((B @ E) = F)) <= (member461830657nres_d @ (produc2075136412nres_d @ A @ B) @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_fun__relD2)).
36.43/11.22	thf(3186,plain,((! [A:((a > refine432681134nres_b) > refine432681134nres_b),B:((c > refine449204144nres_d) > refine449204144nres_d),C:set_Pr589481214nres_d,D:set_Pr1640496404nres_d,E:(c > refine449204144nres_d),F:refine449204144nres_d]: (! [G:(a > refine432681134nres_b)]: ((member1578111221nres_d @ (produc2147164944nres_d @ (A @ (G)) @ F) @ D) | ~ (member936907743nres_d @ (produc210841666nres_d @ (G) @ (E)) @ C)) | ~ ((B @ (E)) = F) | ~ (member461830657nres_d @ (produc2075136412nres_d @ (A) @ (B)) @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])).
36.43/11.22	thf(441,plain,((~ ((((~)) = (^ [A:$o]: (($false)))) => (~ ((^ [A:$o]: (A)) = (^ [A:$o]: (($true)))))) | ~ ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (($true))))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(809,plain,(((^ [A:$o]: (A)) = (^ [A:$o]: (($true)))) | (~ ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (($true))))))),inference(cnf,[status(esa)],[441])).
36.43/11.22	thf(910,plain,(((^ [A:$o]: (A)) = (^ [A:$o]: (($true)))) | ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (($true)))))),inference(lifteq,[status(thm)],[809])).
36.43/11.22	thf(482,plain,((~ (((^ [A:$o]: (A)) = ((~))) => (~ ((^ [A:$o]: (($false))) = ((~))))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))) = (product_Pair_o_o_o_o @ ((~)) @ ((~)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(829,plain,(((^ [A:$o]: (A)) = ((~))) | (~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))) = (product_Pair_o_o_o_o @ ((~)) @ ((~)))))),inference(cnf,[status(esa)],[482])).
36.43/11.22	thf(951,plain,((((~)) = (^ [A:$o]: (A))) | ((product_Pair_o_o_o_o @ ((~)) @ ((~))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))))),inference(lifteq,[status(thm)],[829])).
36.43/11.22	thf(952,plain,(((product_Pair_o_o_o_o @ ((~)) @ ((~))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))))),inference(simp,[status(thm)],[951])).
36.43/11.22	thf(153,axiom,((! [A:set_Product_prod_c_a,B:set_Product_prod_d_b]: (member2039405057nres_b @ (produc183923940nres_b @ refine2092371655nd_c_d @ refine436832839nd_a_b) @ (relAPP1077394663nres_b @ (relAPP1747515631nres_b @ fun_re650017687nres_b @ (relAPP35306343nres_a @ refine245117724el_c_a @ A)) @ (relAPP1033339257nres_b @ (relAPP38185259nres_b @ fun_re1925572817nres_b @ (relAPP1977623725nres_b @ (relAPP774904585nres_b @ fun_re492134875nres_b @ A) @ (relAPP821124455nres_b @ refine1072887132el_d_b @ B))) @ (relAPP821124455nres_b @ refine1072887132el_d_b @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_param__bind)).
36.43/11.22	thf(3233,plain,((! [A:set_Product_prod_c_a,B:set_Product_prod_d_b]: (member2039405057nres_b @ (produc183923940nres_b @ (refine2092371655nd_c_d) @ (refine436832839nd_a_b)) @ (relAPP1077394663nres_b @ (relAPP1747515631nres_b @ fun_re650017687nres_b @ (relAPP35306343nres_a @ refine245117724el_c_a @ A)) @ (relAPP1033339257nres_b @ (relAPP38185259nres_b @ fun_re1925572817nres_b @ (relAPP1977623725nres_b @ (relAPP774904585nres_b @ fun_re492134875nres_b @ A) @ (relAPP821124455nres_b @ refine1072887132el_d_b @ B))) @ (relAPP821124455nres_b @ (refine1072887132el_d_b) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])).
36.43/11.22	thf(2986,plain,(((refine1958703523nres_d) = (^ [A:set_Pr797615136nres_d,B:(((c > refine449204144nres_d) > refine449204144nres_d) > $o),C:((a > refine432681134nres_b) > refine432681134nres_b)]: ? [D:((c > refine449204144nres_d) > refine449204144nres_d)]: ((B @ D) & (member461830657nres_d @ (produc2075136412nres_d @ C @ D) @ A))))),inference(lifteq,[status(thm)],[2985])).
36.43/11.22	thf(134,axiom,((! [A:set_Pr589481214nres_d,B:set_Pr1640496404nres_d]: (member660096835nres_d @ (produc1910095910nres_d @ (^ [C:(a > refine432681134nres_b),D:((a > refine432681134nres_b) > refine432681134nres_b)]: (D @ C)) @ (^ [C:(c > refine449204144nres_d),D:((c > refine449204144nres_d) > refine449204144nres_d)]: (D @ C))) @ (relAPP1388319497nres_d @ (relAPP1716516381nres_d @ fun_re1306413669nres_d @ A) @ (relAPP1552964229nres_d @ (relAPP1953591565nres_d @ fun_re2071856555nres_d @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ A) @ B)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_autoref__Let)).
36.43/11.22	thf(3166,plain,((! [A:set_Pr589481214nres_d,B:set_Pr1640496404nres_d]: (member660096835nres_d @ (produc1910095910nres_d @ (^ [C:(a > refine432681134nres_b),D:((a > refine432681134nres_b) > refine432681134nres_b)]: (D @ C)) @ (^ [C:(c > refine449204144nres_d),D:((c > refine449204144nres_d) > refine449204144nres_d)]: (D @ C))) @ (relAPP1388319497nres_d @ (relAPP1716516381nres_d @ fun_re1306413669nres_d @ A) @ (relAPP1552964229nres_d @ (relAPP1953591565nres_d @ fun_re2071856555nres_d @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ A) @ B)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])).
36.43/11.22	thf(139,axiom,((! [A:set_Product_prod_a_a,B:set_Product_prod_b_b]: (member1700179713nres_b @ (produc1992182244nres_b @ refine436832839nd_a_b @ refine436832839nd_a_b) @ (relAPP869047273nres_b @ (relAPP1111247343nres_b @ fun_re2045802267nres_b @ (relAPP1642956907nres_a @ refine737062558el_a_a @ A)) @ (relAPP2095637113nres_b @ (relAPP1293188647nres_b @ fun_re1579405647nres_b @ (relAPP1936960811nres_b @ (relAPP1536875909nres_b @ fun_re1837693787nres_b @ A) @ (relAPP281291371nres_b @ refine1564831966el_b_b @ B))) @ (relAPP281291371nres_b @ refine1564831966el_b_b @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_param__bind)).
36.43/11.22	thf(3191,plain,((! [A:set_Product_prod_a_a,B:set_Product_prod_b_b]: (member1700179713nres_b @ (produc1992182244nres_b @ (refine436832839nd_a_b) @ (refine436832839nd_a_b)) @ (relAPP869047273nres_b @ (relAPP1111247343nres_b @ fun_re2045802267nres_b @ (relAPP1642956907nres_a @ refine737062558el_a_a @ A)) @ (relAPP2095637113nres_b @ (relAPP1293188647nres_b @ fun_re1579405647nres_b @ (relAPP1936960811nres_b @ (relAPP1536875909nres_b @ fun_re1837693787nres_b @ A) @ (relAPP281291371nres_b @ refine1564831966el_b_b @ B))) @ (relAPP281291371nres_b @ (refine1564831966el_b_b) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])).
36.43/11.22	thf(142,axiom,((! [A:(a > refine432681134nres_b),B:(c > refine449204144nres_d),C:set_Product_prod_a_c,D:set_Pr1640496404nres_d,E:a,F:c]: ((member936907743nres_d @ (produc210841666nres_d @ A @ B) @ (relAPP900772393nres_d @ (relAPP1270454529nres_d @ fun_re1760530651nres_d @ C) @ D)) => ((member466432594od_a_c @ (product_Pair_a_c @ E @ F) @ C) => (member1578111221nres_d @ (produc2147164944nres_d @ (A @ E) @ (B @ F)) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_tagged__fun__relD__both)).
36.43/11.22	thf(3198,plain,((! [A:(a > refine432681134nres_b),B:(c > refine449204144nres_d),C:set_Product_prod_a_c,D:set_Pr1640496404nres_d,E:a,F:c]: ((member936907743nres_d @ (produc210841666nres_d @ (A) @ (B)) @ (relAPP900772393nres_d @ (relAPP1270454529nres_d @ fun_re1760530651nres_d @ C) @ D)) => ((member466432594od_a_c @ (product_Pair_a_c @ E @ F) @ C) => (member1578111221nres_d @ (produc2147164944nres_d @ (A @ E) @ (B @ F)) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])).
36.43/11.22	thf(90,axiom,((! [A:(produc1757587562nres_d > $o),B:produc1757587562nres_d]: ((! [C:((a > refine432681134nres_b) > refine432681134nres_b),D:((c > refine449204144nres_d) > refine449204144nres_d)]: (A @ (produc2075136412nres_d @ C @ D))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_prod__cases)).
36.43/11.22	thf(3033,plain,((! [A:(produc1757587562nres_d > $o),B:produc1757587562nres_d]: ((! [C:((a > refine432681134nres_b) > refine432681134nres_b),D:((c > refine449204144nres_d) > refine449204144nres_d)]: (A @ (produc2075136412nres_d @ (C) @ (D)))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])).
36.43/11.22	thf(41,axiom,((! [A:a,B:c,C:a,D:c]: (((product_Pair_a_c @ A @ B) = (product_Pair_a_c @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_prod_Oinject)).
36.43/11.22	thf(2769,plain,((! [A:a,B:c,C:a,D:c]: (((product_Pair_a_c @ A @ B) = (product_Pair_a_c @ C @ D)) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])).
36.43/11.22	thf(72,axiom,((! [A:produc1677145714nres_d]: ~ (! [B:(a > ((a > refine432681134nres_b) > refine432681134nres_b)),C:(c > ((c > refine449204144nres_d) > refine449204144nres_d))]: (A != (produc627868012nres_d @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_old_Oprod_Oexhaust)).
36.43/11.22	thf(2946,plain,((! [A:produc1677145714nres_d]: ~ (! [B:(a > ((a > refine432681134nres_b) > refine432681134nres_b)),C:(c > ((c > refine449204144nres_d) > refine449204144nres_d))]: ~ (A = (produc627868012nres_d @ (B) @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])).
36.43/11.22	thf(51,axiom,((! [A:refine432681134nres_b]: ((refine1264602246nd_b_b @ A @ refine2063221605TURN_b) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_nres__monad2)).
36.43/11.22	thf(2801,plain,((! [A:refine432681134nres_b]: ((refine1264602246nd_b_b @ A @ (refine2063221605TURN_b)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])).
36.43/11.22	thf(3,axiom,((! [A:product_prod_o_o_o_o]: ? [B:($o > $o),C:($o > $o)]: (A = (product_Pair_o_o_o_o @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_surj__pair)).
36.43/11.22	thf(156,plain,((! [A:product_prod_o_o_o_o]: ? [B:($o > $o),C:($o > $o)]: (A = (product_Pair_o_o_o_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
36.43/11.22	thf(78,axiom,((! [A:$o,B:$o,C:refine440942639nres_c,D:refine440942639nres_c,E:set_Product_prod_c_c]: (((member1424003763nres_c @ (produc976876622nres_c @ (refine1437029929_bnd_c @ B @ C) @ (refine1437029929_bnd_c @ A @ D)) @ (relAPP1067109483nres_c @ refine245117726el_c_c @ E)) <= (((B) => (member1424003763nres_c @ (produc976876622nres_c @ C @ D) @ (relAPP1067109483nres_c @ refine245117726el_c_c @ E))) <= (A))) <= ((A) => (B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_param__op__nres__ASSERT__bnd)).
36.43/11.22	thf(2973,plain,((! [A:$o,B:$o,C:refine440942639nres_c,D:refine440942639nres_c,E:set_Product_prod_c_c]: ((member1424003763nres_c @ (produc976876622nres_c @ (refine1437029929_bnd_c @ B @ C) @ (refine1437029929_bnd_c @ A @ D)) @ (relAPP1067109483nres_c @ (refine245117726el_c_c) @ E)) | ~ (((B) => (member1424003763nres_c @ (produc976876622nres_c @ C @ D) @ (relAPP1067109483nres_c @ (refine245117726el_c_c) @ E))) | ~ (A)) | ~ ((A) => (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])).
36.43/11.22	thf(146,axiom,((relAPP1313094511nres_d = (^ [A:(set_Product_prod_b_d > set_Pr1640496404nres_d)]: (A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_relAPP__def)).
36.43/11.22	thf(3218,plain,(((relAPP1313094511nres_d) = (^ [A:(set_Product_prod_b_d > set_Pr1640496404nres_d)]: (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])).
36.43/11.22	thf(29,axiom,((! [A:set_Product_prod_b_d,B:set_Pr1128439124nres_c]: (member228973321nres_c @ (produc1961734380nres_c @ (^ [C:b,D:(b > refine424419629nres_a)]: (D @ C)) @ (^ [C:d,D:(d > refine440942639nres_c)]: (D @ C))) @ (relAPP131141393nres_c @ (relAPP2017502121nres_c @ fun_re430551721nres_c @ A) @ (relAPP489595641nres_c @ (relAPP1790450405nres_c @ fun_re1366722255nres_c @ (relAPP1564590053nres_c @ (relAPP709871101nres_c @ fun_re1209216603nres_c @ A) @ B)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_autoref__Let)).
36.43/11.22	thf(2726,plain,((! [A:set_Product_prod_b_d,B:set_Pr1128439124nres_c]: (member228973321nres_c @ (produc1961734380nres_c @ (^ [C:b,D:(b > refine424419629nres_a)]: (D @ C)) @ (^ [C:d,D:(d > refine440942639nres_c)]: (D @ C))) @ (relAPP131141393nres_c @ (relAPP2017502121nres_c @ fun_re430551721nres_c @ A) @ (relAPP489595641nres_c @ (relAPP1790450405nres_c @ fun_re1366722255nres_c @ (relAPP1564590053nres_c @ (relAPP709871101nres_c @ fun_re1209216603nres_c @ A) @ B)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])).
36.43/11.22	thf(104,axiom,((! [A:(product_prod_a_c > $o),B:product_prod_a_c]: ((A @ B) <= (! [C:a,D:c]: (A @ (product_Pair_a_c @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_prod__cases)).
36.43/11.22	thf(3078,plain,((! [A:(product_prod_a_c > $o),B:product_prod_a_c]: ((A @ B) | ~ (! [C:a,D:c]: (A @ (product_Pair_a_c @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])).
36.43/11.22	thf(117,axiom,((! [A:(a > refine432681134nres_b),B:(c > refine449204144nres_d),C:set_Product_prod_a_c,D:set_Pr1640496404nres_d,E:c,F:refine449204144nres_d]: ((member936907743nres_d @ (produc210841666nres_d @ A @ B) @ (relAPP900772393nres_d @ (relAPP1270454529nres_d @ fun_re1760530651nres_d @ C) @ D)) => (((B @ E) = F) => (! [G:a]: ((member466432594od_a_c @ (product_Pair_a_c @ G @ E) @ C) => (member1578111221nres_d @ (produc2147164944nres_d @ (A @ G) @ F) @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_fun__relD2)).
36.43/11.22	thf(3119,plain,((! [A:(a > refine432681134nres_b),B:(c > refine449204144nres_d),C:set_Product_prod_a_c,D:set_Pr1640496404nres_d,E:c,F:refine449204144nres_d]: ((member936907743nres_d @ (produc210841666nres_d @ (A) @ (B)) @ (relAPP900772393nres_d @ (relAPP1270454529nres_d @ fun_re1760530651nres_d @ C) @ D)) => (((B @ E) = F) => (! [G:a]: ((member466432594od_a_c @ (product_Pair_a_c @ G @ E) @ C) => (member1578111221nres_d @ (produc2147164944nres_d @ (A @ G) @ F) @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])).
36.43/11.22	thf(107,axiom,((! [A:set_Product_prod_b_d,B:set_Pr1640496404nres_d]: (member2139143049nres_d @ (produc765243756nres_d @ (^ [C:b,D:(b > refine432681134nres_b)]: (D @ C)) @ (^ [C:d,D:(d > refine449204144nres_d)]: (D @ C))) @ (relAPP486948753nres_d @ (relAPP1996600361nres_d @ fun_re1101734569nres_d @ A) @ (relAPP1676317369nres_d @ (relAPP1405476647nres_d @ fun_re884113425nres_d @ (relAPP446928935nres_d @ (relAPP1806806463nres_d @ fun_re55451291nres_d @ A) @ B)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_autoref__Let)).
36.43/11.22	thf(3087,plain,((! [A:set_Product_prod_b_d,B:set_Pr1640496404nres_d]: (member2139143049nres_d @ (produc765243756nres_d @ (^ [C:b,D:(b > refine432681134nres_b)]: (D @ C)) @ (^ [C:d,D:(d > refine449204144nres_d)]: (D @ C))) @ (relAPP486948753nres_d @ (relAPP1996600361nres_d @ fun_re1101734569nres_d @ A) @ (relAPP1676317369nres_d @ (relAPP1405476647nres_d @ fun_re884113425nres_d @ (relAPP446928935nres_d @ (relAPP1806806463nres_d @ fun_re55451291nres_d @ A) @ B)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])).
36.43/11.22	thf(88,axiom,((! [A:(a > refine432681134nres_b),B:(c > refine449204144nres_d),C:set_Pr589481214nres_d,D:((c > refine449204144nres_d) > $o)]: ((member936907743nres_d @ (produc210841666nres_d @ A @ B) @ C) => ((D @ B) => (refine746536475nres_d @ C @ D @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_lift__assnI)).
36.43/11.22	thf(3018,plain,((! [A:(a > refine432681134nres_b),B:(c > refine449204144nres_d),C:set_Pr589481214nres_d,D:((c > refine449204144nres_d) > $o)]: ((member936907743nres_d @ (produc210841666nres_d @ (A) @ (B)) @ C) => ((D @ (B)) => (refine746536475nres_d @ C @ (D) @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])).
36.43/11.22	thf(15,axiom,((! [A:produc809931564nres_d,B:(produc809931564nres_d > $o)]: ((member660096835nres_d @ A @ (collec1321668993nres_d @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_mem__Collect__eq)).
36.43/11.22	thf(2666,plain,((! [A:produc809931564nres_d,B:(produc809931564nres_d > $o)]: ((member660096835nres_d @ A @ (collec1321668993nres_d @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])).
36.43/11.22	thf(420,plain,((~ ((((~)) = (^ [A:$o]: (A))) => (~ (((~)) = (^ [A:$o]: (A))))) | ~ ((product_Pair_o_o_o_o @ ((~)) @ ((~))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(693,plain,((((~)) = (^ [A:$o]: (A))) | (~ ((product_Pair_o_o_o_o @ ((~)) @ ((~))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))))),inference(cnf,[status(esa)],[420])).
36.43/11.22	thf(1038,plain,((((~)) = (^ [A:$o]: (A))) | ((product_Pair_o_o_o_o @ ((~)) @ ((~))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))))),inference(lifteq,[status(thm)],[693])).
36.43/11.22	thf(1039,plain,(((product_Pair_o_o_o_o @ ((~)) @ ((~))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))))),inference(simp,[status(thm)],[1038])).
36.43/11.22	thf(367,plain,((~ (((^ [A:$o]: (A)) = (^ [A:$o]: (A))) => (~ ((^ [A:$o]: (($false))) = (^ [A:$o]: (($true)))))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true))))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(368,plain,((((^ [A:$o]: (($false))) = (^ [A:$o]: (($true)))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true))))))),inference(simp,[status(thm)],[367])).
36.43/11.22	thf(826,plain,(((^ [A:$o]: (($false))) = (^ [A:$o]: (($true)))) | (~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true))))))),inference(cnf,[status(esa)],[368])).
36.43/11.22	thf(1154,plain,(((^ [A:$o]: (($false))) = (^ [A:$o]: (($true)))) | ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true)))))),inference(lifteq,[status(thm)],[826])).
36.43/11.22	thf(1155,plain,(((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true)))))),inference(simp,[status(thm)],[1154])).
36.43/11.22	thf(45,axiom,((! [A:((a > refine432681134nres_b) > refine432681134nres_b),B:((c > refine449204144nres_d) > refine449204144nres_d),C:((a > refine432681134nres_b) > refine432681134nres_b),D:((c > refine449204144nres_d) > refine449204144nres_d)]: ((~ ((B != D) <= (A = C))) <= ((produc2075136412nres_d @ A @ B) = (produc2075136412nres_d @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_Pair__inject)).
36.43/11.22	thf(2781,plain,((! [A:((a > refine432681134nres_b) > refine432681134nres_b),B:((c > refine449204144nres_d) > refine449204144nres_d),C:((a > refine432681134nres_b) > refine432681134nres_b),D:((c > refine449204144nres_d) > refine449204144nres_d)]: (~ (~ ((B) = (D)) | ~ ((A) = (C))) | ~ ((produc2075136412nres_d @ (A) @ (B)) = (produc2075136412nres_d @ (C) @ (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])).
36.43/11.22	thf(234,plain,((~ ((((~)) = (^ [A:$o]: (A))) => (~ ((^ [A:$o]: (A)) = (^ [A:$o]: (($true)))))) | ~ ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true))))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(545,plain,((((~)) = (^ [A:$o]: (A))) | (~ ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true))))))),inference(cnf,[status(esa)],[234])).
36.43/11.22	thf(1149,plain,((((~)) = (^ [A:$o]: (A))) | ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true)))))),inference(lifteq,[status(thm)],[545])).
36.43/11.22	thf(1150,plain,(((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true)))))),inference(simp,[status(thm)],[1149])).
36.43/11.22	thf(119,axiom,((! [A:set_Product_prod_b_d,B:set_Product_prod_a_c]: (member1715717121nres_c @ (produc385572580nres_c @ refine1264602245nd_b_a @ refine772657413nd_d_c) @ (relAPP944912869nres_c @ (relAPP492592111nres_c @ fun_re816936095nres_c @ (relAPP1313094511nres_d @ refine1564831968el_b_d @ A)) @ (relAPP489595641nres_c @ (relAPP1790450405nres_c @ fun_re1366722255nres_c @ (relAPP1564590053nres_c @ (relAPP709871101nres_c @ fun_re1209216603nres_c @ A) @ (relAPP527276399nres_c @ refine737062560el_a_c @ B))) @ (relAPP527276399nres_c @ refine737062560el_a_c @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_param__bind)).
36.43/11.22	thf(3126,plain,((! [A:set_Product_prod_b_d,B:set_Product_prod_a_c]: (member1715717121nres_c @ (produc385572580nres_c @ (refine1264602245nd_b_a) @ (refine772657413nd_d_c)) @ (relAPP944912869nres_c @ (relAPP492592111nres_c @ fun_re816936095nres_c @ (relAPP1313094511nres_d @ refine1564831968el_b_d @ A)) @ (relAPP489595641nres_c @ (relAPP1790450405nres_c @ fun_re1366722255nres_c @ (relAPP1564590053nres_c @ (relAPP709871101nres_c @ fun_re1209216603nres_c @ A) @ (relAPP527276399nres_c @ refine737062560el_a_c @ B))) @ (relAPP527276399nres_c @ (refine737062560el_a_c) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])).
36.43/11.22	thf(62,axiom,((! [A:set_Product_prod_c_c]: (member885256801nres_c @ (produc465280580nres_c @ refine2063221606TURN_c @ refine2063221606TURN_c) @ (relAPP2059096425nres_c @ (relAPP1559031491nres_c @ fun_re1568737051nres_c @ A) @ (relAPP1067109483nres_c @ refine245117726el_c_c @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_autoref__RETURN)).
36.43/11.22	thf(2836,plain,((! [A:set_Product_prod_c_c]: (member885256801nres_c @ (produc465280580nres_c @ (refine2063221606TURN_c) @ (refine2063221606TURN_c)) @ (relAPP2059096425nres_c @ (relAPP1559031491nres_c @ fun_re1568737051nres_c @ A) @ (relAPP1067109483nres_c @ (refine245117726el_c_c) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])).
36.43/11.22	thf(148,axiom,((! [A:set_Pr1128439124nres_c,B:set_Pr797615136nres_d]: (member508530605nres_d @ (produc912866704nres_d @ (^ [C:refine424419629nres_a,D:(refine424419629nres_a > ((a > refine432681134nres_b) > refine432681134nres_b))]: (D @ C)) @ (^ [C:refine440942639nres_c,D:(refine440942639nres_c > ((c > refine449204144nres_d) > refine449204144nres_d))]: (D @ C))) @ (relAPP1095654971nres_d @ (relAPP422583323nres_d @ fun_re1190106143nres_d @ A) @ (relAPP1659518317nres_d @ (relAPP759382665nres_d @ fun_re692194867nres_d @ (relAPP511982311nres_d @ (relAPP1396672239nres_d @ fun_re439246495nres_d @ A) @ B)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_autoref__Let)).
36.43/11.22	thf(3222,plain,((! [A:set_Pr1128439124nres_c,B:set_Pr797615136nres_d]: (member508530605nres_d @ (produc912866704nres_d @ (^ [C:refine424419629nres_a,D:(refine424419629nres_a > ((a > refine432681134nres_b) > refine432681134nres_b))]: (D @ C)) @ (^ [C:refine440942639nres_c,D:(refine440942639nres_c > ((c > refine449204144nres_d) > refine449204144nres_d))]: (D @ C))) @ (relAPP1095654971nres_d @ (relAPP422583323nres_d @ fun_re1190106143nres_d @ A) @ (relAPP1659518317nres_d @ (relAPP759382665nres_d @ fun_re692194867nres_d @ (relAPP511982311nres_d @ (relAPP1396672239nres_d @ fun_re439246495nres_d @ A) @ B)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])).
36.43/11.22	thf(55,axiom,((! [A:a,B:(a > refine424419629nres_a)]: ((refine436832838nd_a_a @ (refine2063221604TURN_a @ A) @ B) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_nres__monad1)).
36.43/11.22	thf(2813,plain,((! [A:a,B:(a > refine424419629nres_a)]: ((refine436832838nd_a_a @ (refine2063221604TURN_a @ A) @ (B)) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])).
36.43/11.22	thf(40,axiom,((! [A:produc2103861704nres_d]: ? [B:(a > refine432681134nres_b),C:(c > refine449204144nres_d)]: (A = (produc210841666nres_d @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_surj__pair)).
36.43/11.22	thf(2766,plain,((! [A:produc2103861704nres_d]: ? [B:(a > refine432681134nres_b),C:(c > refine449204144nres_d)]: (A = (produc210841666nres_d @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])).
36.43/11.22	thf(99,axiom,((! [A:((a > refine432681134nres_b) > refine432681134nres_b),B:((c > refine449204144nres_d) > refine449204144nres_d),C:((a > refine432681134nres_b) > refine432681134nres_b),D:((c > refine449204144nres_d) > refine449204144nres_d)]: (((produc2075136412nres_d @ A @ B) = (produc2075136412nres_d @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_old_Oprod_Oinject)).
36.43/11.22	thf(3064,plain,((! [A:((a > refine432681134nres_b) > refine432681134nres_b),B:((c > refine449204144nres_d) > refine449204144nres_d),C:((a > refine432681134nres_b) > refine432681134nres_b),D:((c > refine449204144nres_d) > refine449204144nres_d)]: (((produc2075136412nres_d @ (A) @ (B)) = (produc2075136412nres_d @ (C) @ (D))) = (((A) = (C)) & ((B) = (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])).
36.43/11.22	thf(143,axiom,((! [A:set_Product_prod_a_c,B:set_Product_prod_b_d]: (member65788417nres_d @ (produc1576596708nres_d @ refine436832839nd_a_b @ refine2092371655nd_c_d) @ (relAPP511982311nres_d @ (relAPP1396672239nres_d @ fun_re439246495nres_d @ (relAPP527276399nres_c @ refine737062560el_a_c @ A)) @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ (relAPP900772393nres_d @ (relAPP1270454529nres_d @ fun_re1760530651nres_d @ A) @ (relAPP1313094511nres_d @ refine1564831968el_b_d @ B))) @ (relAPP1313094511nres_d @ refine1564831968el_b_d @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_param__bind)).
36.43/11.22	thf(3201,plain,((! [A:set_Product_prod_a_c,B:set_Product_prod_b_d]: (member65788417nres_d @ (produc1576596708nres_d @ (refine436832839nd_a_b) @ (refine2092371655nd_c_d)) @ (relAPP511982311nres_d @ (relAPP1396672239nres_d @ fun_re439246495nres_d @ (relAPP527276399nres_c @ refine737062560el_a_c @ A)) @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ (relAPP900772393nres_d @ (relAPP1270454529nres_d @ fun_re1760530651nres_d @ A) @ (relAPP1313094511nres_d @ refine1564831968el_b_d @ B))) @ (relAPP1313094511nres_d @ (refine1564831968el_b_d) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])).
36.43/11.22	thf(115,axiom,((! [A:a,B:c,C:set_Product_prod_a_c,D:(a > refine432681134nres_b),E:(c > refine449204144nres_d),F:set_Pr1640496404nres_d]: ((member466432594od_a_c @ (product_Pair_a_c @ A @ B) @ C) => ((member1578111221nres_d @ (produc2147164944nres_d @ (D @ A) @ (autore1159379066nres_d @ (autore430131799nres_d @ (autore241567778nres_d @ (autore2004709357nres_d @ (^ [G:c,H:(c > refine449204144nres_d)]: (H @ G))) @ (autore349294361nres_d @ (relAPP1354295571nres_d @ (relAPP1135042155nres_d @ fun_re1089848935nres_d @ C) @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ (relAPP900772393nres_d @ (relAPP1270454529nres_d @ fun_re1760530651nres_d @ C) @ F)) @ F)))) @ B) @ E)) @ F) <= (! [G:c]: ((autore1113312320RNAL_o @ (B = G)) => (! [H:a]: ((member1578111221nres_d @ (produc2147164944nres_d @ (D @ H) @ (autore1981686764nres_d @ E @ G)) @ F) <= (member466432594od_a_c @ (product_Pair_a_c @ H @ G) @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_autoref__Let__cong)).
36.43/11.22	thf(3109,plain,((! [A:a,B:c,C:set_Product_prod_a_c,D:(a > refine432681134nres_b),E:(c > refine449204144nres_d),F:set_Pr1640496404nres_d]: ((member466432594od_a_c @ (product_Pair_a_c @ A @ B) @ C) => ((member1578111221nres_d @ (produc2147164944nres_d @ (D @ A) @ (autore1159379066nres_d @ (autore430131799nres_d @ (autore241567778nres_d @ (autore2004709357nres_d @ (^ [G:c,H:(c > refine449204144nres_d)]: (H @ G))) @ (autore349294361nres_d @ (relAPP1354295571nres_d @ (relAPP1135042155nres_d @ fun_re1089848935nres_d @ C) @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ (relAPP900772393nres_d @ (relAPP1270454529nres_d @ fun_re1760530651nres_d @ C) @ F)) @ F)))) @ B) @ (E))) @ F) | ~ (! [G:c]: ((autore1113312320RNAL_o @ (B = G)) => (! [H:a]: ((member1578111221nres_d @ (produc2147164944nres_d @ (D @ H) @ (autore1981686764nres_d @ (E) @ G)) @ F) | ~ (member466432594od_a_c @ (product_Pair_a_c @ H @ G) @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])).
36.43/11.22	thf(84,axiom,((! [A:(b > refine432681134nres_b),B:(d > refine449204144nres_d),C:set_Product_prod_b_d,D:set_Pr1640496404nres_d,E:b,F:d]: ((member776304031nres_d @ (produc847298946nres_d @ A @ B) @ (relAPP446928935nres_d @ (relAPP1806806463nres_d @ fun_re55451291nres_d @ C) @ D)) => ((member1578111221nres_d @ (produc2147164944nres_d @ (autore1677914089nres_b @ A @ E) @ (autore121452781nres_d @ B @ F)) @ D) <= (member1302463506od_b_d @ (product_Pair_b_d @ E @ F) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_autoref__APP)).
36.43/11.22	thf(3005,plain,((! [A:(b > refine432681134nres_b),B:(d > refine449204144nres_d),C:set_Product_prod_b_d,D:set_Pr1640496404nres_d,E:b,F:d]: ((member776304031nres_d @ (produc847298946nres_d @ (A) @ (B)) @ (relAPP446928935nres_d @ (relAPP1806806463nres_d @ fun_re55451291nres_d @ C) @ D)) => ((member1578111221nres_d @ (produc2147164944nres_d @ (autore1677914089nres_b @ (A) @ E) @ (autore121452781nres_d @ (B) @ F)) @ D) | ~ (member1302463506od_b_d @ (product_Pair_b_d @ E @ F) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])).
36.43/11.22	thf(46,axiom,((! [A:((a > refine432681134nres_b) > refine432681134nres_b),B:((c > refine449204144nres_d) > refine449204144nres_d),C:set_Pr797615136nres_d,D:((a > refine432681134nres_b) > refine432681134nres_b)]: ((member461830657nres_d @ (produc2075136412nres_d @ A @ B) @ C) => ((member461830657nres_d @ (produc2075136412nres_d @ D @ B) @ C) <= (autore1360171649nres_b @ A @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_autoref__REMOVE__INTERNAL__EQ)).
36.43/11.22	thf(2788,plain,((! [A:((a > refine432681134nres_b) > refine432681134nres_b),B:((c > refine449204144nres_d) > refine449204144nres_d),C:set_Pr797615136nres_d,D:((a > refine432681134nres_b) > refine432681134nres_b)]: ((member461830657nres_d @ (produc2075136412nres_d @ (A) @ (B)) @ C) => ((member461830657nres_d @ (produc2075136412nres_d @ (D) @ (B)) @ C) | ~ (autore1360171649nres_b @ (A) @ (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])).
36.43/11.22	thf(39,axiom,((! [A:b,B:d,C:set_Product_prod_b_d,D:(b > refine432681134nres_b),E:(d > refine449204144nres_d),F:set_Pr1640496404nres_d]: (((member1578111221nres_d @ (produc2147164944nres_d @ (D @ A) @ (autore38794169nres_d @ (autore48395543nres_d @ (autore1505592162nres_d @ (autore1121250093nres_d @ (^ [G:d,H:(d > refine449204144nres_d)]: (H @ G))) @ (autore486670105nres_d @ (relAPP486948753nres_d @ (relAPP1996600361nres_d @ fun_re1101734569nres_d @ C) @ (relAPP1676317369nres_d @ (relAPP1405476647nres_d @ fun_re884113425nres_d @ (relAPP446928935nres_d @ (relAPP1806806463nres_d @ fun_re55451291nres_d @ C) @ F)) @ F)))) @ B) @ E)) @ F) <= (! [G:d]: ((autore1113312320RNAL_o @ (B = G)) => (! [H:b]: ((member1302463506od_b_d @ (product_Pair_b_d @ H @ G) @ C) => (member1578111221nres_d @ (produc2147164944nres_d @ (D @ H) @ (autore121452781nres_d @ E @ G)) @ F)))))) <= (member1302463506od_b_d @ (product_Pair_b_d @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_autoref__Let__cong)).
36.43/11.22	thf(2761,plain,((! [A:b,B:d,C:set_Product_prod_b_d,D:(b > refine432681134nres_b),E:(d > refine449204144nres_d),F:set_Pr1640496404nres_d]: ((member1578111221nres_d @ (produc2147164944nres_d @ (D @ A) @ (autore38794169nres_d @ (autore48395543nres_d @ (autore1505592162nres_d @ (autore1121250093nres_d @ (^ [G:d,H:(d > refine449204144nres_d)]: (H @ G))) @ (autore486670105nres_d @ (relAPP486948753nres_d @ (relAPP1996600361nres_d @ fun_re1101734569nres_d @ C) @ (relAPP1676317369nres_d @ (relAPP1405476647nres_d @ fun_re884113425nres_d @ (relAPP446928935nres_d @ (relAPP1806806463nres_d @ fun_re55451291nres_d @ C) @ F)) @ F)))) @ B) @ (E))) @ F) | ~ (! [G:d]: ((autore1113312320RNAL_o @ (B = G)) => (! [H:b]: ((member1302463506od_b_d @ (product_Pair_b_d @ H @ G) @ C) => (member1578111221nres_d @ (produc2147164944nres_d @ (D @ H) @ (autore121452781nres_d @ (E) @ G)) @ F))))) | ~ (member1302463506od_b_d @ (product_Pair_b_d @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])).
36.43/11.22	thf(226,plain,((~ ((((~)) = (^ [A:$o]: (($true)))) => (~ (((~)) = ((~))))) | ~ ((product_Pair_o_o_o_o @ ((~)) @ ((~))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ ((~)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(227,plain,(((((~)) = (^ [A:$o]: (($true)))) | ~ ((product_Pair_o_o_o_o @ ((~)) @ ((~))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ ((~)))))),inference(simp,[status(thm)],[226])).
36.43/11.22	thf(909,plain,((((~)) = (^ [A:$o]: (($true)))) | (~ ((product_Pair_o_o_o_o @ ((~)) @ ((~))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ ((~)))))),inference(cnf,[status(esa)],[227])).
36.43/11.22	thf(921,plain,((((~)) = (^ [A:$o]: (($true)))) | ((product_Pair_o_o_o_o @ ((~)) @ ((~))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ ((~))))),inference(lifteq,[status(thm)],[909])).
36.43/11.22	thf(35,axiom,((! [A:(a > refine424419629nres_a),B:(c > refine440942639nres_c),C:set_Product_prod_a_c,D:set_Pr1128439124nres_c,E:a,F:c]: (((member466432594od_a_c @ (product_Pair_a_c @ E @ F) @ C) => (member1600573749nres_c @ (produc1153446608nres_c @ (autore1382402919nres_a @ A @ E) @ (autore1973425259nres_c @ B @ F)) @ D)) <= (member100096605nres_c @ (produc1827604032nres_c @ A @ B) @ (relAPP2018433511nres_c @ (relAPP173519167nres_c @ fun_re766812315nres_c @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_autoref__APP)).
36.43/11.22	thf(2748,plain,((! [A:(a > refine424419629nres_a),B:(c > refine440942639nres_c),C:set_Product_prod_a_c,D:set_Pr1128439124nres_c,E:a,F:c]: (((member466432594od_a_c @ (product_Pair_a_c @ E @ F) @ C) => (member1600573749nres_c @ (produc1153446608nres_c @ (autore1382402919nres_a @ (A) @ E) @ (autore1973425259nres_c @ (B) @ F)) @ D)) | ~ (member100096605nres_c @ (produc1827604032nres_c @ (A) @ (B)) @ (relAPP2018433511nres_c @ (relAPP173519167nres_c @ fun_re766812315nres_c @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])).
36.43/11.22	thf(48,axiom,((! [A:c,B:(c > refine440942639nres_c)]: ((refine2092371654nd_c_c @ (refine2063221606TURN_c @ A) @ B) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_nres__monad1)).
36.43/11.22	thf(2793,plain,((! [A:c,B:(c > refine440942639nres_c)]: ((refine2092371654nd_c_c @ (refine2063221606TURN_c @ A) @ (B)) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])).
36.43/11.22	thf(82,axiom,((! [A:(a > ((a > refine432681134nres_b) > refine432681134nres_b)),B:(c > ((c > refine449204144nres_d) > refine449204144nres_d)),C:(a > ((a > refine432681134nres_b) > refine432681134nres_b)),D:(c > ((c > refine449204144nres_d) > refine449204144nres_d))]: (((produc627868012nres_d @ A @ B) = (produc627868012nres_d @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_old_Oprod_Oinject)).
36.43/11.22	thf(2995,plain,((! [A:(a > ((a > refine432681134nres_b) > refine432681134nres_b)),B:(c > ((c > refine449204144nres_d) > refine449204144nres_d)),C:(a > ((a > refine432681134nres_b) > refine432681134nres_b)),D:(c > ((c > refine449204144nres_d) > refine449204144nres_d))]: (((produc627868012nres_d @ (A) @ (B)) = (produc627868012nres_d @ (C) @ (D))) = (((A) = (C)) & ((B) = (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])).
36.43/11.22	thf(13,axiom,((! [A:($o > $o),B:($o > $o),C:($o > $o),D:($o > $o)]: (((product_Pair_o_o_o_o @ A @ B) = (product_Pair_o_o_o_o @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_old_Oprod_Oinject)).
36.43/11.22	thf(2043,plain,((! [A:($o > $o),B:($o > $o),C:($o > $o),D:($o > $o)]: (((product_Pair_o_o_o_o @ (A) @ (B)) = (product_Pair_o_o_o_o @ (C) @ (D))) = (((B) = (D)) & ((A) = (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
36.43/11.22	thf(137,axiom,((! [A:((a > refine432681134nres_b) > refine432681134nres_b),B:((c > refine449204144nres_d) > refine449204144nres_d),C:set_Pr589481214nres_d,D:set_Pr1640496404nres_d,E:(a > refine432681134nres_b),F:(c > refine449204144nres_d)]: (((member1578111221nres_d @ (produc2147164944nres_d @ (A @ E) @ (B @ F)) @ D) <= (member936907743nres_d @ (produc210841666nres_d @ E @ F) @ C)) <= (member461830657nres_d @ (produc2075136412nres_d @ A @ B) @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_tagged__fun__relD__rhs)).
36.43/11.22	thf(3183,plain,((! [A:((a > refine432681134nres_b) > refine432681134nres_b),B:((c > refine449204144nres_d) > refine449204144nres_d),C:set_Pr589481214nres_d,D:set_Pr1640496404nres_d,E:(a > refine432681134nres_b),F:(c > refine449204144nres_d)]: ((member1578111221nres_d @ (produc2147164944nres_d @ (A @ (E)) @ (B @ (F))) @ D) | ~ (member936907743nres_d @ (produc210841666nres_d @ (E) @ (F)) @ C) | ~ (member461830657nres_d @ (produc2075136412nres_d @ (A) @ (B)) @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])).
36.43/11.22	thf(305,plain,((~ (((^ [A:$o]: (A)) = (^ [A:$o]: (($true)))) => (~ ((^ [A:$o]: (A)) = (^ [A:$o]: (A))))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (A)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(306,plain,((((^ [A:$o]: (A)) = (^ [A:$o]: (($true)))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (A)))))),inference(simp,[status(thm)],[305])).
36.43/11.22	thf(785,plain,(((^ [A:$o]: (A)) = (^ [A:$o]: (($true)))) | (~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (A)))))),inference(cnf,[status(esa)],[306])).
36.43/11.22	thf(965,plain,(((^ [A:$o]: (A)) = (^ [A:$o]: (($true)))) | ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (A))))),inference(lifteq,[status(thm)],[785])).
36.43/11.22	thf(121,axiom,((! [A:((a > refine432681134nres_b) > refine432681134nres_b),B:((c > refine449204144nres_d) > refine449204144nres_d),C:set_Pr589481214nres_d,D:set_Pr1640496404nres_d,E:(a > refine432681134nres_b),F:(c > refine449204144nres_d)]: (((member936907743nres_d @ (produc210841666nres_d @ E @ F) @ C) => (member1578111221nres_d @ (produc2147164944nres_d @ (A @ E) @ (B @ F)) @ D)) <= (member461830657nres_d @ (produc2075136412nres_d @ A @ B) @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_tagged__fun__relD__both)).
36.43/11.22	thf(3130,plain,((! [A:((a > refine432681134nres_b) > refine432681134nres_b),B:((c > refine449204144nres_d) > refine449204144nres_d),C:set_Pr589481214nres_d,D:set_Pr1640496404nres_d,E:(a > refine432681134nres_b),F:(c > refine449204144nres_d)]: (((member936907743nres_d @ (produc210841666nres_d @ (E) @ (F)) @ C) => (member1578111221nres_d @ (produc2147164944nres_d @ (A @ (E)) @ (B @ (F))) @ D)) | ~ (member461830657nres_d @ (produc2075136412nres_d @ (A) @ (B)) @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])).
36.43/11.22	thf(93,axiom,((! [A:(produc809931564nres_d > $o),B:produc809931564nres_d]: ((! [C:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)),D:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d))]: (A @ (produc1910095910nres_d @ C @ D))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_old_Oprod_Oinducts)).
36.43/11.22	thf(3042,plain,((! [A:(produc809931564nres_d > $o),B:produc809931564nres_d]: ((! [C:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)),D:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d))]: (A @ (produc1910095910nres_d @ (C) @ (D)))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])).
36.43/11.22	thf(26,axiom,((! [A:produc1757587562nres_d]: ? [B:((a > refine432681134nres_b) > refine432681134nres_b),C:((c > refine449204144nres_d) > refine449204144nres_d)]: (A = (produc2075136412nres_d @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_surj__pair)).
36.43/11.22	thf(2717,plain,((! [A:produc1757587562nres_d]: ? [B:((a > refine432681134nres_b) > refine432681134nres_b),C:((c > refine449204144nres_d) > refine449204144nres_d)]: (A = (produc2075136412nres_d @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])).
36.43/11.22	thf(70,axiom,((relAPP1536875909nres_b = (^ [A:(set_Product_prod_a_a > (set_Pr896671762nres_b > set_Pr1815766654nres_b))]: (A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_relAPP__def)).
36.43/11.22	thf(2941,plain,(((relAPP1536875909nres_b) = (^ [A:(set_Product_prod_a_a > (set_Pr896671762nres_b > set_Pr1815766654nres_b))]: (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])).
36.43/11.22	thf(101,axiom,((relAPP1642956907nres_a = (^ [A:(set_Product_prod_a_a > set_Pr384614482nres_a)]: (A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_relAPP__def)).
36.43/11.22	thf(3070,plain,(((relAPP1642956907nres_a) = (^ [A:(set_Product_prod_a_a > set_Pr384614482nres_a)]: (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])).
36.43/11.22	thf(77,axiom,((! [A:(a > ((a > refine432681134nres_b) > refine432681134nres_b)),B:(c > ((c > refine449204144nres_d) > refine449204144nres_d)),C:set_Pr2080238504nres_d,D:(a > ((a > refine432681134nres_b) > refine432681134nres_b))]: (((member189721481nres_d @ (produc627868012nres_d @ D @ B) @ C) <= (autore1318775848nres_b @ A @ D)) <= (member189721481nres_d @ (produc627868012nres_d @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_autoref__REMOVE__INTERNAL__EQ)).
36.43/11.22	thf(2970,plain,((! [A:(a > ((a > refine432681134nres_b) > refine432681134nres_b)),B:(c > ((c > refine449204144nres_d) > refine449204144nres_d)),C:set_Pr2080238504nres_d,D:(a > ((a > refine432681134nres_b) > refine432681134nres_b))]: ((member189721481nres_d @ (produc627868012nres_d @ (D) @ (B)) @ C) | ~ (autore1318775848nres_b @ (A) @ (D)) | ~ (member189721481nres_d @ (produc627868012nres_d @ (A) @ (B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])).
36.43/11.22	thf(47,axiom,((! [A:set_Product_prod_b_b]: (member209049375nres_b @ (produc1445585666nres_b @ refine2063221605TURN_b @ refine2063221605TURN_b) @ (relAPP1483117353nres_b @ (relAPP2073227843nres_b @ fun_re132614427nres_b @ A) @ (relAPP281291371nres_b @ refine1564831966el_b_b @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_autoref__RETURN)).
36.43/11.22	thf(2791,plain,((! [A:set_Product_prod_b_b]: (member209049375nres_b @ (produc1445585666nres_b @ (refine2063221605TURN_b) @ (refine2063221605TURN_b)) @ (relAPP1483117353nres_b @ (relAPP2073227843nres_b @ fun_re132614427nres_b @ A) @ (relAPP281291371nres_b @ (refine1564831966el_b_b) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])).
36.43/11.22	thf(105,axiom,((! [A:refine424419629nres_a]: ((refine436832838nd_a_a @ A @ refine2063221604TURN_a) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_nres__monad2)).
36.43/11.22	thf(3081,plain,((! [A:refine424419629nres_a]: ((refine436832838nd_a_a @ A @ (refine2063221604TURN_a)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])).
36.43/11.22	thf(17,axiom,((refine1711024813nres_d = (^ [A:set_Pr613277282nres_d,B:(((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d)) > $o),C:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b))]: ? [D:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d))]: ((member660096835nres_d @ (produc1910095910nres_d @ C @ D) @ A) & (B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_lift__assn__def)).
36.43/11.22	thf(2674,plain,(((refine1711024813nres_d) = (^ [A:set_Pr613277282nres_d,B:(((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d)) > $o),C:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b))]: ? [D:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d))]: ((member660096835nres_d @ (produc1910095910nres_d @ C @ D) @ A) & (B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])).
36.43/11.22	thf(60,axiom,((refine408412177nres_d = (^ [A:set_Pr2080238504nres_d,B:((c > ((c > refine449204144nres_d) > refine449204144nres_d)) > $o),C:(a > ((a > refine432681134nres_b) > refine432681134nres_b))]: ? [D:(c > ((c > refine449204144nres_d) > refine449204144nres_d))]: ((member189721481nres_d @ (produc627868012nres_d @ C @ D) @ A) & (B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_lift__assn__def)).
36.43/11.22	thf(2827,plain,(((refine408412177nres_d) = (^ [A:set_Pr2080238504nres_d,B:((c > ((c > refine449204144nres_d) > refine449204144nres_d)) > $o),C:(a > ((a > refine432681134nres_b) > refine432681134nres_b))]: ? [D:(c > ((c > refine449204144nres_d) > refine449204144nres_d))]: ((member189721481nres_d @ (produc627868012nres_d @ C @ D) @ A) & (B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])).
36.43/11.22	thf(96,axiom,((! [A:(a > ((a > refine432681134nres_b) > refine432681134nres_b)),B:(c > ((c > refine449204144nres_d) > refine449204144nres_d)),C:(a > ((a > refine432681134nres_b) > refine432681134nres_b)),D:(c > ((c > refine449204144nres_d) > refine449204144nres_d))]: ((~ ((B != D) <= (A = C))) <= ((produc627868012nres_d @ A @ B) = (produc627868012nres_d @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_Pair__inject)).
36.43/11.22	thf(3051,plain,((! [A:(a > ((a > refine432681134nres_b) > refine432681134nres_b)),B:(c > ((c > refine449204144nres_d) > refine449204144nres_d)),C:(a > ((a > refine432681134nres_b) > refine432681134nres_b)),D:(c > ((c > refine449204144nres_d) > refine449204144nres_d))]: (~ (~ ((B) = (D)) | ~ ((A) = (C))) | ~ ((produc627868012nres_d @ (A) @ (B)) = (produc627868012nres_d @ (C) @ (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])).
36.43/11.22	thf(290,plain,((~ (((^ [A:$o]: (($false))) = (^ [A:$o]: (($true)))) => (~ ((^ [A:$o]: (($false))) = (^ [A:$o]: (A))))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (($false)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (A)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(847,plain,(((^ [A:$o]: (($false))) = (^ [A:$o]: (($true)))) | (~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (($false)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (A)))))),inference(cnf,[status(esa)],[290])).
36.43/11.22	thf(1057,plain,(((^ [A:$o]: (($false))) = (^ [A:$o]: (($true)))) | ((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (($false)))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (A))))),inference(lifteq,[status(thm)],[847])).
36.43/11.22	thf(1058,plain,(((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (($false)))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (A))))),inference(simp,[status(thm)],[1057])).
36.43/11.22	thf(38,axiom,((! [A:set_Product_prod_a_a]: (member1680325597nres_a @ (produc278407104nres_a @ refine2063221604TURN_a @ refine2063221604TURN_a) @ (relAPP907138281nres_a @ (relAPP439940547nres_a @ fun_re843975451nres_a @ A) @ (relAPP1642956907nres_a @ refine737062558el_a_a @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_autoref__RETURN)).
36.43/11.22	thf(2759,plain,((! [A:set_Product_prod_a_a]: (member1680325597nres_a @ (produc278407104nres_a @ (refine2063221604TURN_a) @ (refine2063221604TURN_a)) @ (relAPP907138281nres_a @ (relAPP439940547nres_a @ fun_re843975451nres_a @ A) @ (relAPP1642956907nres_a @ (refine737062558el_a_a) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])).
36.43/11.22	thf(22,axiom,((relAPP281291371nres_b = (^ [A:(set_Product_prod_b_b > set_Pr896671762nres_b)]: (A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_relAPP__def)).
36.43/11.22	thf(2706,plain,(((relAPP281291371nres_b) = (^ [A:(set_Product_prod_b_b > set_Pr896671762nres_b)]: (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])).
36.43/11.22	thf(534,plain,((~ (((^ [A:$o]: (($false))) = (^ [A:$o]: (A))) => (~ (((~)) = (^ [A:$o]: (A))))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ ((~))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(645,plain,(((^ [A:$o]: (($false))) = (^ [A:$o]: (A))) | (~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ ((~))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))))),inference(cnf,[status(esa)],[534])).
36.43/11.22	thf(919,plain,(((^ [A:$o]: (($false))) = (^ [A:$o]: (A))) | ((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ ((~))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))))),inference(lifteq,[status(thm)],[645])).
36.43/11.22	thf(109,axiom,((relAPP173519167nres_c = (^ [A:(set_Product_prod_a_c > (set_Pr1128439124nres_c > set_Pr134917244nres_c))]: (A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_relAPP__def)).
36.43/11.22	thf(3091,plain,(((relAPP173519167nres_c) = (^ [A:(set_Product_prod_a_c > (set_Pr1128439124nres_c > set_Pr134917244nres_c))]: (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])).
36.43/11.22	thf(3518,plain,(((^ [A:$o]: (A)) != (^ [A:$o]: (($true)))) | ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))))),inference(paramod_ordered,[status(thm)],[3457,1155])).
36.43/11.22	thf(3601,plain,(((^ [A:$o]: (A)) != (^ [A:$o]: (($true)))) | ((^ [A:$o]: (A)) != (^ [A:$o]: (A))) | ((^ [A:$o]: (A)) != (^ [A:$o]: (($false))))),inference(simp,[status(thm)],[3518])).
36.43/11.22	thf(3719,plain,(((^ [A:$o]: (A)) != (^ [A:$o]: (($true)))) | ((^ [A:$o]: (A)) != (^ [A:$o]: (($false))))),inference(simp,[status(thm)],[3601])).
36.43/11.22	thf(4,axiom,((! [A:(a > refine432681134nres_b),B:(a > refine432681134nres_b),C:set_Pr896671762nres_b,D:refine432681134nres_b,E:a]: ((member369653087nres_b @ (produc809128386nres_b @ A @ B) @ (relAPP1936960811nres_b @ (relAPP1536875909nres_b @ fun_re1837693787nres_b @ id_a) @ C)) => ((D = (B @ E)) => (member1446466291nres_b @ (produc2130641934nres_b @ (A @ E) @ D) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_fun__relE1)).
36.43/11.22	thf(159,plain,((! [A:(a > refine432681134nres_b),B:(a > refine432681134nres_b),C:set_Pr896671762nres_b,D:refine432681134nres_b,E:a]: ((member369653087nres_b @ (produc809128386nres_b @ (A) @ (B)) @ (relAPP1936960811nres_b @ (relAPP1536875909nres_b @ fun_re1837693787nres_b @ id_a) @ C)) => ((D = (B @ E)) => (member1446466291nres_b @ (produc2130641934nres_b @ (A @ E) @ D) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
36.43/11.22	thf(19,axiom,((! [A:$o,B:$o,C:refine440942639nres_c,D:refine424419629nres_a,E:set_Product_prod_c_a]: (((member1292358833nres_a @ (produc960353612nres_a @ (refine1437029929_bnd_c @ B @ C) @ (refine1437029927_bnd_a @ A @ D)) @ (relAPP35306343nres_a @ refine245117724el_c_a @ E)) <= (((B) => (member1292358833nres_a @ (produc960353612nres_a @ C @ D) @ (relAPP35306343nres_a @ refine245117724el_c_a @ E))) <= (A))) <= ((A) => (B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_param__op__nres__ASSERT__bnd)).
36.43/11.22	thf(2679,plain,((! [A:$o,B:$o,C:refine440942639nres_c,D:refine424419629nres_a,E:set_Product_prod_c_a]: ((member1292358833nres_a @ (produc960353612nres_a @ (refine1437029929_bnd_c @ B @ C) @ (refine1437029927_bnd_a @ A @ D)) @ (relAPP35306343nres_a @ (refine245117724el_c_a) @ E)) | ~ (((B) => (member1292358833nres_a @ (produc960353612nres_a @ C @ D) @ (relAPP35306343nres_a @ (refine245117724el_c_a) @ E))) | ~ (A)) | ~ ((A) => (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])).
36.43/11.22	thf(129,axiom,((relAPP511982311nres_d = (^ [A:(set_Pr797615136nres_d > set_Pr24800800nres_d)]: (A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_relAPP__def)).
36.43/11.22	thf(3155,plain,(((relAPP511982311nres_d) = (^ [A:(set_Pr797615136nres_d > set_Pr24800800nres_d)]: (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])).
36.43/11.22	thf(80,axiom,((! [A:b,B:d,C:set_Product_prod_b_d,D:(b > refine424419629nres_a),E:(d > refine440942639nres_c),F:set_Pr1128439124nres_c]: (((member1600573749nres_c @ (produc1153446608nres_c @ (D @ A) @ (autore964129529nres_c @ (autore1989911767nres_c @ (autore73061154nres_c @ (autore1836202733nres_c @ (^ [G:d,H:(d > refine440942639nres_c)]: (H @ G))) @ (autore1683160729nres_c @ (relAPP131141393nres_c @ (relAPP2017502121nres_c @ fun_re430551721nres_c @ C) @ (relAPP489595641nres_c @ (relAPP1790450405nres_c @ fun_re1366722255nres_c @ (relAPP1564590053nres_c @ (relAPP709871101nres_c @ fun_re1209216603nres_c @ C) @ F)) @ F)))) @ B) @ E)) @ F) <= (! [G:d]: ((! [H:b]: ((member1302463506od_b_d @ (product_Pair_b_d @ H @ G) @ C) => (member1600573749nres_c @ (produc1153446608nres_c @ (D @ H) @ (autore113191276nres_c @ E @ G)) @ F))) <= (autore1113312320RNAL_o @ (B = G))))) <= (member1302463506od_b_d @ (product_Pair_b_d @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_autoref__Let__cong)).
36.43/11.22	thf(2987,plain,((! [A:b,B:d,C:set_Product_prod_b_d,D:(b > refine424419629nres_a),E:(d > refine440942639nres_c),F:set_Pr1128439124nres_c]: ((member1600573749nres_c @ (produc1153446608nres_c @ (D @ A) @ (autore964129529nres_c @ (autore1989911767nres_c @ (autore73061154nres_c @ (autore1836202733nres_c @ (^ [G:d,H:(d > refine440942639nres_c)]: (H @ G))) @ (autore1683160729nres_c @ (relAPP131141393nres_c @ (relAPP2017502121nres_c @ fun_re430551721nres_c @ C) @ (relAPP489595641nres_c @ (relAPP1790450405nres_c @ fun_re1366722255nres_c @ (relAPP1564590053nres_c @ (relAPP709871101nres_c @ fun_re1209216603nres_c @ C) @ F)) @ F)))) @ B) @ (E))) @ F) | ~ (! [G:d]: (! [H:b]: ((member1302463506od_b_d @ (product_Pair_b_d @ H @ G) @ C) => (member1600573749nres_c @ (produc1153446608nres_c @ (D @ H) @ (autore113191276nres_c @ (E) @ G)) @ F)) | ~ (autore1113312320RNAL_o @ (B = G)))) | ~ (member1302463506od_b_d @ (product_Pair_b_d @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])).
36.43/11.22	thf(16,axiom,((! [A:a,B:c,C:set_Product_prod_a_c,D:(a > a),E:(c > c),F:set_Product_prod_a_c]: ((member466432594od_a_c @ (product_Pair_a_c @ A @ B) @ C) => ((member466432594od_a_c @ (product_Pair_a_c @ (D @ A) @ (autoref_APP_c_c_c @ (autoref_APP_c_c_c_c @ (autore1422848225_c_c_c @ (autoref_OP_c_c_c_c @ (^ [G:c,H:(c > c)]: (H @ G))) @ (autore464253722_c_c_c @ (relAPP1804623572_c_c_c @ (relAPP1889825126_c_c_c @ fun_re836380558_c_c_c @ C) @ (relAPP1311785006_c_c_c @ (relAPP981449866_c_c_c @ fun_rel_a_a_c_c_a_c @ (relAPP237429680_a_c_c @ (relAPP887115074_a_c_c @ fun_rel_a_c_a_c @ C) @ F)) @ F)))) @ B) @ E)) @ F) <= (! [G:c]: ((! [H:a]: ((member466432594od_a_c @ (product_Pair_a_c @ H @ G) @ C) => (member466432594od_a_c @ (product_Pair_a_c @ (D @ H) @ (autoref_APP_c_c @ E @ G)) @ F))) <= (autore1113312320RNAL_o @ (B = G)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_autoref__Let__cong)).
36.43/11.22	thf(2669,plain,((! [A:a,B:c,C:set_Product_prod_a_c,D:(a > a),E:(c > c),F:set_Product_prod_a_c]: ((member466432594od_a_c @ (product_Pair_a_c @ A @ B) @ C) => ((member466432594od_a_c @ (product_Pair_a_c @ (D @ A) @ (autoref_APP_c_c_c @ (autoref_APP_c_c_c_c @ (autore1422848225_c_c_c @ (autoref_OP_c_c_c_c @ (^ [G:c,H:(c > c)]: (H @ G))) @ (autore464253722_c_c_c @ (relAPP1804623572_c_c_c @ (relAPP1889825126_c_c_c @ fun_re836380558_c_c_c @ C) @ (relAPP1311785006_c_c_c @ (relAPP981449866_c_c_c @ fun_rel_a_a_c_c_a_c @ (relAPP237429680_a_c_c @ (relAPP887115074_a_c_c @ fun_rel_a_c_a_c @ C) @ F)) @ F)))) @ B) @ (E))) @ F) | ~ (! [G:c]: (! [H:a]: ((member466432594od_a_c @ (product_Pair_a_c @ H @ G) @ C) => (member466432594od_a_c @ (product_Pair_a_c @ (D @ H) @ (autoref_APP_c_c @ (E) @ G)) @ F)) | ~ (autore1113312320RNAL_o @ (B = G)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])).
36.43/11.22	thf(71,axiom,((! [A:(a > refine432681134nres_b),B:(c > refine449204144nres_d),C:(a > refine432681134nres_b),D:(c > refine449204144nres_d)]: (((produc210841666nres_d @ A @ B) = (produc210841666nres_d @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_prod_Oinject)).
36.43/11.22	thf(2943,plain,((! [A:(a > refine432681134nres_b),B:(c > refine449204144nres_d),C:(a > refine432681134nres_b),D:(c > refine449204144nres_d)]: (((produc210841666nres_d @ (A) @ (B)) = (produc210841666nres_d @ (C) @ (D))) = (((B) = (D)) & ((A) = (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])).
36.43/11.22	thf(131,axiom,((relAPP1270454529nres_d = (^ [A:(set_Product_prod_a_c > (set_Pr1640496404nres_d > set_Pr589481214nres_d))]: (A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_relAPP__def)).
36.43/11.22	thf(3159,plain,(((relAPP1270454529nres_d) = (^ [A:(set_Product_prod_a_c > (set_Pr1640496404nres_d > set_Pr589481214nres_d))]: (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])).
36.43/11.22	thf(3160,plain,(((relAPP1270454529nres_d) = (^ [A:(set_Product_prod_a_c > (set_Pr1640496404nres_d > set_Pr589481214nres_d))]: (A)))),inference(lifteq,[status(thm)],[3159])).
36.43/11.22	thf(1750,plain,((((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ ((~))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))) = (((^ [A:$o]: (A)) = (^ [A:$o]: (A))) & (((~)) = (^ [A:$o]: (A)))))),inference(instance,[status(thm)],[1419])).
36.43/11.22	thf(1751,plain,((((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ ((~))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))) = (((~)) = (^ [A:$o]: (A))))),inference(simp,[status(thm)],[1750])).
36.43/11.22	thf(1877,plain,((((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ ((~))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))) = (((~)) = (^ [A:$o]: (A))))),inference(lifteq,[status(thm)],[1751])).
36.43/11.22	thf(332,plain,((~ (((^ [A:$o]: (($true))) = (^ [A:$o]: (($false)))) => (~ ((^ [A:$o]: (($false))) = (^ [A:$o]: (A))))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (($false)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(884,plain,(((^ [A:$o]: (($true))) = (^ [A:$o]: (($false)))) | (~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (($false)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A)))))),inference(cnf,[status(esa)],[332])).
36.43/11.22	thf(1079,plain,(((^ [A:$o]: (($false))) = (^ [A:$o]: (($true)))) | ((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (($false)))))),inference(lifteq,[status(thm)],[884])).
36.43/11.22	thf(1080,plain,(((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (($false)))))),inference(simp,[status(thm)],[1079])).
36.43/11.22	thf(33,axiom,((! [A:produc2103861704nres_d]: ~ (! [B:(a > refine432681134nres_b),C:(c > refine449204144nres_d)]: (A != (produc210841666nres_d @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_old_Oprod_Oexhaust)).
36.43/11.22	thf(2742,plain,((! [A:produc2103861704nres_d]: ~ (! [B:(a > refine432681134nres_b),C:(c > refine449204144nres_d)]: ~ (A = (produc210841666nres_d @ (B) @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])).
36.43/11.22	thf(122,axiom,((! [A:((a > refine432681134nres_b) > refine432681134nres_b),B:((c > refine449204144nres_d) > refine449204144nres_d),C:set_Pr589481214nres_d,D:set_Pr1640496404nres_d,E:(a > refine432681134nres_b),F:(c > refine449204144nres_d)]: ((member461830657nres_d @ (produc2075136412nres_d @ A @ B) @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ C) @ D)) => ((member936907743nres_d @ (produc210841666nres_d @ E @ F) @ C) => (member1578111221nres_d @ (produc2147164944nres_d @ (A @ E) @ (B @ F)) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_tagged__fun__relD__lhs)).
36.43/11.22	thf(3133,plain,((! [A:((a > refine432681134nres_b) > refine432681134nres_b),B:((c > refine449204144nres_d) > refine449204144nres_d),C:set_Pr589481214nres_d,D:set_Pr1640496404nres_d,E:(a > refine432681134nres_b),F:(c > refine449204144nres_d)]: ((member461830657nres_d @ (produc2075136412nres_d @ (A) @ (B)) @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ C) @ D)) => ((member936907743nres_d @ (produc210841666nres_d @ (E) @ (F)) @ C) => (member1578111221nres_d @ (produc2147164944nres_d @ (A @ (E)) @ (B @ (F))) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])).
36.43/11.22	thf(3486,plain,(((^ [A:$o]: (A)) != (^ [A:$o]: (($true)))) | ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ ((~))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true))))) | ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (A))))),inference(paramod_ordered,[status(thm)],[3457,1228])).
36.43/11.22	thf(3604,plain,(((^ [A:$o]: (A)) != (^ [A:$o]: (($true)))) | ((^ [A:$o]: (A)) != (^ [A:$o]: (A))) | (((~)) != (^ [A:$o]: (($true)))) | ((^ [A:$o]: (A)) != (^ [A:$o]: (($true)))) | ((^ [A:$o]: (A)) != (^ [A:$o]: (A)))),inference(simp,[status(thm)],[3486])).
36.43/11.22	thf(3722,plain,(((^ [A:$o]: (A)) != (^ [A:$o]: (($true)))) | (((~)) != (^ [A:$o]: (($true))))),inference(simp,[status(thm)],[3604])).
36.43/11.22	thf(4063,plain,(~ (sk112) | (~ (~ (sk113)))),inference(func_ext,[status(esa)],[3722])).
36.43/11.22	thf(4064,plain,(sk113 | ~ (sk112)),inference(cnf,[status(esa)],[4063])).
36.43/11.22	thf(1563,plain,((((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false))))) = (((^ [A:$o]: (A)) = (^ [A:$o]: (A))) & ((^ [A:$o]: (A)) = (^ [A:$o]: (($false))))))),inference(instance,[status(thm)],[1419])).
36.43/11.22	thf(1564,plain,((((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false))))) = ((^ [A:$o]: (A)) = (^ [A:$o]: (($false)))))),inference(simp,[status(thm)],[1563])).
36.43/11.22	thf(1862,plain,((((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false))))) = ((^ [A:$o]: (A)) = (^ [A:$o]: (($false)))))),inference(lifteq,[status(thm)],[1564])).
36.43/11.22	thf(535,plain,((~ ((((~)) = (^ [A:$o]: (($false)))) => (~ ((^ [A:$o]: (($true))) = (^ [A:$o]: (($true)))))) | ~ ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (($true)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (($true))))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(536,plain,(((((~)) = (^ [A:$o]: (($false)))) | ~ ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (($true)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (($true))))))),inference(simp,[status(thm)],[535])).
36.43/11.22	thf(846,plain,((((~)) = (^ [A:$o]: (($false)))) | (~ ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (($true)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (($true))))))),inference(cnf,[status(esa)],[536])).
36.43/11.22	thf(915,plain,((((~)) = (^ [A:$o]: (($false)))) | ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (($true)))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (($true)))))),inference(lifteq,[status(thm)],[846])).
36.43/11.22	thf(14,axiom,((! [A:set_Product_prod_a_a,B:set_Pr896671762nres_b]: (member757031305nres_b @ (produc295171948nres_b @ (^ [C:a,D:(a > refine432681134nres_b)]: (D @ C)) @ (^ [C:a,D:(a > refine432681134nres_b)]: (D @ C))) @ (relAPP91071253nres_b @ (relAPP1740535279nres_b @ fun_re1165441639nres_b @ A) @ (relAPP2095637113nres_b @ (relAPP1293188647nres_b @ fun_re1579405647nres_b @ (relAPP1936960811nres_b @ (relAPP1536875909nres_b @ fun_re1837693787nres_b @ A) @ B)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_autoref__Let)).
36.43/11.22	thf(2664,plain,((! [A:set_Product_prod_a_a,B:set_Pr896671762nres_b]: (member757031305nres_b @ (produc295171948nres_b @ (^ [C:a,D:(a > refine432681134nres_b)]: (D @ C)) @ (^ [C:a,D:(a > refine432681134nres_b)]: (D @ C))) @ (relAPP91071253nres_b @ (relAPP1740535279nres_b @ fun_re1165441639nres_b @ A) @ (relAPP2095637113nres_b @ (relAPP1293188647nres_b @ fun_re1579405647nres_b @ (relAPP1936960811nres_b @ (relAPP1536875909nres_b @ fun_re1837693787nres_b @ A) @ B)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
36.43/11.22	thf(1,conjecture,((member65788417nres_d @ (produc1576596708nres_d @ refine436832839nd_a_b @ refine2092371655nd_c_d) @ (relAPP511982311nres_d @ (relAPP1396672239nres_d @ fun_re439246495nres_d @ (relAPP527276399nres_c @ refine737062560el_a_c @ r1)) @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ (relAPP900772393nres_d @ (relAPP1270454529nres_d @ fun_re1760530651nres_d @ r1) @ (relAPP1313094511nres_d @ refine1564831968el_b_d @ r2))) @ (relAPP1313094511nres_d @ refine1564831968el_b_d @ r2))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
36.43/11.22	thf(2,negated_conjecture,((~ (member65788417nres_d @ (produc1576596708nres_d @ refine436832839nd_a_b @ refine2092371655nd_c_d) @ (relAPP511982311nres_d @ (relAPP1396672239nres_d @ fun_re439246495nres_d @ (relAPP527276399nres_c @ refine737062560el_a_c @ r1)) @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ (relAPP900772393nres_d @ (relAPP1270454529nres_d @ fun_re1760530651nres_d @ r1) @ (relAPP1313094511nres_d @ refine1564831968el_b_d @ r2))) @ (relAPP1313094511nres_d @ refine1564831968el_b_d @ r2)))))),inference(neg_conjecture,[status(cth)],[1])).
36.43/11.22	thf(155,plain,((~ (member65788417nres_d @ (produc1576596708nres_d @ (refine436832839nd_a_b) @ (refine2092371655nd_c_d)) @ (relAPP511982311nres_d @ (relAPP1396672239nres_d @ fun_re439246495nres_d @ (relAPP527276399nres_c @ refine737062560el_a_c @ r1)) @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ (relAPP900772393nres_d @ (relAPP1270454529nres_d @ fun_re1760530651nres_d @ r1) @ (relAPP1313094511nres_d @ refine1564831968el_b_d @ r2))) @ (relAPP1313094511nres_d @ (refine1564831968el_b_d) @ r2)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
36.43/11.22	thf(128,axiom,((! [A:((a > refine432681134nres_b) > refine432681134nres_b),B:((c > refine449204144nres_d) > refine449204144nres_d),C:set_Pr589481214nres_d,D:set_Pr1640496404nres_d,E:(a > refine432681134nres_b),F:refine432681134nres_b]: ((((A @ E) = F) => (! [G:(c > refine449204144nres_d)]: ((member936907743nres_d @ (produc210841666nres_d @ E @ G) @ C) => (member1578111221nres_d @ (produc2147164944nres_d @ F @ (B @ G)) @ D)))) <= (member461830657nres_d @ (produc2075136412nres_d @ A @ B) @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_fun__relD1)).
36.43/11.22	thf(3150,plain,((! [A:((a > refine432681134nres_b) > refine432681134nres_b),B:((c > refine449204144nres_d) > refine449204144nres_d),C:set_Pr589481214nres_d,D:set_Pr1640496404nres_d,E:(a > refine432681134nres_b),F:refine432681134nres_b]: ((((A @ (E)) = F) => (! [G:(c > refine449204144nres_d)]: ((member936907743nres_d @ (produc210841666nres_d @ (E) @ (G)) @ C) => (member1578111221nres_d @ (produc2147164944nres_d @ F @ (B @ (G))) @ D)))) | ~ (member461830657nres_d @ (produc2075136412nres_d @ (A) @ (B)) @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])).
36.43/11.22	thf(3219,plain,(((relAPP1313094511nres_d) = (^ [A:(set_Product_prod_b_d > set_Pr1640496404nres_d)]: (A)))),inference(lifteq,[status(thm)],[3218])).
36.43/11.22	thf(59,axiom,((! [A:(produc1677145714nres_d > $o),B:produc1677145714nres_d]: ((! [C:(a > ((a > refine432681134nres_b) > refine432681134nres_b)),D:(c > ((c > refine449204144nres_d) > refine449204144nres_d))]: (A @ (produc627868012nres_d @ C @ D))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_old_Oprod_Oinducts)).
36.43/11.22	thf(2824,plain,((! [A:(produc1677145714nres_d > $o),B:produc1677145714nres_d]: ((! [C:(a > ((a > refine432681134nres_b) > refine432681134nres_b)),D:(c > ((c > refine449204144nres_d) > refine449204144nres_d))]: (A @ (produc627868012nres_d @ (C) @ (D)))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])).
36.43/11.22	thf(312,plain,((~ (((^ [A:$o]: (($false))) = (^ [A:$o]: (($true)))) => (~ ((^ [A:$o]: (($false))) = (^ [A:$o]: (($true)))))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (($false)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (($true))))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(629,plain,(((^ [A:$o]: (($false))) = (^ [A:$o]: (($true)))) | (~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (($false)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (($true))))))),inference(cnf,[status(esa)],[312])).
36.43/11.22	thf(911,plain,(((^ [A:$o]: (($false))) = (^ [A:$o]: (($true)))) | ((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (($false)))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (($true)))))),inference(lifteq,[status(thm)],[629])).
36.43/11.22	thf(912,plain,(((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (($false)))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (($true)))))),inference(simp,[status(thm)],[911])).
36.43/11.22	thf(125,axiom,((! [A:(a > refine432681134nres_b),B:(c > refine449204144nres_d),C:set_Product_prod_a_c,D:set_Pr1640496404nres_d,E:a,F:c]: ((member936907743nres_d @ (produc210841666nres_d @ A @ B) @ (relAPP900772393nres_d @ (relAPP1270454529nres_d @ fun_re1760530651nres_d @ C) @ D)) => ((member1578111221nres_d @ (produc2147164944nres_d @ (autore1390664424nres_b @ A @ E) @ (autore1981686764nres_d @ B @ F)) @ D) <= (member466432594od_a_c @ (product_Pair_a_c @ E @ F) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_autoref__APP)).
36.43/11.22	thf(3142,plain,((! [A:(a > refine432681134nres_b),B:(c > refine449204144nres_d),C:set_Product_prod_a_c,D:set_Pr1640496404nres_d,E:a,F:c]: ((member936907743nres_d @ (produc210841666nres_d @ (A) @ (B)) @ (relAPP900772393nres_d @ (relAPP1270454529nres_d @ fun_re1760530651nres_d @ C) @ D)) => ((member1578111221nres_d @ (produc2147164944nres_d @ (autore1390664424nres_b @ (A) @ E) @ (autore1981686764nres_d @ (B) @ F)) @ D) | ~ (member466432594od_a_c @ (product_Pair_a_c @ E @ F) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])).
36.43/11.22	thf(76,axiom,((! [A:(product_prod_a_c > $o),B:product_prod_a_c]: ((A @ B) <= (! [C:a,D:c]: (A @ (product_Pair_a_c @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_old_Oprod_Oinducts)).
36.43/11.22	thf(2967,plain,((! [A:(product_prod_a_c > $o),B:product_prod_a_c]: ((A @ B) | ~ (! [C:a,D:c]: (A @ (product_Pair_a_c @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])).
36.43/11.22	thf(56,axiom,((! [A:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)),B:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d)),C:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)),D:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d))]: (((produc1910095910nres_d @ A @ B) = (produc1910095910nres_d @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_prod_Oinject)).
36.43/11.22	thf(2816,plain,((! [A:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)),B:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d)),C:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)),D:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d))]: (((produc1910095910nres_d @ (A) @ (B)) = (produc1910095910nres_d @ (C) @ (D))) = (((A) = (C)) & ((B) = (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])).
36.43/11.22	thf(140,axiom,((! [A:((a > refine432681134nres_b) > refine432681134nres_b),B:((c > refine449204144nres_d) > refine449204144nres_d),C:set_Pr589481214nres_d,D:set_Pr1640496404nres_d,E:(a > refine432681134nres_b),F:(c > refine449204144nres_d)]: ((member461830657nres_d @ (produc2075136412nres_d @ A @ B) @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ C) @ D)) => ((member1578111221nres_d @ (produc2147164944nres_d @ (A @ E) @ (B @ F)) @ D) <= (member936907743nres_d @ (produc210841666nres_d @ E @ F) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_tagged__fun__relD__none)).
36.43/11.22	thf(3193,plain,((! [A:((a > refine432681134nres_b) > refine432681134nres_b),B:((c > refine449204144nres_d) > refine449204144nres_d),C:set_Pr589481214nres_d,D:set_Pr1640496404nres_d,E:(a > refine432681134nres_b),F:(c > refine449204144nres_d)]: ((member461830657nres_d @ (produc2075136412nres_d @ (A) @ (B)) @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ C) @ D)) => ((member1578111221nres_d @ (produc2147164944nres_d @ (A @ (E)) @ (B @ (F))) @ D) | ~ (member936907743nres_d @ (produc210841666nres_d @ (E) @ (F)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])).
36.43/11.22	thf(192,plain,((~ (((^ [A:$o]: (A)) = (^ [A:$o]: (A))) => (~ ((^ [A:$o]: (A)) = (^ [A:$o]: (($true)))))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true))))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(193,plain,((((^ [A:$o]: (A)) = (^ [A:$o]: (($true)))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true))))))),inference(simp,[status(thm)],[192])).
36.43/11.22	thf(704,plain,(((^ [A:$o]: (A)) = (^ [A:$o]: (($true)))) | (~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true))))))),inference(cnf,[status(esa)],[193])).
36.43/11.22	thf(1166,plain,(((^ [A:$o]: (A)) = (^ [A:$o]: (($true)))) | ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true)))))),inference(lifteq,[status(thm)],[704])).
36.43/11.22	thf(145,axiom,((! [A:$o,B:$o,C:refine432681134nres_b,D:refine449204144nres_d,E:set_Product_prod_b_d]: ((((A) => ((B) => (member1578111221nres_d @ (produc2147164944nres_d @ C @ D) @ (relAPP1313094511nres_d @ refine1564831968el_b_d @ E)))) => (member1578111221nres_d @ (produc2147164944nres_d @ (refine1437029928_bnd_b @ B @ C) @ (refine1437029930_bnd_d @ A @ D)) @ (relAPP1313094511nres_d @ refine1564831968el_b_d @ E))) <= ((B) <= (A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_param__op__nres__ASSERT__bnd)).
36.43/11.22	thf(3206,plain,((! [A:$o,B:$o,C:refine432681134nres_b,D:refine449204144nres_d,E:set_Product_prod_b_d]: ((((A) => ((B) => (member1578111221nres_d @ (produc2147164944nres_d @ C @ D) @ (relAPP1313094511nres_d @ (refine1564831968el_b_d) @ E)))) => (member1578111221nres_d @ (produc2147164944nres_d @ (refine1437029928_bnd_b @ B @ C) @ (refine1437029930_bnd_d @ A @ D)) @ (relAPP1313094511nres_d @ (refine1564831968el_b_d) @ E))) | ~ ((B) | ~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])).
36.43/11.22	thf(132,axiom,((! [A:set_Product_prod_a_c,B:(a > refine432681134nres_b),C:(c > refine449204144nres_d),D:set_Pr1640496404nres_d]: ((member936907743nres_d @ (produc210841666nres_d @ B @ C) @ (relAPP900772393nres_d @ (relAPP1270454529nres_d @ fun_re1760530651nres_d @ A) @ D)) <= (! [E:a,F:c]: ((member1578111221nres_d @ (produc2147164944nres_d @ (B @ E) @ (C @ F)) @ D) <= (member466432594od_a_c @ (product_Pair_a_c @ E @ F) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_fun__relI)).
36.43/11.22	thf(3161,plain,((! [A:set_Product_prod_a_c,B:(a > refine432681134nres_b),C:(c > refine449204144nres_d),D:set_Pr1640496404nres_d]: ((member936907743nres_d @ (produc210841666nres_d @ (B) @ (C)) @ (relAPP900772393nres_d @ (relAPP1270454529nres_d @ fun_re1760530651nres_d @ A) @ D)) | ~ (! [E:a,F:c]: ((member1578111221nres_d @ (produc2147164944nres_d @ (B @ E) @ (C @ F)) @ D) | ~ (member466432594od_a_c @ (product_Pair_a_c @ E @ F) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])).
36.43/11.22	thf(95,axiom,((! [A:(a > refine432681134nres_b),B:(a > refine432681134nres_b),C:set_Product_prod_a_a,D:set_Pr896671762nres_b,E:a,F:a]: (((member449909584od_a_a @ (product_Pair_a_a @ E @ F) @ C) => (member1446466291nres_b @ (produc2130641934nres_b @ (autore1390664424nres_b @ A @ E) @ (autore1390664424nres_b @ B @ F)) @ D)) <= (member369653087nres_b @ (produc809128386nres_b @ A @ B) @ (relAPP1936960811nres_b @ (relAPP1536875909nres_b @ fun_re1837693787nres_b @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_autoref__APP)).
36.43/11.22	thf(3048,plain,((! [A:(a > refine432681134nres_b),B:(a > refine432681134nres_b),C:set_Product_prod_a_a,D:set_Pr896671762nres_b,E:a,F:a]: (((member449909584od_a_a @ (product_Pair_a_a @ E @ F) @ C) => (member1446466291nres_b @ (produc2130641934nres_b @ (autore1390664424nres_b @ (A) @ E) @ (autore1390664424nres_b @ (B) @ F)) @ D)) | ~ (member369653087nres_b @ (produc809128386nres_b @ (A) @ (B)) @ (relAPP1936960811nres_b @ (relAPP1536875909nres_b @ fun_re1837693787nres_b @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])).
36.43/11.22	thf(458,plain,((~ ((((~)) = ((~))) => (~ ((^ [A:$o]: (A)) = ((~))))) | ~ ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ ((~)) @ ((~)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(459,plain,((((^ [A:$o]: (A)) = ((~))) | ~ ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ ((~)) @ ((~)))))),inference(simp,[status(thm)],[458])).
36.43/11.22	thf(889,plain,(((^ [A:$o]: (A)) = ((~))) | (~ ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ ((~)) @ ((~)))))),inference(cnf,[status(esa)],[459])).
36.43/11.22	thf(1048,plain,((((~)) = (^ [A:$o]: (A))) | ((product_Pair_o_o_o_o @ ((~)) @ ((~))) != (product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A))))),inference(lifteq,[status(thm)],[889])).
36.43/11.22	thf(1049,plain,(((product_Pair_o_o_o_o @ ((~)) @ ((~))) != (product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A))))),inference(simp,[status(thm)],[1048])).
36.43/11.22	thf(2942,plain,(((relAPP1536875909nres_b) = (^ [A:(set_Product_prod_a_a > (set_Pr896671762nres_b > set_Pr1815766654nres_b))]: (A)))),inference(lifteq,[status(thm)],[2941])).
36.43/11.22	thf(422,plain,((~ ((((~)) = (^ [A:$o]: (A))) => (~ ((^ [A:$o]: (($false))) = (^ [A:$o]: (($true)))))) | ~ ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (($false)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true))))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(866,plain,(((^ [A:$o]: (($false))) = (^ [A:$o]: (($true)))) | (~ ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (($false)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true))))))),inference(cnf,[status(esa)],[422])).
36.43/11.22	thf(1002,plain,(((^ [A:$o]: (($false))) = (^ [A:$o]: (($true)))) | ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (($false)))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true)))))),inference(lifteq,[status(thm)],[866])).
36.43/11.22	thf(1003,plain,(((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (($false)))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true)))))),inference(simp,[status(thm)],[1002])).
36.43/11.22	thf(352,plain,((~ ((((~)) = (^ [A:$o]: (A))) => (~ ((^ [A:$o]: (($true))) = (^ [A:$o]: (($true)))))) | ~ ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (($true)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true))))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(353,plain,(((((~)) = (^ [A:$o]: (A))) | ~ ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (($true)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true))))))),inference(simp,[status(thm)],[352])).
36.43/11.22	thf(615,plain,((((~)) = (^ [A:$o]: (A))) | (~ ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (($true)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true))))))),inference(cnf,[status(esa)],[353])).
36.43/11.22	thf(1069,plain,((((~)) = (^ [A:$o]: (A))) | ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (($true)))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true)))))),inference(lifteq,[status(thm)],[615])).
36.43/11.22	thf(1070,plain,(((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (($true)))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true)))))),inference(simp,[status(thm)],[1069])).
36.43/11.22	thf(120,axiom,((relAPP98076839nres_d = (^ [A:(set_Pr589481214nres_d > (set_Pr1640496404nres_d > set_Pr797615136nres_d))]: (A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_relAPP__def)).
36.43/11.22	thf(3128,plain,(((relAPP98076839nres_d) = (^ [A:(set_Pr589481214nres_d > (set_Pr1640496404nres_d > set_Pr797615136nres_d))]: (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])).
36.43/11.22	thf(3129,plain,(((relAPP98076839nres_d) = (^ [A:(set_Pr589481214nres_d > (set_Pr1640496404nres_d > set_Pr797615136nres_d))]: (A)))),inference(lifteq,[status(thm)],[3128])).
36.43/11.22	thf(151,axiom,((! [A:set_Product_prod_a_c,B:set_Pr1640496404nres_d]: (member189721481nres_d @ (produc627868012nres_d @ (^ [C:a,D:(a > refine432681134nres_b)]: (D @ C)) @ (^ [C:c,D:(c > refine449204144nres_d)]: (D @ C))) @ (relAPP1354295571nres_d @ (relAPP1135042155nres_d @ fun_re1089848935nres_d @ A) @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ (relAPP900772393nres_d @ (relAPP1270454529nres_d @ fun_re1760530651nres_d @ A) @ B)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_autoref__Let)).
36.43/11.22	thf(3228,plain,((! [A:set_Product_prod_a_c,B:set_Pr1640496404nres_d]: (member189721481nres_d @ (produc627868012nres_d @ (^ [C:a,D:(a > refine432681134nres_b)]: (D @ C)) @ (^ [C:c,D:(c > refine449204144nres_d)]: (D @ C))) @ (relAPP1354295571nres_d @ (relAPP1135042155nres_d @ fun_re1089848935nres_d @ A) @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ (relAPP900772393nres_d @ (relAPP1270454529nres_d @ fun_re1760530651nres_d @ A) @ B)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])).
36.43/11.22	thf(58,axiom,((! [A:((a > refine432681134nres_b) > refine432681134nres_b),B:((c > refine449204144nres_d) > refine449204144nres_d),C:((a > refine432681134nres_b) > refine432681134nres_b),D:((c > refine449204144nres_d) > refine449204144nres_d)]: (((produc2075136412nres_d @ A @ B) = (produc2075136412nres_d @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_prod_Oinject)).
36.43/11.22	thf(2821,plain,((! [A:((a > refine432681134nres_b) > refine432681134nres_b),B:((c > refine449204144nres_d) > refine449204144nres_d),C:((a > refine432681134nres_b) > refine432681134nres_b),D:((c > refine449204144nres_d) > refine449204144nres_d)]: (((produc2075136412nres_d @ (A) @ (B)) = (produc2075136412nres_d @ (C) @ (D))) = (((B) = (D)) & ((A) = (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])).
36.43/11.22	thf(97,axiom,((! [A:produc1677145714nres_d]: ? [B:(a > ((a > refine432681134nres_b) > refine432681134nres_b)),C:(c > ((c > refine449204144nres_d) > refine449204144nres_d))]: (A = (produc627868012nres_d @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_surj__pair)).
36.43/11.22	thf(3058,plain,((! [A:produc1677145714nres_d]: ? [B:(a > ((a > refine432681134nres_b) > refine432681134nres_b)),C:(c > ((c > refine449204144nres_d) > refine449204144nres_d))]: (A = (produc627868012nres_d @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])).
36.43/11.22	thf(27,axiom,((! [A:(a > ((a > refine432681134nres_b) > refine432681134nres_b)),B:(c > ((c > refine449204144nres_d) > refine449204144nres_d)),C:(a > ((a > refine432681134nres_b) > refine432681134nres_b)),D:(c > ((c > refine449204144nres_d) > refine449204144nres_d))]: (((produc627868012nres_d @ A @ B) = (produc627868012nres_d @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_prod_Oinject)).
36.43/11.22	thf(2720,plain,((! [A:(a > ((a > refine432681134nres_b) > refine432681134nres_b)),B:(c > ((c > refine449204144nres_d) > refine449204144nres_d)),C:(a > ((a > refine432681134nres_b) > refine432681134nres_b)),D:(c > ((c > refine449204144nres_d) > refine449204144nres_d))]: (((produc627868012nres_d @ (A) @ (B)) = (produc627868012nres_d @ (C) @ (D))) = (((B) = (D)) & ((A) = (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])).
36.43/11.22	thf(34,axiom,((refine321891363sn_a_c = (^ [A:set_Product_prod_a_c,B:(c > $o),C:a]: ? [D:c]: ((B @ D) & (member466432594od_a_c @ (product_Pair_a_c @ C @ D) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_lift__assn__def)).
36.43/11.22	thf(2746,plain,(((refine321891363sn_a_c) = (^ [A:set_Product_prod_a_c,B:(c > $o),C:a]: ? [D:c]: ((B @ D) & (member466432594od_a_c @ (product_Pair_a_c @ C @ D) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])).
36.43/11.22	thf(2747,plain,(((refine321891363sn_a_c) = (^ [A:set_Product_prod_a_c,B:(c > $o),C:a]: ? [D:c]: ((B @ D) & (member466432594od_a_c @ (product_Pair_a_c @ C @ D) @ A))))),inference(lifteq,[status(thm)],[2746])).
36.43/11.22	thf(116,axiom,((! [A:(a > refine432681134nres_b),B:(c > refine449204144nres_d),C:set_Product_prod_a_c,D:set_Pr1640496404nres_d,E:a,F:refine432681134nres_b]: ((((A @ E) = F) => (! [G:c]: ((member466432594od_a_c @ (product_Pair_a_c @ E @ G) @ C) => (member1578111221nres_d @ (produc2147164944nres_d @ F @ (B @ G)) @ D)))) <= (member936907743nres_d @ (produc210841666nres_d @ A @ B) @ (relAPP900772393nres_d @ (relAPP1270454529nres_d @ fun_re1760530651nres_d @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_fun__relD1)).
36.43/11.22	thf(3114,plain,((! [A:(a > refine432681134nres_b),B:(c > refine449204144nres_d),C:set_Product_prod_a_c,D:set_Pr1640496404nres_d,E:a,F:refine432681134nres_b]: ((((A @ E) = F) => (! [G:c]: ((member466432594od_a_c @ (product_Pair_a_c @ E @ G) @ C) => (member1578111221nres_d @ (produc2147164944nres_d @ F @ (B @ G)) @ D)))) | ~ (member936907743nres_d @ (produc210841666nres_d @ (A) @ (B)) @ (relAPP900772393nres_d @ (relAPP1270454529nres_d @ fun_re1760530651nres_d @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])).
36.43/11.22	thf(2675,plain,(((refine1711024813nres_d) = (^ [A:set_Pr613277282nres_d,B:(((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d)) > $o),C:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b))]: ? [D:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d))]: ((member660096835nres_d @ (produc1910095910nres_d @ C @ D) @ A) & (B @ D))))),inference(lifteq,[status(thm)],[2674])).
36.43/11.22	thf(63,axiom,((! [A:($o > $o),B:($o > $o),C:set_Pr934623755_o_o_o,D:(($o > $o) > a),E:(($o > $o) > c),F:set_Product_prod_a_c]: (((member466432594od_a_c @ (product_Pair_a_c @ (D @ A) @ (autoref_APP_o_o_c_c @ (autore1733926270_o_c_c @ (autore867490625_o_c_c @ (autore971224502_o_c_c @ (^ [G:($o > $o),H:(($o > $o) > c)]: (H @ G))) @ (autore821969498_o_c_c @ (relAPP1562327022_o_c_c @ (relAPP2129980178_o_c_c @ fun_re1144975870_o_c_c @ C) @ (relAPP1774770060_o_c_c @ (relAPP412764446_o_c_c @ fun_re1859931662_c_a_c @ (relAPP970620078_o_o_c @ (relAPP1750172554_o_o_c @ fun_rel_o_o_o_o_a_c @ C) @ F)) @ F)))) @ B) @ E)) @ F) <= (! [G:($o > $o)]: ((! [H:($o > $o)]: ((member466432594od_a_c @ (product_Pair_a_c @ (D @ H) @ (autoref_APP_o_o_c @ E @ G)) @ F) <= (member250723412_o_o_o @ (product_Pair_o_o_o_o @ H @ G) @ C))) <= (autore1113312320RNAL_o @ (B = G))))) <= (member250723412_o_o_o @ (product_Pair_o_o_o_o @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_autoref__Let__cong)).
36.43/11.22	thf(2838,plain,((! [A:($o > $o),B:($o > $o),C:set_Pr934623755_o_o_o,D:(($o > $o) > a),E:(($o > $o) > c),F:set_Product_prod_a_c]: ((member466432594od_a_c @ (product_Pair_a_c @ (D @ (A)) @ (autoref_APP_o_o_c_c @ (autore1733926270_o_c_c @ (autore867490625_o_c_c @ (autore971224502_o_c_c @ (^ [G:($o > $o),H:(($o > $o) > c)]: (H @ G))) @ (autore821969498_o_c_c @ (relAPP1562327022_o_c_c @ (relAPP2129980178_o_c_c @ fun_re1144975870_o_c_c @ C) @ (relAPP1774770060_o_c_c @ (relAPP412764446_o_c_c @ fun_re1859931662_c_a_c @ (relAPP970620078_o_o_c @ (relAPP1750172554_o_o_c @ fun_rel_o_o_o_o_a_c @ C) @ F)) @ F)))) @ B) @ (E))) @ F) | ~ (! [G:($o > $o)]: (! [H:($o > $o)]: ((member466432594od_a_c @ (product_Pair_a_c @ (D @ (H)) @ (autoref_APP_o_o_c @ (E) @ (G))) @ F) | ~ (member250723412_o_o_o @ (product_Pair_o_o_o_o @ (H) @ (G)) @ C)) | ~ (autore1113312320RNAL_o @ ((B) = (G))))) | ~ (member250723412_o_o_o @ (product_Pair_o_o_o_o @ (A) @ (B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])).
36.43/11.22	thf(24,axiom,((! [A:(produc1677145714nres_d > $o),B:produc1677145714nres_d]: ((A @ B) <= (! [C:(a > ((a > refine432681134nres_b) > refine432681134nres_b)),D:(c > ((c > refine449204144nres_d) > refine449204144nres_d))]: (A @ (produc627868012nres_d @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_prod__cases)).
36.43/11.22	thf(2711,plain,((! [A:(produc1677145714nres_d > $o),B:produc1677145714nres_d]: ((A @ B) | ~ (! [C:(a > ((a > refine432681134nres_b) > refine432681134nres_b)),D:(c > ((c > refine449204144nres_d) > refine449204144nres_d))]: (A @ (produc627868012nres_d @ (C) @ (D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])).
36.43/11.22	thf(149,axiom,((! [A:set_Product_prod_a_c]: (member100096605nres_c @ (produc1827604032nres_c @ refine2063221604TURN_a @ refine2063221606TURN_c) @ (relAPP2018433511nres_c @ (relAPP173519167nres_c @ fun_re766812315nres_c @ A) @ (relAPP527276399nres_c @ refine737062560el_a_c @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_autoref__RETURN)).
36.43/11.22	thf(3224,plain,((! [A:set_Product_prod_a_c]: (member100096605nres_c @ (produc1827604032nres_c @ (refine2063221604TURN_a) @ (refine2063221606TURN_c)) @ (relAPP2018433511nres_c @ (relAPP173519167nres_c @ fun_re766812315nres_c @ A) @ (relAPP527276399nres_c @ (refine737062560el_a_c) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])).
36.43/11.22	thf(474,plain,((~ (((^ [A:$o]: (($true))) = (^ [A:$o]: (($false)))) => (~ ((^ [A:$o]: (A)) = (^ [A:$o]: (A))))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(475,plain,((((^ [A:$o]: (($true))) = (^ [A:$o]: (($false)))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A)))))),inference(simp,[status(thm)],[474])).
36.43/11.22	thf(606,plain,(((^ [A:$o]: (($true))) = (^ [A:$o]: (($false)))) | (~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A)))))),inference(cnf,[status(esa)],[475])).
36.43/11.22	thf(977,plain,(((^ [A:$o]: (($false))) = (^ [A:$o]: (($true)))) | ((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (A))))),inference(lifteq,[status(thm)],[606])).
36.43/11.22	thf(978,plain,(((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (A))))),inference(simp,[status(thm)],[977])).
36.43/11.22	thf(274,plain,((~ (((^ [A:$o]: (A)) = ((~))) => (~ ((^ [A:$o]: (($false))) = (^ [A:$o]: (A))))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))) = (product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(766,plain,(((^ [A:$o]: (A)) = ((~))) | (~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))) = (product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A)))))),inference(cnf,[status(esa)],[274])).
36.43/11.22	thf(1007,plain,((((~)) = (^ [A:$o]: (A))) | ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))))),inference(lifteq,[status(thm)],[766])).
36.43/11.22	thf(1008,plain,(((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))))),inference(simp,[status(thm)],[1007])).
36.43/11.22	thf(30,axiom,((! [A:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)),B:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d)),C:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)),D:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d))]: ((~ ((A = C) => (B != D))) <= ((produc1910095910nres_d @ A @ B) = (produc1910095910nres_d @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_Pair__inject)).
36.43/11.22	thf(2728,plain,((! [A:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)),B:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d)),C:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)),D:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d))]: (~ (((A) = (C)) => (~ ((B) = (D)))) | ~ ((produc1910095910nres_d @ (A) @ (B)) = (produc1910095910nres_d @ (C) @ (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])).
36.43/11.22	thf(69,axiom,((! [A:set_Product_prod_d_b]: (member994209571nres_b @ (produc83262214nres_b @ refine2063221607TURN_d @ refine2063221605TURN_b) @ (relAPP1523780267nres_b @ (relAPP1311256519nres_b @ fun_re934539163nres_b @ A) @ (relAPP821124455nres_b @ refine1072887132el_d_b @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_autoref__RETURN)).
36.43/11.22	thf(2939,plain,((! [A:set_Product_prod_d_b]: (member994209571nres_b @ (produc83262214nres_b @ (refine2063221607TURN_d) @ (refine2063221605TURN_b)) @ (relAPP1523780267nres_b @ (relAPP1311256519nres_b @ fun_re934539163nres_b @ A) @ (relAPP821124455nres_b @ (refine1072887132el_d_b) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])).
36.43/11.22	thf(3071,plain,(((relAPP1642956907nres_a) = (^ [A:(set_Product_prod_a_a > set_Pr384614482nres_a)]: (A)))),inference(lifteq,[status(thm)],[3070])).
36.43/11.22	thf(81,axiom,((! [A:b,B:(b > refine432681134nres_b)]: ((refine1264602246nd_b_b @ (refine2063221605TURN_b @ A) @ B) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_nres__monad1)).
36.43/11.22	thf(2992,plain,((! [A:b,B:(b > refine432681134nres_b)]: ((refine1264602246nd_b_b @ (refine2063221605TURN_b @ A) @ (B)) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])).
36.43/11.22	thf(53,axiom,((! [A:d,B:(d > refine440942639nres_c)]: ((refine772657413nd_d_c @ (refine2063221607TURN_d @ A) @ B) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_nres__monad1)).
36.43/11.22	thf(2807,plain,((! [A:d,B:(d > refine440942639nres_c)]: ((refine772657413nd_d_c @ (refine2063221607TURN_d @ A) @ (B)) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])).
36.43/11.22	thf(3156,plain,(((relAPP511982311nres_d) = (^ [A:(set_Pr797615136nres_d > set_Pr24800800nres_d)]: (A)))),inference(lifteq,[status(thm)],[3155])).
36.43/11.22	thf(135,axiom,((! [A:set_Pr589481214nres_d,B:((a > refine432681134nres_b) > refine432681134nres_b),C:((c > refine449204144nres_d) > refine449204144nres_d),D:set_Pr1640496404nres_d]: ((member461830657nres_d @ (produc2075136412nres_d @ B @ C) @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ A) @ D)) <= (! [E:(a > refine432681134nres_b),F:(c > refine449204144nres_d)]: ((member936907743nres_d @ (produc210841666nres_d @ E @ F) @ A) => (member1578111221nres_d @ (produc2147164944nres_d @ (B @ E) @ (C @ F)) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_fun__relI)).
36.43/11.22	thf(3168,plain,((! [A:set_Pr589481214nres_d,B:((a > refine432681134nres_b) > refine432681134nres_b),C:((c > refine449204144nres_d) > refine449204144nres_d),D:set_Pr1640496404nres_d]: ((member461830657nres_d @ (produc2075136412nres_d @ (B) @ (C)) @ (relAPP813854073nres_d @ (relAPP98076839nres_d @ fun_re1394577105nres_d @ A) @ D)) | ~ (! [E:(a > refine432681134nres_b),F:(c > refine449204144nres_d)]: ((member936907743nres_d @ (produc210841666nres_d @ (E) @ (F)) @ A) => (member1578111221nres_d @ (produc2147164944nres_d @ (B @ (E)) @ (C @ (F))) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])).
36.43/11.22	thf(124,axiom,((! [A:(a > refine432681134nres_b),B:(c > refine449204144nres_d),C:set_Product_prod_a_c,D:set_Pr1640496404nres_d,E:a,F:c]: (((member1578111221nres_d @ (produc2147164944nres_d @ (A @ E) @ (B @ F)) @ D) <= (member466432594od_a_c @ (product_Pair_a_c @ E @ F) @ C)) <= (member936907743nres_d @ (produc210841666nres_d @ A @ B) @ (relAPP900772393nres_d @ (relAPP1270454529nres_d @ fun_re1760530651nres_d @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_tagged__fun__relD__lhs)).
36.43/11.22	thf(3139,plain,((! [A:(a > refine432681134nres_b),B:(c > refine449204144nres_d),C:set_Product_prod_a_c,D:set_Pr1640496404nres_d,E:a,F:c]: ((member1578111221nres_d @ (produc2147164944nres_d @ (A @ E) @ (B @ F)) @ D) | ~ (member466432594od_a_c @ (product_Pair_a_c @ E @ F) @ C) | ~ (member936907743nres_d @ (produc210841666nres_d @ (A) @ (B)) @ (relAPP900772393nres_d @ (relAPP1270454529nres_d @ fun_re1760530651nres_d @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])).
36.43/11.22	thf(3092,plain,(((relAPP173519167nres_c) = (^ [A:(set_Product_prod_a_c > (set_Pr1128439124nres_c > set_Pr134917244nres_c))]: (A)))),inference(lifteq,[status(thm)],[3091])).
36.43/11.22	thf(100,axiom,((! [A:set_Pr797615136nres_d]: ((collec1671161663nres_d @ (^ [B:produc1757587562nres_d]: (member461830657nres_d @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_Collect__mem__eq)).
36.43/11.22	thf(3067,plain,((! [A:set_Pr797615136nres_d]: ((collec1671161663nres_d @ (^ [B:produc1757587562nres_d]: (member461830657nres_d @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])).
36.43/11.22	thf(2828,plain,(((refine408412177nres_d) = (^ [A:set_Pr2080238504nres_d,B:((c > ((c > refine449204144nres_d) > refine449204144nres_d)) > $o),C:(a > ((a > refine432681134nres_b) > refine432681134nres_b))]: ? [D:(c > ((c > refine449204144nres_d) > refine449204144nres_d))]: ((member189721481nres_d @ (produc627868012nres_d @ C @ D) @ A) & (B @ D))))),inference(lifteq,[status(thm)],[2827])).
36.43/11.22	thf(136,axiom,((! [A:$o,B:$o,C:refine424419629nres_a,D:refine440942639nres_c,E:set_Product_prod_a_c]: ((((A) => ((B) => (member1600573749nres_c @ (produc1153446608nres_c @ C @ D) @ (relAPP527276399nres_c @ refine737062560el_a_c @ E)))) => (member1600573749nres_c @ (produc1153446608nres_c @ (refine1437029927_bnd_a @ B @ C) @ (refine1437029929_bnd_c @ A @ D)) @ (relAPP527276399nres_c @ refine737062560el_a_c @ E))) <= ((B) <= (A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_param__op__nres__ASSERT__bnd)).
36.43/11.22	thf(3171,plain,((! [A:$o,B:$o,C:refine424419629nres_a,D:refine440942639nres_c,E:set_Product_prod_a_c]: ((((A) => ((B) => (member1600573749nres_c @ (produc1153446608nres_c @ C @ D) @ (relAPP527276399nres_c @ (refine737062560el_a_c) @ E)))) => (member1600573749nres_c @ (produc1153446608nres_c @ (refine1437029927_bnd_a @ B @ C) @ (refine1437029929_bnd_c @ A @ D)) @ (relAPP527276399nres_c @ (refine737062560el_a_c) @ E))) | ~ ((B) | ~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])).
36.43/11.22	thf(9,axiom,((! [A:(product_prod_o_o_o_o > $o),B:product_prod_o_o_o_o]: ((A @ B) <= (! [C:($o > $o),D:($o > $o)]: (A @ (product_Pair_o_o_o_o @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_old_Oprod_Oinducts)).
36.43/11.22	thf(1412,plain,((! [A:(product_prod_o_o_o_o > $o),B:product_prod_o_o_o_o]: ((A @ B) | ~ (! [C:($o > $o),D:($o > $o)]: (A @ (product_Pair_o_o_o_o @ (C) @ (D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
36.43/11.22	thf(3928,plain,(~ (sk110) | sk111),inference(func_ext,[status(esa)],[3719])).
36.43/11.22	thf(43,axiom,((! [A:a,B:c,C:set_Product_prod_a_c,D:(c > $o)]: (((refine321891363sn_a_c @ C @ D @ A) <= (D @ B)) <= (member466432594od_a_c @ (product_Pair_a_c @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_lift__assnI)).
36.43/11.22	thf(2775,plain,((! [A:a,B:c,C:set_Product_prod_a_c,D:(c > $o)]: ((refine321891363sn_a_c @ C @ (D) @ A) | ~ (D @ B) | ~ (member466432594od_a_c @ (product_Pair_a_c @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])).
36.43/11.22	thf(92,axiom,((! [A:produc1677145714nres_d,B:(produc1677145714nres_d > $o)]: ((member189721481nres_d @ A @ (collec554837959nres_d @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_mem__Collect__eq)).
36.43/11.22	thf(3039,plain,((! [A:produc1677145714nres_d,B:(produc1677145714nres_d > $o)]: ((member189721481nres_d @ A @ (collec554837959nres_d @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])).
36.43/11.22	thf(436,plain,((~ (((^ [A:$o]: (($false))) = (^ [A:$o]: (($false)))) => (~ ((^ [A:$o]: (A)) = ((~))))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ ((~)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(437,plain,((((^ [A:$o]: (A)) = ((~))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ ((~)))))),inference(simp,[status(thm)],[436])).
36.43/11.22	thf(877,plain,(((^ [A:$o]: (A)) = ((~))) | (~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ ((~)))))),inference(cnf,[status(esa)],[437])).
36.43/11.22	thf(1009,plain,((((~)) = (^ [A:$o]: (A))) | ((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ ((~))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A))))),inference(lifteq,[status(thm)],[877])).
36.43/11.22	thf(1010,plain,(((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ ((~))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A))))),inference(simp,[status(thm)],[1009])).
36.43/11.22	thf(64,axiom,((! [A:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)),B:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d)),C:set_Pr613277282nres_d,D:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b))]: (((autore233619284nres_b @ A @ D) => (member660096835nres_d @ (produc1910095910nres_d @ D @ B) @ C)) <= (member660096835nres_d @ (produc1910095910nres_d @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_autoref__REMOVE__INTERNAL__EQ)).
36.43/11.22	thf(2919,plain,((! [A:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)),B:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d)),C:set_Pr613277282nres_d,D:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b))]: (((autore233619284nres_b @ (A) @ (D)) => (member660096835nres_d @ (produc1910095910nres_d @ (D) @ (B)) @ C)) | ~ (member660096835nres_d @ (produc1910095910nres_d @ (A) @ (B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])).
36.43/11.22	thf(2707,plain,(((relAPP281291371nres_b) = (^ [A:(set_Product_prod_b_b > set_Pr896671762nres_b)]: (A)))),inference(lifteq,[status(thm)],[2706])).
36.43/11.22	thf(334,plain,((~ (((^ [A:$o]: (A)) = (^ [A:$o]: (($true)))) => (~ ((^ [A:$o]: (A)) = ((~))))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ ((~)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(651,plain,(((^ [A:$o]: (A)) = ((~))) | (~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ ((~)))))),inference(cnf,[status(esa)],[334])).
36.43/11.22	thf(960,plain,((((~)) = (^ [A:$o]: (A))) | ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ ((~))))),inference(lifteq,[status(thm)],[651])).
36.43/11.22	thf(961,plain,(((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ ((~))))),inference(simp,[status(thm)],[960])).
36.43/11.22	thf(157,plain,(! [A:product_prod_o_o_o_o] : ((A = (product_Pair_o_o_o_o @ (sk1 @ A) @ (sk2 @ A))))),inference(cnf,[status(esa)],[156])).
36.43/11.22	thf(158,plain,(! [A:product_prod_o_o_o_o] : ((A = (product_Pair_o_o_o_o @ (sk1 @ A) @ (sk2 @ A))))),inference(lifteq,[status(thm)],[157])).
36.43/11.22	thf(147,axiom,((! [A:set_Product_prod_c_c,B:set_Product_prod_d_d]: (member405013761nres_d @ (produc1915822052nres_d @ refine2092371655nd_c_d @ refine2092371655nd_c_d) @ (relAPP720329701nres_d @ (relAPP2032940527nres_d @ fun_re1190945563nres_d @ (relAPP1067109483nres_c @ refine245117726el_c_c @ A)) @ (relAPP1899039865nres_d @ (relAPP990557099nres_d @ fun_re1740744275nres_d @ (relAPP941435307nres_d @ (relAPP508483205nres_d @ fun_re414971739nres_d @ A) @ (relAPP1852927595nres_d @ refine1072887134el_d_d @ B))) @ (relAPP1852927595nres_d @ refine1072887134el_d_d @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_param__bind)).
36.43/11.22	thf(3220,plain,((! [A:set_Product_prod_c_c,B:set_Product_prod_d_d]: (member405013761nres_d @ (produc1915822052nres_d @ (refine2092371655nd_c_d) @ (refine2092371655nd_c_d)) @ (relAPP720329701nres_d @ (relAPP2032940527nres_d @ fun_re1190945563nres_d @ (relAPP1067109483nres_c @ refine245117726el_c_c @ A)) @ (relAPP1899039865nres_d @ (relAPP990557099nres_d @ fun_re1740744275nres_d @ (relAPP941435307nres_d @ (relAPP508483205nres_d @ fun_re414971739nres_d @ A) @ (relAPP1852927595nres_d @ refine1072887134el_d_d @ B))) @ (relAPP1852927595nres_d @ (refine1072887134el_d_d) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])).
36.43/11.22	thf(114,axiom,((! [A:a,B:a,C:set_Product_prod_a_a,D:(a > refine432681134nres_b),E:(a > refine432681134nres_b),F:set_Pr896671762nres_b]: (((member1446466291nres_b @ (produc2130641934nres_b @ (D @ A) @ (autore956252284nres_b @ (autore781669463nres_b @ (autore1290907938nres_b @ (autore906565869nres_b @ (^ [G:a,H:(a > refine432681134nres_b)]: (H @ G))) @ (autore16598297nres_b @ (relAPP91071253nres_b @ (relAPP1740535279nres_b @ fun_re1165441639nres_b @ C) @ (relAPP2095637113nres_b @ (relAPP1293188647nres_b @ fun_re1579405647nres_b @ (relAPP1936960811nres_b @ (relAPP1536875909nres_b @ fun_re1837693787nres_b @ C) @ F)) @ F)))) @ B) @ E)) @ F) <= (! [G:a]: ((! [H:a]: ((member1446466291nres_b @ (produc2130641934nres_b @ (D @ H) @ (autore1390664424nres_b @ E @ G)) @ F) <= (member449909584od_a_a @ (product_Pair_a_a @ H @ G) @ C))) <= (autore1113312320RNAL_o @ (B = G))))) <= (member449909584od_a_a @ (product_Pair_a_a @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_autoref__Let__cong)).
36.43/11.22	thf(3104,plain,((! [A:a,B:a,C:set_Product_prod_a_a,D:(a > refine432681134nres_b),E:(a > refine432681134nres_b),F:set_Pr896671762nres_b]: ((member1446466291nres_b @ (produc2130641934nres_b @ (D @ A) @ (autore956252284nres_b @ (autore781669463nres_b @ (autore1290907938nres_b @ (autore906565869nres_b @ (^ [G:a,H:(a > refine432681134nres_b)]: (H @ G))) @ (autore16598297nres_b @ (relAPP91071253nres_b @ (relAPP1740535279nres_b @ fun_re1165441639nres_b @ C) @ (relAPP2095637113nres_b @ (relAPP1293188647nres_b @ fun_re1579405647nres_b @ (relAPP1936960811nres_b @ (relAPP1536875909nres_b @ fun_re1837693787nres_b @ C) @ F)) @ F)))) @ B) @ (E))) @ F) | ~ (! [G:a]: (! [H:a]: ((member1446466291nres_b @ (produc2130641934nres_b @ (D @ H) @ (autore1390664424nres_b @ (E) @ G)) @ F) | ~ (member449909584od_a_a @ (product_Pair_a_a @ H @ G) @ C)) | ~ (autore1113312320RNAL_o @ (B = G)))) | ~ (member449909584od_a_a @ (product_Pair_a_a @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])).
36.43/11.22	thf(154,axiom,((! [A:set_Product_prod_b_d]: (member776304031nres_d @ (produc847298946nres_d @ refine2063221605TURN_b @ refine2063221607TURN_d) @ (relAPP446928935nres_d @ (relAPP1806806463nres_d @ fun_re55451291nres_d @ A) @ (relAPP1313094511nres_d @ refine1564831968el_b_d @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_autoref__RETURN)).
36.43/11.22	thf(3235,plain,((! [A:set_Product_prod_b_d]: (member776304031nres_d @ (produc847298946nres_d @ (refine2063221605TURN_b) @ (refine2063221607TURN_d)) @ (relAPP446928935nres_d @ (relAPP1806806463nres_d @ fun_re55451291nres_d @ A) @ (relAPP1313094511nres_d @ (refine1564831968el_b_d) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])).
36.43/11.22	thf(401,plain,((~ (((^ [A:$o]: (A)) = (^ [A:$o]: (A))) => (~ (((~)) = (^ [A:$o]: (A))))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ ((~))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(402,plain,(((((~)) = (^ [A:$o]: (A))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ ((~))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))))),inference(simp,[status(thm)],[401])).
36.43/11.22	thf(749,plain,((((~)) = (^ [A:$o]: (A))) | (~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ ((~))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))))),inference(cnf,[status(esa)],[402])).
36.43/11.22	thf(1243,plain,((((~)) = (^ [A:$o]: (A))) | ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ ((~))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))))),inference(lifteq,[status(thm)],[749])).
36.43/11.22	thf(1244,plain,(((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ ((~))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))))),inference(simp,[status(thm)],[1243])).
36.43/11.22	thf(123,axiom,((! [A:a,B:(a > refine432681134nres_b)]: ((refine436832839nd_a_b @ (refine2063221604TURN_a @ A) @ B) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_nres__monad1)).
36.43/11.22	thf(3136,plain,((! [A:a,B:(a > refine432681134nres_b)]: ((refine436832839nd_a_b @ (refine2063221604TURN_a @ A) @ (B)) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])).
36.43/11.22	thf(288,plain,((~ (((^ [A:$o]: (A)) = (^ [A:$o]: (($true)))) => (~ ((^ [A:$o]: (($false))) = (^ [A:$o]: (($true)))))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (($true))))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(574,plain,(((^ [A:$o]: (($false))) = (^ [A:$o]: (($true)))) | (~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (($true))))))),inference(cnf,[status(esa)],[288])).
36.43/11.22	thf(994,plain,(((^ [A:$o]: (($false))) = (^ [A:$o]: (($true)))) | ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (($true)))))),inference(lifteq,[status(thm)],[574])).
36.43/11.22	thf(995,plain,(((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (($true)))))),inference(simp,[status(thm)],[994])).
36.43/11.22	thf(68,axiom,((! [A:a,B:c,C:set_Product_prod_a_c,D:(a > refine424419629nres_a),E:(c > refine440942639nres_c),F:set_Pr1128439124nres_c]: (((member1600573749nres_c @ (produc1153446608nres_c @ (D @ A) @ (autore2084714426nres_c @ (autore224164375nres_c @ (autore956520418nres_c @ (autore572178349nres_c @ (^ [G:c,H:(c > refine440942639nres_c)]: (H @ G))) @ (autore1545784985nres_c @ (relAPP998488211nres_c @ (relAPP1155943915nres_c @ fun_re418666087nres_c @ C) @ (relAPP1774615993nres_c @ (relAPP483050597nres_c @ fun_re1877185935nres_c @ (relAPP2018433511nres_c @ (relAPP173519167nres_c @ fun_re766812315nres_c @ C) @ F)) @ F)))) @ B) @ E)) @ F) <= (! [G:c]: ((! [H:a]: ((member1600573749nres_c @ (produc1153446608nres_c @ (D @ H) @ (autore1973425259nres_c @ E @ G)) @ F) <= (member466432594od_a_c @ (product_Pair_a_c @ H @ G) @ C))) <= (autore1113312320RNAL_o @ (B = G))))) <= (member466432594od_a_c @ (product_Pair_a_c @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_autoref__Let__cong)).
36.43/11.22	thf(2934,plain,((! [A:a,B:c,C:set_Product_prod_a_c,D:(a > refine424419629nres_a),E:(c > refine440942639nres_c),F:set_Pr1128439124nres_c]: ((member1600573749nres_c @ (produc1153446608nres_c @ (D @ A) @ (autore2084714426nres_c @ (autore224164375nres_c @ (autore956520418nres_c @ (autore572178349nres_c @ (^ [G:c,H:(c > refine440942639nres_c)]: (H @ G))) @ (autore1545784985nres_c @ (relAPP998488211nres_c @ (relAPP1155943915nres_c @ fun_re418666087nres_c @ C) @ (relAPP1774615993nres_c @ (relAPP483050597nres_c @ fun_re1877185935nres_c @ (relAPP2018433511nres_c @ (relAPP173519167nres_c @ fun_re766812315nres_c @ C) @ F)) @ F)))) @ B) @ (E))) @ F) | ~ (! [G:c]: (! [H:a]: ((member1600573749nres_c @ (produc1153446608nres_c @ (D @ H) @ (autore1973425259nres_c @ (E) @ G)) @ F) | ~ (member466432594od_a_c @ (product_Pair_a_c @ H @ G) @ C)) | ~ (autore1113312320RNAL_o @ (B = G)))) | ~ (member466432594od_a_c @ (product_Pair_a_c @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])).
36.43/11.22	thf(340,plain,((~ (((^ [A:$o]: (A)) = ((~))) => (~ (((~)) = ((~))))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ ((~))) = (product_Pair_o_o_o_o @ ((~)) @ ((~)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(341,plain,((((^ [A:$o]: (A)) = ((~))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ ((~))) = (product_Pair_o_o_o_o @ ((~)) @ ((~)))))),inference(simp,[status(thm)],[340])).
36.43/11.22	thf(873,plain,(((^ [A:$o]: (A)) = ((~))) | (~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ ((~))) = (product_Pair_o_o_o_o @ ((~)) @ ((~)))))),inference(cnf,[status(esa)],[341])).
36.43/11.22	thf(928,plain,((((~)) = (^ [A:$o]: (A))) | ((product_Pair_o_o_o_o @ ((~)) @ ((~))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ ((~))))),inference(lifteq,[status(thm)],[873])).
36.43/11.22	thf(929,plain,(((product_Pair_o_o_o_o @ ((~)) @ ((~))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ ((~))))),inference(simp,[status(thm)],[928])).
36.43/11.22	thf(32,axiom,((! [A:set_Pr2080238504nres_d]: ((collec554837959nres_d @ (^ [B:produc1677145714nres_d]: (member189721481nres_d @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_Collect__mem__eq)).
36.43/11.22	thf(2739,plain,((! [A:set_Pr2080238504nres_d]: ((collec554837959nres_d @ (^ [B:produc1677145714nres_d]: (member189721481nres_d @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])).
36.43/11.22	thf(49,axiom,((! [A:b,B:(b > refine424419629nres_a)]: ((refine1264602245nd_b_a @ (refine2063221605TURN_b @ A) @ B) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_nres__monad1)).
36.43/11.22	thf(2796,plain,((! [A:b,B:(b > refine424419629nres_a)]: ((refine1264602245nd_b_a @ (refine2063221605TURN_b @ A) @ (B)) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])).
36.43/11.22	thf(350,plain,((~ (((^ [A:$o]: (($true))) = (^ [A:$o]: (($false)))) => (~ (((~)) = (^ [A:$o]: (A))))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ ((~))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(760,plain,(((^ [A:$o]: (($true))) = (^ [A:$o]: (($false)))) | (~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ ((~))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A)))))),inference(cnf,[status(esa)],[350])).
36.43/11.22	thf(913,plain,(((^ [A:$o]: (($false))) = (^ [A:$o]: (($true)))) | ((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ ((~))))),inference(lifteq,[status(thm)],[760])).
36.43/11.22	thf(914,plain,(((product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($true))) @ ((~))))),inference(simp,[status(thm)],[913])).
36.43/11.22	thf(67,axiom,((! [A:produc1757587562nres_d]: ~ (! [B:((a > refine432681134nres_b) > refine432681134nres_b),C:((c > refine449204144nres_d) > refine449204144nres_d)]: (A != (produc2075136412nres_d @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_old_Oprod_Oexhaust)).
36.43/11.22	thf(2930,plain,((! [A:produc1757587562nres_d]: ~ (! [B:((a > refine432681134nres_b) > refine432681134nres_b),C:((c > refine449204144nres_d) > refine449204144nres_d)]: ~ (A = (produc2075136412nres_d @ (B) @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])).
36.43/11.22	thf(144,axiom,((! [A:(a > refine432681134nres_b),B:(c > refine449204144nres_d),C:set_Product_prod_a_c,D:set_Pr1640496404nres_d,E:a,F:c]: ((member936907743nres_d @ (produc210841666nres_d @ A @ B) @ (relAPP900772393nres_d @ (relAPP1270454529nres_d @ fun_re1760530651nres_d @ C) @ D)) => ((member466432594od_a_c @ (product_Pair_a_c @ E @ F) @ C) => (member1578111221nres_d @ (produc2147164944nres_d @ (A @ E) @ (B @ F)) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_tagged__fun__relD__rhs)).
36.43/11.22	thf(3203,plain,((! [A:(a > refine432681134nres_b),B:(c > refine449204144nres_d),C:set_Product_prod_a_c,D:set_Pr1640496404nres_d,E:a,F:c]: ((member936907743nres_d @ (produc210841666nres_d @ (A) @ (B)) @ (relAPP900772393nres_d @ (relAPP1270454529nres_d @ fun_re1760530651nres_d @ C) @ D)) => ((member466432594od_a_c @ (product_Pair_a_c @ E @ F) @ C) => (member1578111221nres_d @ (produc2147164944nres_d @ (A @ E) @ (B @ F)) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])).
36.43/11.22	thf(133,axiom,((! [A:set_Product_prod_b_d,B:set_Product_prod_b_d]: (member30090369nres_d @ (produc2035736420nres_d @ refine1264602246nd_b_b @ refine772657414nd_d_d) @ (relAPP691268197nres_d @ (relAPP1711926383nres_d @ fun_re1488118943nres_d @ (relAPP1313094511nres_d @ refine1564831968el_b_d @ A)) @ (relAPP1676317369nres_d @ (relAPP1405476647nres_d @ fun_re884113425nres_d @ (relAPP446928935nres_d @ (relAPP1806806463nres_d @ fun_re55451291nres_d @ A) @ (relAPP1313094511nres_d @ refine1564831968el_b_d @ B))) @ (relAPP1313094511nres_d @ refine1564831968el_b_d @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_param__bind)).
36.43/11.22	thf(3164,plain,((! [A:set_Product_prod_b_d,B:set_Product_prod_b_d]: (member30090369nres_d @ (produc2035736420nres_d @ (refine1264602246nd_b_b) @ (refine772657414nd_d_d)) @ (relAPP691268197nres_d @ (relAPP1711926383nres_d @ fun_re1488118943nres_d @ (relAPP1313094511nres_d @ refine1564831968el_b_d @ A)) @ (relAPP1676317369nres_d @ (relAPP1405476647nres_d @ fun_re884113425nres_d @ (relAPP446928935nres_d @ (relAPP1806806463nres_d @ fun_re55451291nres_d @ A) @ (relAPP1313094511nres_d @ refine1564831968el_b_d @ B))) @ (relAPP1313094511nres_d @ (refine1564831968el_b_d) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])).
36.43/11.22	thf(126,axiom,((! [A:c,B:(c > refine449204144nres_d)]: ((refine2092371655nd_c_d @ (refine2063221606TURN_c @ A) @ B) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_nres__monad1)).
36.43/11.22	thf(3145,plain,((! [A:c,B:(c > refine449204144nres_d)]: ((refine2092371655nd_c_d @ (refine2063221606TURN_c @ A) @ (B)) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])).
36.43/11.22	thf(87,axiom,((! [A:set_Pr613277282nres_d]: ((collec1321668993nres_d @ (^ [B:produc809931564nres_d]: (member660096835nres_d @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_Collect__mem__eq)).
36.43/11.22	thf(3015,plain,((! [A:set_Pr613277282nres_d]: ((collec1321668993nres_d @ (^ [B:produc809931564nres_d]: (member660096835nres_d @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])).
36.43/11.22	thf(466,plain,((~ ((((~)) = (^ [A:$o]: (($false)))) => (~ (((~)) = ((~))))) | ~ ((product_Pair_o_o_o_o @ ((~)) @ ((~))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ ((~)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(467,plain,(((((~)) = (^ [A:$o]: (($false)))) | ~ ((product_Pair_o_o_o_o @ ((~)) @ ((~))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ ((~)))))),inference(simp,[status(thm)],[466])).
36.43/11.22	thf(666,plain,((((~)) = (^ [A:$o]: (($false)))) | (~ ((product_Pair_o_o_o_o @ ((~)) @ ((~))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ ((~)))))),inference(cnf,[status(esa)],[467])).
36.43/11.22	thf(918,plain,((((~)) = (^ [A:$o]: (($false)))) | ((product_Pair_o_o_o_o @ ((~)) @ ((~))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ ((~))))),inference(lifteq,[status(thm)],[666])).
36.43/11.22	thf(12,axiom,((! [A:(a > ($o > $o)),B:(c > ($o > $o)),C:set_Product_prod_a_c,D:set_Pr934623755_o_o_o,E:a,F:c]: (((member466432594od_a_c @ (product_Pair_a_c @ E @ F) @ C) => (member250723412_o_o_o @ (product_Pair_o_o_o_o @ (autoref_APP_a_o_o @ A @ E) @ (autoref_APP_c_o_o @ B @ F)) @ D)) <= (member1051493202_c_o_o @ (produc1393542937_c_o_o @ A @ B) @ (relAPP1525934692_c_o_o @ (relAPP589338430_c_o_o @ fun_rel_a_c_o_o_o_o @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_autoref__APP)).
36.43/11.22	thf(2040,plain,((! [A:(a > ($o > $o)),B:(c > ($o > $o)),C:set_Product_prod_a_c,D:set_Pr934623755_o_o_o,E:a,F:c]: (((member466432594od_a_c @ (product_Pair_a_c @ E @ F) @ C) => (member250723412_o_o_o @ (product_Pair_o_o_o_o @ (autoref_APP_a_o_o @ A @ E) @ (autoref_APP_c_o_o @ B @ F)) @ D)) | ~ (member1051493202_c_o_o @ (produc1393542937_c_o_o @ (A) @ (B)) @ (relAPP1525934692_c_o_o @ (relAPP589338430_c_o_o @ fun_rel_a_c_o_o_o_o @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
36.43/11.22	thf(94,axiom,((! [A:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)),B:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d)),C:set_Pr613277282nres_d,D:(((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d)) > $o)]: ((member660096835nres_d @ (produc1910095910nres_d @ A @ B) @ C) => ((D @ B) => (refine1711024813nres_d @ C @ D @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_lift__assnI)).
36.43/11.22	thf(3045,plain,((! [A:((a > refine432681134nres_b) > (((a > refine432681134nres_b) > refine432681134nres_b) > refine432681134nres_b)),B:((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d)),C:set_Pr613277282nres_d,D:(((c > refine449204144nres_d) > (((c > refine449204144nres_d) > refine449204144nres_d) > refine449204144nres_d)) > $o)]: ((member660096835nres_d @ (produc1910095910nres_d @ (A) @ (B)) @ C) => ((D @ (B)) => (refine1711024813nres_d @ C @ (D) @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])).
36.43/11.22	thf(36,axiom,((! [A:(a > ((a > refine432681134nres_b) > refine432681134nres_b)),B:(c > ((c > refine449204144nres_d) > refine449204144nres_d)),C:set_Pr2080238504nres_d,D:((c > ((c > refine449204144nres_d) > refine449204144nres_d)) > $o)]: (((refine408412177nres_d @ C @ D @ A) <= (D @ B)) <= (member189721481nres_d @ (produc627868012nres_d @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_lift__assnI)).
36.43/11.22	thf(2751,plain,((! [A:(a > ((a > refine432681134nres_b) > refine432681134nres_b)),B:(c > ((c > refine449204144nres_d) > refine449204144nres_d)),C:set_Pr2080238504nres_d,D:((c > ((c > refine449204144nres_d) > refine449204144nres_d)) > $o)]: ((refine408412177nres_d @ C @ (D) @ (A)) | ~ (D @ (B)) | ~ (member189721481nres_d @ (produc627868012nres_d @ (A) @ (B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])).
36.43/11.22	thf(2800,plain,(((refine746536475nres_d) = (^ [A:set_Pr589481214nres_d,B:((c > refine449204144nres_d) > $o),C:(a > refine432681134nres_b)]: ? [D:(c > refine449204144nres_d)]: ((B @ D) & (member936907743nres_d @ (produc210841666nres_d @ C @ D) @ A))))),inference(lifteq,[status(thm)],[2799])).
36.43/11.22	thf(25,axiom,((! [A:refine440942639nres_c]: ((refine2092371654nd_c_c @ A @ refine2063221606TURN_c) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_nres__monad2)).
36.43/11.22	thf(2714,plain,((! [A:refine440942639nres_c]: ((refine2092371654nd_c_c @ A @ (refine2063221606TURN_c)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])).
36.43/11.22	thf(141,axiom,((! [A:set_Product_prod_a_c,B:set_Product_prod_a_c]: (member1751415169nres_c @ (produc2073916516nres_c @ refine436832838nd_a_a @ refine2092371654nd_c_c) @ (relAPP765626983nres_c @ (relAPP177337967nres_c @ fun_re1915547295nres_c @ (relAPP527276399nres_c @ refine737062560el_a_c @ A)) @ (relAPP1774615993nres_c @ (relAPP483050597nres_c @ fun_re1877185935nres_c @ (relAPP2018433511nres_c @ (relAPP173519167nres_c @ fun_re766812315nres_c @ A) @ (relAPP527276399nres_c @ refine737062560el_a_c @ B))) @ (relAPP527276399nres_c @ refine737062560el_a_c @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_param__bind)).
36.43/11.22	thf(3196,plain,((! [A:set_Product_prod_a_c,B:set_Product_prod_a_c]: (member1751415169nres_c @ (produc2073916516nres_c @ (refine436832838nd_a_a) @ (refine2092371654nd_c_c)) @ (relAPP765626983nres_c @ (relAPP177337967nres_c @ fun_re1915547295nres_c @ (relAPP527276399nres_c @ refine737062560el_a_c @ A)) @ (relAPP1774615993nres_c @ (relAPP483050597nres_c @ fun_re1877185935nres_c @ (relAPP2018433511nres_c @ (relAPP173519167nres_c @ fun_re766812315nres_c @ A) @ (relAPP527276399nres_c @ refine737062560el_a_c @ B))) @ (relAPP527276399nres_c @ (refine737062560el_a_c) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])).
36.43/11.22	thf(54,axiom,((! [A:a,B:c,C:set_Product_prod_a_c,D:a]: ((member466432594od_a_c @ (product_Pair_a_c @ A @ B) @ C) => ((autore1904863386L_EQ_a @ A @ D) => (member466432594od_a_c @ (product_Pair_a_c @ D @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_autoref__REMOVE__INTERNAL__EQ)).
36.43/11.22	thf(2810,plain,((! [A:a,B:c,C:set_Product_prod_a_c,D:a]: ((member466432594od_a_c @ (product_Pair_a_c @ A @ B) @ C) => ((autore1904863386L_EQ_a @ A @ D) => (member466432594od_a_c @ (product_Pair_a_c @ D @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])).
36.43/11.22	thf(173,plain,((~ (((^ [A:$o]: (A)) = ((~))) => (~ (((~)) = (^ [A:$o]: (A))))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ ((~))) = (product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(714,plain,((((~)) = (^ [A:$o]: (A))) | (~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ ((~))) = (product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A)))))),inference(cnf,[status(esa)],[173])).
36.43/11.22	thf(1018,plain,((((~)) = (^ [A:$o]: (A))) | ((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ ((~))))),inference(lifteq,[status(thm)],[714])).
36.43/11.22	thf(1019,plain,(((product_Pair_o_o_o_o @ ((~)) @ (^ [A:$o]: (A))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ ((~))))),inference(simp,[status(thm)],[1018])).
36.43/11.22	thf(160,plain,((! [A:(a > refine432681134nres_b),B:(a > refine432681134nres_b),C:set_Pr896671762nres_b]: ((member369653087nres_b @ (produc809128386nres_b @ (A) @ (B)) @ (relAPP1936960811nres_b @ (relAPP1536875909nres_b @ fun_re1837693787nres_b @ id_a) @ C)) => (! [D:refine432681134nres_b,E:a]: ((D = (B @ E)) => (member1446466291nres_b @ (produc2130641934nres_b @ (A @ E) @ D) @ C)))))),inference(miniscope,[status(thm)],[159])).
36.43/11.22	thf(161,plain,(! [E:a,D:refine432681134nres_b,C:set_Pr896671762nres_b,B:(a > refine432681134nres_b),A:(a > refine432681134nres_b)] : ((~ (member369653087nres_b @ (produc809128386nres_b @ (A) @ (B)) @ (relAPP1936960811nres_b @ (relAPP1536875909nres_b @ fun_re1837693787nres_b @ id_a) @ C))) | (~ (D = (B @ E))) | (member1446466291nres_b @ (produc2130641934nres_b @ (A @ E) @ D) @ C))),inference(cnf,[status(esa)],[160])).
36.43/11.22	thf(162,plain,(! [E:a,D:refine432681134nres_b,C:set_Pr896671762nres_b,B:(a > refine432681134nres_b),A:(a > refine432681134nres_b)] : ((D != (B @ E)) | (~ (member369653087nres_b @ (produc809128386nres_b @ (A) @ (B)) @ (relAPP1936960811nres_b @ (relAPP1536875909nres_b @ fun_re1837693787nres_b @ id_a) @ C))) | (member1446466291nres_b @ (produc2130641934nres_b @ (A @ E) @ D) @ C))),inference(lifteq,[status(thm)],[161])).
36.43/11.22	thf(163,plain,(! [D:a,C:set_Pr896671762nres_b,B:(a > refine432681134nres_b),A:(a > refine432681134nres_b)] : ((~ (member369653087nres_b @ (produc809128386nres_b @ (A) @ (B)) @ (relAPP1936960811nres_b @ (relAPP1536875909nres_b @ fun_re1837693787nres_b @ id_a) @ C))) | (member1446466291nres_b @ (produc2130641934nres_b @ (A @ D) @ (B @ D)) @ C))),inference(simp,[status(thm)],[162])).
36.43/11.22	thf(231,plain,((~ (((^ [A:$o]: (A)) = (^ [A:$o]: (A))) => (~ ((^ [A:$o]: (($false))) = (^ [A:$o]: (A))))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))))),inference(instance,[status(thm)],[169])).
36.43/11.22	thf(232,plain,((((^ [A:$o]: (($false))) = (^ [A:$o]: (A))) | ~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))))),inference(simp,[status(thm)],[231])).
36.43/11.22	thf(906,plain,(((^ [A:$o]: (($false))) = (^ [A:$o]: (A))) | (~ ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))))),inference(cnf,[status(esa)],[232])).
36.43/11.22	thf(1129,plain,(((^ [A:$o]: (($false))) = (^ [A:$o]: (A))) | ((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))) != (product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))))),inference(lifteq,[status(thm)],[906])).
36.43/11.22	thf(37,axiom,((! [A:set_Product_prod_a_a,B:set_Pr896671762nres_b]: ((A = id_a) => (((relAPP1936960811nres_b @ (relAPP1536875909nres_b @ fun_re1837693787nres_b @ A) @ B) = id_a_R351071993nres_b) <= (B = id_Ref1256934482nres_b))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_fun__rel__id)).
36.43/11.22	thf(2754,plain,((! [A:set_Product_prod_a_a,B:set_Pr896671762nres_b]: ((A = id_a) => (((relAPP1936960811nres_b @ (relAPP1536875909nres_b @ fun_re1837693787nres_b @ A) @ B) = id_a_R351071993nres_b) | ~ (B = id_Ref1256934482nres_b))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])).
36.43/11.22	thf(111,axiom,((! [A:(b > refine424419629nres_a),B:(d > refine440942639nres_c),C:set_Product_prod_b_d,D:set_Pr1128439124nres_c,E:b,F:d]: ((member2086976541nres_c @ (produc316577664nres_c @ A @ B) @ (relAPP1564590053nres_c @ (relAPP709871101nres_c @ fun_re1209216603nres_c @ C) @ D)) => ((member1600573749nres_c @ (produc1153446608nres_c @ (autore1669652584nres_a @ A @ E) @ (autore113191276nres_c @ B @ F)) @ D) <= (member1302463506od_b_d @ (product_Pair_b_d @ E @ F) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_autoref__APP)).
36.43/11.22	thf(3096,plain,((! [A:(b > refine424419629nres_a),B:(d > refine440942639nres_c),C:set_Product_prod_b_d,D:set_Pr1128439124nres_c,E:b,F:d]: ((member2086976541nres_c @ (produc316577664nres_c @ (A) @ (B)) @ (relAPP1564590053nres_c @ (relAPP709871101nres_c @ fun_re1209216603nres_c @ C) @ D)) => ((member1600573749nres_c @ (produc1153446608nres_c @ (autore1669652584nres_a @ (A) @ E) @ (autore113191276nres_c @ (B) @ F)) @ D) | ~ (member1302463506od_b_d @ (product_Pair_b_d @ E @ F) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])).
36.43/11.22	thf(83,axiom,((! [A:a,B:c,C:a,D:c]: ((~ ((A = C) => (B != D))) <= ((product_Pair_a_c @ A @ B) = (product_Pair_a_c @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_Pair__inject)).
36.43/11.22	thf(2998,plain,((! [A:a,B:c,C:a,D:c]: (~ ((A = C) => (~ (B = D))) | ~ ((product_Pair_a_c @ A @ B) = (product_Pair_a_c @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])).
36.43/11.22	thf(1518,plain,((((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A)))) = (((^ [A:$o]: (A)) = (^ [A:$o]: (($false)))) & ((^ [A:$o]: (A)) = (^ [A:$o]: (A)))))),inference(instance,[status(thm)],[1419])).
36.43/11.22	thf(1519,plain,((((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A)))) = ((^ [A:$o]: (A)) = (^ [A:$o]: (($false)))))),inference(simp,[status(thm)],[1518])).
36.43/11.22	thf(1870,plain,((((product_Pair_o_o_o_o @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))) = (product_Pair_o_o_o_o @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A)))) = ((^ [A:$o]: (A)) = (^ [A:$o]: (($false)))))),inference(lifteq,[status(thm)],[1519])).
36.43/11.22	thf(5501,plain,(($false)),inference(e,[status(thm)],[3021,1168,3008,2778,3072,1406,3230,2953,3460,2676,3012,1041,3103,2723,2985,2819,1228,2735,3061,2708,3148,917,3089,949,2703,1055,1409,3125,1826,3099,969,3084,1100,2829,1922,2691,164,3075,2925,3093,2950,1415,981,3036,3226,2772,3157,988,2799,2804,2965,2922,1206,3186,910,952,3233,2986,3166,3191,3198,3033,2769,2946,2801,156,2973,3218,3102,2726,3078,169,3119,3087,3018,2666,1039,1155,2781,1419,1150,3126,2836,3222,2813,2766,3064,3201,3109,3005,2788,2761,921,2748,2793,2995,2043,3183,965,3130,3042,2717,2941,3070,2970,2791,3081,2674,2827,3051,1058,2759,2706,919,3091,3719,159,2679,3155,2987,2669,2943,3160,1877,1080,2742,3133,4064,1862,915,2664,155,3150,3219,2824,912,3159,3142,2967,2816,3193,1166,3206,3161,3048,1049,2942,1003,1070,3129,3228,2821,3058,2720,2747,3114,3722,2675,2838,2711,3224,978,1008,2728,2939,3071,3124,2992,2807,3156,3168,3139,3457,3092,3067,2828,3171,1412,3928,2775,3039,1010,2919,2707,961,158,3220,3104,3235,1244,3136,995,2934,929,2739,2796,914,2930,3203,3164,3145,3015,918,2746,2040,3045,2751,2800,2714,3196,2810,1019,163,3128,1129,2754,3096,2998,1870])).
36.43/11.22	% SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
36.43/11.22	% [INFO] 	 Killing All external provers ... 
36.52/11.26	EOF