TSTP Solution File: KRS116+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS116+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 17:44:49 EDT 2022
% Result : Unsatisfiable 0.14s 0.35s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : KRS116+1 : TPTP v8.1.0. Released v3.1.0.
% 0.04/0.09 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.29 % Computer : n029.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Thu Sep 1 09:44:58 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.30 Usage: tptp [options] [-file:]file
% 0.09/0.30 -h, -? prints this message.
% 0.09/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.30 -m, -model generate model.
% 0.09/0.30 -p, -proof generate proof.
% 0.09/0.30 -c, -core generate unsat core of named formulas.
% 0.09/0.30 -st, -statistics display statistics.
% 0.09/0.30 -t:timeout set timeout (in second).
% 0.09/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.30 -<param>:<value> configuration parameter and value.
% 0.09/0.30 -o:<output-file> file to place output in.
% 0.14/0.35 % SZS status Unsatisfiable
% 0.14/0.35 % SZS output start Proof
% 0.14/0.35 tff(caxcomp_type, type, (
% 0.14/0.35 caxcomp: $i > $o)).
% 0.14/0.35 tff(i2003_11_14_17_21_33997_type, type, (
% 0.14/0.35 i2003_11_14_17_21_33997: $i)).
% 0.14/0.35 tff(ra_Px1_type, type, (
% 0.14/0.35 ra_Px1: ( $i * $i ) > $o)).
% 0.14/0.35 tff(tptp_fun_Y0_2_type, type, (
% 0.14/0.35 tptp_fun_Y0_2: $i > $i)).
% 0.14/0.35 tff(ca_type, type, (
% 0.14/0.35 ca: $i > $o)).
% 0.14/0.35 tff(tptp_fun_Y_1_type, type, (
% 0.14/0.35 tptp_fun_Y_1: $i > $i)).
% 0.14/0.35 tff(cUnsatisfiable_type, type, (
% 0.14/0.35 cUnsatisfiable: $i > $o)).
% 0.14/0.35 tff(rinvS_type, type, (
% 0.14/0.35 rinvS: ( $i * $i ) > $o)).
% 0.14/0.35 tff(tptp_fun_Y_0_type, type, (
% 0.14/0.35 tptp_fun_Y_0: $i > $i)).
% 0.14/0.35 tff(ca_Vx6_type, type, (
% 0.14/0.35 ca_Vx6: $i > $o)).
% 0.14/0.35 tff(tptp_fun_Y_10_type, type, (
% 0.14/0.35 tptp_fun_Y_10: $i > $i)).
% 0.14/0.35 tff(rinvP_type, type, (
% 0.14/0.35 rinvP: ( $i * $i ) > $o)).
% 0.14/0.35 tff(tptp_fun_Y_5_type, type, (
% 0.14/0.35 tptp_fun_Y_5: $i > $i)).
% 0.14/0.35 tff(ca_Vx7_type, type, (
% 0.14/0.35 ca_Vx7: $i > $o)).
% 0.14/0.35 tff(tptp_fun_Y_11_type, type, (
% 0.14/0.35 tptp_fun_Y_11: $i > $i)).
% 0.14/0.35 tff(rinvR_type, type, (
% 0.14/0.35 rinvR: ( $i * $i ) > $o)).
% 0.14/0.35 tff(tptp_fun_Y_4_type, type, (
% 0.14/0.35 tptp_fun_Y_4: $i > $i)).
% 0.14/0.35 tff(cc_type, type, (
% 0.14/0.35 cc: $i > $o)).
% 0.14/0.35 tff(tptp_fun_Y_3_type, type, (
% 0.14/0.35 tptp_fun_Y_3: $i > $i)).
% 0.14/0.35 tff(rr_type, type, (
% 0.14/0.35 rr: ( $i * $i ) > $o)).
% 0.14/0.35 tff(ca_Vx5_type, type, (
% 0.14/0.35 ca_Vx5: $i > $o)).
% 0.14/0.35 tff(tptp_fun_Y_8_type, type, (
% 0.14/0.35 tptp_fun_Y_8: $i > $i)).
% 0.14/0.35 tff(rp_type, type, (
% 0.14/0.35 rp: ( $i * $i ) > $o)).
% 0.14/0.35 tff(ca_Vx4_type, type, (
% 0.14/0.35 ca_Vx4: $i > $o)).
% 0.14/0.35 tff(ca_Vx3_type, type, (
% 0.14/0.35 ca_Vx3: $i > $o)).
% 0.14/0.35 tff(cowlThing_type, type, (
% 0.14/0.35 cowlThing: $i > $o)).
% 0.14/0.35 tff(ca_Ax2_type, type, (
% 0.14/0.35 ca_Ax2: $i > $o)).
% 0.14/0.35 tff(tptp_fun_Y_9_type, type, (
% 0.14/0.35 tptp_fun_Y_9: $i > $i)).
% 0.14/0.35 tff(tptp_fun_Y_7_type, type, (
% 0.14/0.35 tptp_fun_Y_7: $i > $i)).
% 0.14/0.35 tff(tptp_fun_Y_6_type, type, (
% 0.14/0.35 tptp_fun_Y_6: $i > $i)).
% 0.14/0.35 tff(rs_type, type, (
% 0.14/0.35 rs: ( $i * $i ) > $o)).
% 0.14/0.35 tff(1,assumption,((~((~caxcomp(i2003_11_14_17_21_33997)) | ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y0_2(i2003_11_14_17_21_33997)))) | (~(caxcomp(i2003_11_14_17_21_33997) | ![Y0: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y0))))), introduced(assumption)).
% 0.14/0.35 tff(2,plain,
% 0.14/0.35 (^[X: $i] : refl((~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(3,plain,
% 0.14/0.35 (![X: $i] : (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> ![X: $i] : (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[2])).
% 0.14/0.35 tff(4,plain,
% 0.14/0.35 (^[X: $i] : rewrite((~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(5,plain,
% 0.14/0.35 (![X: $i] : (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> ![X: $i] : (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[4])).
% 0.14/0.35 tff(6,plain,
% 0.14/0.35 (![X: $i] : (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> ![X: $i] : (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.14/0.35 inference(transitivity,[status(thm)],[5, 3])).
% 0.14/0.35 tff(7,plain,
% 0.14/0.35 (^[X: $i] : trans(monotonicity(rewrite((caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))) <=> (caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))), ((((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X))) & (caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> (((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X))) & (caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))), rewrite((((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X))) & (caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))), ((((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X))) & (caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(8,plain,
% 0.14/0.35 (![X: $i] : (((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X))) & (caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> ![X: $i] : (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[7])).
% 0.14/0.35 tff(9,plain,
% 0.14/0.35 (![X: $i] : (caxcomp(X) <=> ?[Y0: $i] : ra_Px1(X, Y0)) <=> ![X: $i] : (caxcomp(X) <=> ?[Y0: $i] : ra_Px1(X, Y0))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(10,axiom,(![X: $i] : (caxcomp(X) <=> ?[Y0: $i] : ra_Px1(X, Y0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_5')).
% 0.14/0.35 tff(11,plain,
% 0.14/0.35 (![X: $i] : (caxcomp(X) <=> ?[Y0: $i] : ra_Px1(X, Y0))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.14/0.35 tff(12,plain,(
% 0.14/0.35 ![X: $i] : (((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X))) & (caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))),
% 0.14/0.35 inference(skolemize,[status(sab)],[11])).
% 0.14/0.35 tff(13,plain,
% 0.14/0.35 (![X: $i] : (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.14/0.35 tff(14,plain,
% 0.14/0.35 (![X: $i] : (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.14/0.35 tff(15,plain,
% 0.14/0.35 ((~![X: $i] : (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))) | (~((~((~caxcomp(i2003_11_14_17_21_33997)) | ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y0_2(i2003_11_14_17_21_33997)))) | (~(caxcomp(i2003_11_14_17_21_33997) | ![Y0: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y0))))))),
% 0.14/0.35 inference(quant_inst,[status(thm)],[])).
% 0.14/0.35 tff(16,plain,
% 0.14/0.35 ($false),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[15, 14, 1])).
% 0.14/0.35 tff(17,plain,(~((~((~caxcomp(i2003_11_14_17_21_33997)) | ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y0_2(i2003_11_14_17_21_33997)))) | (~(caxcomp(i2003_11_14_17_21_33997) | ![Y0: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y0)))))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.35 tff(18,plain,
% 0.14/0.35 (((~((~caxcomp(i2003_11_14_17_21_33997)) | ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y0_2(i2003_11_14_17_21_33997)))) | (~(caxcomp(i2003_11_14_17_21_33997) | ![Y0: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y0))))) | ((~caxcomp(i2003_11_14_17_21_33997)) | ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y0_2(i2003_11_14_17_21_33997)))),
% 0.14/0.35 inference(tautology,[status(thm)],[])).
% 0.14/0.35 tff(19,plain,
% 0.14/0.35 ((~caxcomp(i2003_11_14_17_21_33997)) | ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y0_2(i2003_11_14_17_21_33997))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.14/0.35 tff(20,assumption,(ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y0_2(i2003_11_14_17_21_33997))), introduced(assumption)).
% 0.14/0.35 tff(21,plain,
% 0.14/0.35 (^[X: $i] : rewrite((~((~((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))))) <=> (~((~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y)))))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(22,plain,
% 0.14/0.35 (![X: $i] : (~((~((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))))) <=> ![X: $i] : (~((~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[21])).
% 0.14/0.35 tff(23,plain,
% 0.14/0.35 (^[X: $i] : refl((~((~((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))))) <=> (~((~((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(24,plain,
% 0.14/0.35 (![X: $i] : (~((~((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))))) <=> ![X: $i] : (~((~((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X))))))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[23])).
% 0.14/0.35 tff(25,plain,
% 0.14/0.35 (^[X: $i] : rewrite((~((~((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))))) <=> (~((~((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(26,plain,
% 0.14/0.35 (![X: $i] : (~((~((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))))) <=> ![X: $i] : (~((~((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X))))))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[25])).
% 0.14/0.35 tff(27,plain,
% 0.14/0.35 (![X: $i] : (~((~((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))))) <=> ![X: $i] : (~((~((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X))))))),
% 0.14/0.35 inference(transitivity,[status(thm)],[26, 24])).
% 0.14/0.35 tff(28,plain,
% 0.14/0.35 (^[X: $i] : trans(monotonicity(rewrite(((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y))) <=> ((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y)))), ((((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y))) & (ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) <=> (((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y))) & (ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))))), rewrite((((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y))) & (ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) <=> (~((~((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X))))))), ((((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y))) & (ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) <=> (~((~((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X))))))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(29,plain,
% 0.14/0.35 (![X: $i] : (((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y))) & (ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) <=> ![X: $i] : (~((~((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X))))))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[28])).
% 0.14/0.35 tff(30,plain,
% 0.14/0.35 (![X: $i] : (ca(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> ![X: $i] : (ca(X) <=> (~?[Y: $i] : ra_Px1(X, Y)))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(31,axiom,(![X: $i] : (ca(X) <=> (~?[Y: $i] : ra_Px1(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_4')).
% 0.14/0.35 tff(32,plain,
% 0.14/0.35 (![X: $i] : (ca(X) <=> (~?[Y: $i] : ra_Px1(X, Y)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.14/0.35 tff(33,plain,(
% 0.14/0.35 ![X: $i] : (((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y))) & (ca(X) | ra_Px1(X, tptp_fun_Y_1(X))))),
% 0.14/0.35 inference(skolemize,[status(sab)],[32])).
% 0.14/0.35 tff(34,plain,
% 0.14/0.35 (![X: $i] : (~((~((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X))))))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.14/0.35 tff(35,plain,
% 0.14/0.35 (![X: $i] : (~((~((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X))))))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.14/0.35 tff(36,plain,
% 0.14/0.35 (![X: $i] : (~((~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[35, 22])).
% 0.14/0.35 tff(37,plain,
% 0.14/0.35 ((~![X: $i] : (~((~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))) | (~((~(ca(i2003_11_14_17_21_33997) | ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y_1(i2003_11_14_17_21_33997)))) | (~((~ca(i2003_11_14_17_21_33997)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y))))))),
% 0.14/0.35 inference(quant_inst,[status(thm)],[])).
% 0.14/0.35 tff(38,plain,
% 0.14/0.35 (~((~(ca(i2003_11_14_17_21_33997) | ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y_1(i2003_11_14_17_21_33997)))) | (~((~ca(i2003_11_14_17_21_33997)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y)))))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.14/0.35 tff(39,plain,
% 0.14/0.35 (((~(ca(i2003_11_14_17_21_33997) | ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y_1(i2003_11_14_17_21_33997)))) | (~((~ca(i2003_11_14_17_21_33997)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y))))) | ((~ca(i2003_11_14_17_21_33997)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y)))),
% 0.14/0.35 inference(tautology,[status(thm)],[])).
% 0.14/0.35 tff(40,plain,
% 0.14/0.35 ((~ca(i2003_11_14_17_21_33997)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.14/0.35 tff(41,plain,
% 0.14/0.35 (cUnsatisfiable(i2003_11_14_17_21_33997) <=> cUnsatisfiable(i2003_11_14_17_21_33997)),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(42,axiom,(cUnsatisfiable(i2003_11_14_17_21_33997)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_17')).
% 0.14/0.35 tff(43,plain,
% 0.14/0.35 (cUnsatisfiable(i2003_11_14_17_21_33997)),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.14/0.35 tff(44,plain,
% 0.14/0.35 (^[X: $i] : refl((ca(X) | (~cUnsatisfiable(X))) <=> (ca(X) | (~cUnsatisfiable(X))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(45,plain,
% 0.14/0.35 (![X: $i] : (ca(X) | (~cUnsatisfiable(X))) <=> ![X: $i] : (ca(X) | (~cUnsatisfiable(X)))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[44])).
% 0.14/0.35 tff(46,plain,
% 0.14/0.35 (![X: $i] : (ca(X) | (~cUnsatisfiable(X))) <=> ![X: $i] : (ca(X) | (~cUnsatisfiable(X)))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(47,plain,
% 0.14/0.35 (^[X: $i] : rewrite((cUnsatisfiable(X) => ca(X)) <=> (ca(X) | (~cUnsatisfiable(X))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(48,plain,
% 0.14/0.35 (![X: $i] : (cUnsatisfiable(X) => ca(X)) <=> ![X: $i] : (ca(X) | (~cUnsatisfiable(X)))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[47])).
% 0.14/0.35 tff(49,axiom,(![X: $i] : (cUnsatisfiable(X) => ca(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_2')).
% 0.14/0.35 tff(50,plain,
% 0.14/0.35 (![X: $i] : (ca(X) | (~cUnsatisfiable(X)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.14/0.35 tff(51,plain,
% 0.14/0.35 (![X: $i] : (ca(X) | (~cUnsatisfiable(X)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.14/0.35 tff(52,plain,(
% 0.14/0.35 ![X: $i] : (ca(X) | (~cUnsatisfiable(X)))),
% 0.14/0.35 inference(skolemize,[status(sab)],[51])).
% 0.14/0.35 tff(53,plain,
% 0.14/0.35 (![X: $i] : (ca(X) | (~cUnsatisfiable(X)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.14/0.35 tff(54,plain,
% 0.14/0.35 (((~![X: $i] : (ca(X) | (~cUnsatisfiable(X)))) | (ca(i2003_11_14_17_21_33997) | (~cUnsatisfiable(i2003_11_14_17_21_33997)))) <=> ((~![X: $i] : (ca(X) | (~cUnsatisfiable(X)))) | ca(i2003_11_14_17_21_33997) | (~cUnsatisfiable(i2003_11_14_17_21_33997)))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(55,plain,
% 0.14/0.35 ((~![X: $i] : (ca(X) | (~cUnsatisfiable(X)))) | (ca(i2003_11_14_17_21_33997) | (~cUnsatisfiable(i2003_11_14_17_21_33997)))),
% 0.14/0.35 inference(quant_inst,[status(thm)],[])).
% 0.14/0.35 tff(56,plain,
% 0.14/0.35 ((~![X: $i] : (ca(X) | (~cUnsatisfiable(X)))) | ca(i2003_11_14_17_21_33997) | (~cUnsatisfiable(i2003_11_14_17_21_33997))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.14/0.35 tff(57,plain,
% 0.14/0.35 (ca(i2003_11_14_17_21_33997)),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[56, 53, 43])).
% 0.14/0.35 tff(58,plain,
% 0.14/0.35 ((~((~ca(i2003_11_14_17_21_33997)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y)))) | (~ca(i2003_11_14_17_21_33997)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y))),
% 0.14/0.35 inference(tautology,[status(thm)],[])).
% 0.14/0.35 tff(59,plain,
% 0.14/0.35 ((~((~ca(i2003_11_14_17_21_33997)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y)))) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.14/0.35 tff(60,plain,
% 0.14/0.35 (![Y: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[59, 40])).
% 0.14/0.35 tff(61,plain,
% 0.14/0.35 ((~![Y: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y))) | (~ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y0_2(i2003_11_14_17_21_33997)))),
% 0.14/0.35 inference(quant_inst,[status(thm)],[])).
% 0.14/0.35 tff(62,plain,
% 0.14/0.35 ($false),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[61, 60, 20])).
% 0.14/0.35 tff(63,plain,(~ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y0_2(i2003_11_14_17_21_33997))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.35 tff(64,plain,
% 0.14/0.35 ((~((~caxcomp(i2003_11_14_17_21_33997)) | ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y0_2(i2003_11_14_17_21_33997)))) | (~caxcomp(i2003_11_14_17_21_33997)) | ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y0_2(i2003_11_14_17_21_33997))),
% 0.14/0.35 inference(tautology,[status(thm)],[])).
% 0.14/0.35 tff(65,plain,
% 0.14/0.35 ((~((~caxcomp(i2003_11_14_17_21_33997)) | ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y0_2(i2003_11_14_17_21_33997)))) | (~caxcomp(i2003_11_14_17_21_33997))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.14/0.35 tff(66,plain,
% 0.14/0.35 (~caxcomp(i2003_11_14_17_21_33997)),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[65, 19])).
% 0.14/0.35 tff(67,plain,
% 0.14/0.35 (^[X: $i] : refl((~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X))))))))) <=> (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X))))))))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(68,plain,
% 0.14/0.36 (![X: $i] : (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X))))))))) <=> ![X: $i] : (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X)))))))))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[67])).
% 0.14/0.36 tff(69,plain,
% 0.14/0.36 (^[X: $i] : rewrite((~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X))))))))) <=> (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X))))))))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(70,plain,
% 0.14/0.36 (![X: $i] : (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X))))))))) <=> ![X: $i] : (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X)))))))))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[69])).
% 0.14/0.36 tff(71,plain,
% 0.14/0.36 (![X: $i] : (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X))))))))) <=> ![X: $i] : (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X)))))))))),
% 0.14/0.36 inference(transitivity,[status(thm)],[70, 68])).
% 0.14/0.36 tff(72,plain,
% 0.14/0.36 (^[X: $i] : trans(monotonicity(rewrite(((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y)))) <=> ((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))), ((((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y)))) & (ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X))))))) <=> (((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y)))) & (ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X))))))))), rewrite((((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y)))) & (ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X))))))) <=> (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X)))))))))), ((((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y)))) & (ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X))))))) <=> (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X)))))))))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(73,plain,
% 0.14/0.36 (![X: $i] : (((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y)))) & (ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X))))))) <=> ![X: $i] : (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X)))))))))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[72])).
% 0.14/0.36 tff(74,plain,
% 0.14/0.36 (![X: $i] : (ca_Vx6(X) <=> ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y)))) <=> ![X: $i] : (ca_Vx6(X) <=> ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))),
% 0.14/0.36 inference(rewrite,[status(thm)],[])).
% 0.14/0.36 tff(75,plain,
% 0.14/0.36 (^[X: $i] : rewrite((ca_Vx6(X) <=> ![Y: $i] : (rinvS(X, Y) => caxcomp(Y))) <=> (ca_Vx6(X) <=> ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y)))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(76,plain,
% 0.14/0.36 (![X: $i] : (ca_Vx6(X) <=> ![Y: $i] : (rinvS(X, Y) => caxcomp(Y))) <=> ![X: $i] : (ca_Vx6(X) <=> ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[75])).
% 0.14/0.36 tff(77,axiom,(![X: $i] : (ca_Vx6(X) <=> ![Y: $i] : (rinvS(X, Y) => caxcomp(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_11')).
% 0.14/0.36 tff(78,plain,
% 0.14/0.36 (![X: $i] : (ca_Vx6(X) <=> ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.14/0.36 tff(79,plain,
% 0.14/0.36 (![X: $i] : (ca_Vx6(X) <=> ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.14/0.36 tff(80,plain,(
% 0.14/0.36 ![X: $i] : (((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y)))) & (ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X)))))))),
% 0.14/0.36 inference(skolemize,[status(sab)],[79])).
% 0.14/0.36 tff(81,plain,
% 0.14/0.36 (![X: $i] : (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X)))))))))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.14/0.36 tff(82,plain,
% 0.14/0.36 (![X: $i] : (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X)))))))))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[81, 71])).
% 0.14/0.36 tff(83,plain,
% 0.14/0.36 ((~![X: $i] : (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X)))))))))) | (~((~((~ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | (~(ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(caxcomp(tptp_fun_Y_10(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_10(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))))),
% 0.14/0.36 inference(quant_inst,[status(thm)],[])).
% 0.14/0.36 tff(84,plain,
% 0.14/0.36 (~((~((~ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | (~(ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(caxcomp(tptp_fun_Y_10(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_10(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))))))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.14/0.36 tff(85,plain,
% 0.14/0.36 (((~((~ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | (~(ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(caxcomp(tptp_fun_Y_10(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_10(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | ((~ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))),
% 0.14/0.36 inference(tautology,[status(thm)],[])).
% 0.14/0.36 tff(86,plain,
% 0.14/0.36 ((~ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.14/0.36 tff(87,plain,
% 0.14/0.36 (^[X: $i] : refl((~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X))))))))) <=> (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X))))))))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(88,plain,
% 0.14/0.36 (![X: $i] : (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X))))))))) <=> ![X: $i] : (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X)))))))))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[87])).
% 0.14/0.36 tff(89,plain,
% 0.14/0.36 (^[X: $i] : rewrite((~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X))))))))) <=> (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X))))))))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(90,plain,
% 0.14/0.36 (![X: $i] : (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X))))))))) <=> ![X: $i] : (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X)))))))))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[89])).
% 0.14/0.36 tff(91,plain,
% 0.14/0.36 (![X: $i] : (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X))))))))) <=> ![X: $i] : (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X)))))))))),
% 0.14/0.36 inference(transitivity,[status(thm)],[90, 88])).
% 0.14/0.36 tff(92,plain,
% 0.14/0.36 (^[X: $i] : trans(monotonicity(rewrite(((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y)))) <=> ((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))), ((((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y)))) & (ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X))))))) <=> (((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y)))) & (ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X))))))))), rewrite((((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y)))) & (ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X))))))) <=> (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X)))))))))), ((((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y)))) & (ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X))))))) <=> (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X)))))))))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(93,plain,
% 0.14/0.36 (![X: $i] : (((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y)))) & (ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X))))))) <=> ![X: $i] : (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X)))))))))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[92])).
% 0.14/0.36 tff(94,plain,
% 0.14/0.36 (![X: $i] : (ca_Vx7(X) <=> ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y)))) <=> ![X: $i] : (ca_Vx7(X) <=> ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))),
% 0.14/0.36 inference(rewrite,[status(thm)],[])).
% 0.14/0.36 tff(95,plain,
% 0.14/0.36 (^[X: $i] : rewrite((ca_Vx7(X) <=> ![Y: $i] : (rinvP(X, Y) => ca_Vx6(Y))) <=> (ca_Vx7(X) <=> ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y)))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(96,plain,
% 0.14/0.36 (![X: $i] : (ca_Vx7(X) <=> ![Y: $i] : (rinvP(X, Y) => ca_Vx6(Y))) <=> ![X: $i] : (ca_Vx7(X) <=> ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[95])).
% 0.14/0.36 tff(97,axiom,(![X: $i] : (ca_Vx7(X) <=> ![Y: $i] : (rinvP(X, Y) => ca_Vx6(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_12')).
% 0.14/0.36 tff(98,plain,
% 0.14/0.36 (![X: $i] : (ca_Vx7(X) <=> ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.14/0.36 tff(99,plain,
% 0.14/0.36 (![X: $i] : (ca_Vx7(X) <=> ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.14/0.36 tff(100,plain,(
% 0.14/0.36 ![X: $i] : (((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y)))) & (ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X)))))))),
% 0.14/0.36 inference(skolemize,[status(sab)],[99])).
% 0.14/0.36 tff(101,plain,
% 0.14/0.36 (![X: $i] : (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X)))))))))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.14/0.36 tff(102,plain,
% 0.14/0.36 (![X: $i] : (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X)))))))))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[101, 91])).
% 0.14/0.36 tff(103,plain,
% 0.14/0.36 ((~![X: $i] : (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X)))))))))) | (~((~((~ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))) | (~(ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~(ca_Vx6(tptp_fun_Y_11(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_11(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))))))))),
% 0.14/0.36 inference(quant_inst,[status(thm)],[])).
% 0.14/0.36 tff(104,plain,
% 0.14/0.36 (~((~((~ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))) | (~(ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~(ca_Vx6(tptp_fun_Y_11(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_11(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.14/0.36 tff(105,plain,
% 0.14/0.36 (((~((~ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))) | (~(ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~(ca_Vx6(tptp_fun_Y_11(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_11(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))))))) | ((~ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))),
% 0.14/0.36 inference(tautology,[status(thm)],[])).
% 0.14/0.36 tff(106,plain,
% 0.14/0.36 ((~ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.14/0.36 tff(107,plain,
% 0.14/0.36 (^[X: $i] : refl((~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X))))))))) <=> (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X))))))))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(108,plain,
% 0.14/0.36 (![X: $i] : (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X))))))))) <=> ![X: $i] : (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X)))))))))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[107])).
% 0.14/0.36 tff(109,plain,
% 0.14/0.36 (^[X: $i] : rewrite((~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X))))))))) <=> (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X))))))))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(110,plain,
% 0.14/0.36 (![X: $i] : (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X))))))))) <=> ![X: $i] : (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X)))))))))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[109])).
% 0.14/0.36 tff(111,plain,
% 0.14/0.36 (![X: $i] : (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X))))))))) <=> ![X: $i] : (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X)))))))))),
% 0.14/0.36 inference(transitivity,[status(thm)],[110, 108])).
% 0.14/0.36 tff(112,plain,
% 0.14/0.36 (^[X: $i] : trans(monotonicity(rewrite(((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y)))) <=> ((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))), ((((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y)))) & (cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X))))))) <=> (((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y)))) & (cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X))))))))), rewrite((((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y)))) & (cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X))))))) <=> (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X)))))))))), ((((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y)))) & (cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X))))))) <=> (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X)))))))))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(113,plain,
% 0.14/0.36 (![X: $i] : (((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y)))) & (cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X))))))) <=> ![X: $i] : (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X)))))))))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[112])).
% 0.14/0.36 tff(114,plain,
% 0.14/0.36 (![X: $i] : (cc(X) <=> ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y)))) <=> ![X: $i] : (cc(X) <=> ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))),
% 0.14/0.36 inference(rewrite,[status(thm)],[])).
% 0.14/0.36 tff(115,plain,
% 0.14/0.36 (^[X: $i] : rewrite((cc(X) <=> ![Y: $i] : (rinvR(X, Y) => ca_Vx7(Y))) <=> (cc(X) <=> ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y)))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(116,plain,
% 0.14/0.36 (![X: $i] : (cc(X) <=> ![Y: $i] : (rinvR(X, Y) => ca_Vx7(Y))) <=> ![X: $i] : (cc(X) <=> ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[115])).
% 0.14/0.36 tff(117,axiom,(![X: $i] : (cc(X) <=> ![Y: $i] : (rinvR(X, Y) => ca_Vx7(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_6')).
% 0.14/0.36 tff(118,plain,
% 0.14/0.36 (![X: $i] : (cc(X) <=> ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.14/0.36 tff(119,plain,
% 0.14/0.36 (![X: $i] : (cc(X) <=> ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.14/0.36 tff(120,plain,(
% 0.14/0.36 ![X: $i] : (((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y)))) & (cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X)))))))),
% 0.14/0.36 inference(skolemize,[status(sab)],[119])).
% 0.14/0.36 tff(121,plain,
% 0.14/0.36 (![X: $i] : (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X)))))))))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.14/0.36 tff(122,plain,
% 0.14/0.36 (![X: $i] : (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X)))))))))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[121, 111])).
% 0.14/0.36 tff(123,plain,
% 0.14/0.36 ((~![X: $i] : (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X)))))))))) | (~((~((~cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y))))) | (~(cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~(ca_Vx7(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))))))),
% 0.14/0.36 inference(quant_inst,[status(thm)],[])).
% 0.14/0.36 tff(124,plain,
% 0.14/0.36 (~((~((~cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y))))) | (~(cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~(ca_Vx7(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))))))))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.14/0.36 tff(125,plain,
% 0.14/0.36 (((~((~cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y))))) | (~(cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~(ca_Vx7(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))))) | ((~cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y))))),
% 0.14/0.36 inference(tautology,[status(thm)],[])).
% 0.14/0.36 tff(126,plain,
% 0.14/0.36 ((~cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y)))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.14/0.36 tff(127,plain,
% 0.14/0.36 (^[X: $i] : refl((~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))))))) <=> (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))))))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(128,plain,
% 0.14/0.36 (![X: $i] : (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))))))) <=> ![X: $i] : (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X)))))))))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[127])).
% 0.14/0.36 tff(129,plain,
% 0.14/0.36 (^[X: $i] : rewrite((~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))))))) <=> (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))))))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(130,plain,
% 0.14/0.36 (![X: $i] : (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))))))) <=> ![X: $i] : (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X)))))))))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[129])).
% 0.14/0.36 tff(131,plain,
% 0.14/0.36 (![X: $i] : (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))))))) <=> ![X: $i] : (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X)))))))))),
% 0.14/0.36 inference(transitivity,[status(thm)],[130, 128])).
% 0.14/0.36 tff(132,plain,
% 0.14/0.36 (^[X: $i] : trans(monotonicity(rewrite(((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) <=> ((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))), ((((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) & (ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))))) <=> (((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) & (ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))))))), rewrite((((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) & (ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))))) <=> (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X)))))))))), ((((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) & (ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))))) <=> (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X)))))))))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(133,plain,
% 0.14/0.36 (![X: $i] : (((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) & (ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))))) <=> ![X: $i] : (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X)))))))))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[132])).
% 0.14/0.36 tff(134,plain,
% 0.14/0.36 (![X: $i] : (ca_Vx5(X) <=> ![Y: $i] : (cc(Y) | (~rr(X, Y)))) <=> ![X: $i] : (ca_Vx5(X) <=> ![Y: $i] : (cc(Y) | (~rr(X, Y))))),
% 0.14/0.36 inference(rewrite,[status(thm)],[])).
% 0.14/0.36 tff(135,plain,
% 0.14/0.36 (^[X: $i] : rewrite((ca_Vx5(X) <=> ![Y: $i] : (rr(X, Y) => cc(Y))) <=> (ca_Vx5(X) <=> ![Y: $i] : (cc(Y) | (~rr(X, Y)))))),
% 0.14/0.37 inference(bind,[status(th)],[])).
% 0.14/0.37 tff(136,plain,
% 0.14/0.37 (![X: $i] : (ca_Vx5(X) <=> ![Y: $i] : (rr(X, Y) => cc(Y))) <=> ![X: $i] : (ca_Vx5(X) <=> ![Y: $i] : (cc(Y) | (~rr(X, Y))))),
% 0.14/0.37 inference(quant_intro,[status(thm)],[135])).
% 0.14/0.37 tff(137,axiom,(![X: $i] : (ca_Vx5(X) <=> ![Y: $i] : (rr(X, Y) => cc(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_10')).
% 0.14/0.37 tff(138,plain,
% 0.14/0.37 (![X: $i] : (ca_Vx5(X) <=> ![Y: $i] : (cc(Y) | (~rr(X, Y))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.14/0.37 tff(139,plain,
% 0.14/0.37 (![X: $i] : (ca_Vx5(X) <=> ![Y: $i] : (cc(Y) | (~rr(X, Y))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.14/0.37 tff(140,plain,(
% 0.14/0.37 ![X: $i] : (((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) & (ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X)))))))),
% 0.14/0.37 inference(skolemize,[status(sab)],[139])).
% 0.14/0.37 tff(141,plain,
% 0.14/0.37 (![X: $i] : (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X)))))))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[140, 133])).
% 0.14/0.37 tff(142,plain,
% 0.14/0.37 (![X: $i] : (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X)))))))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[141, 131])).
% 0.14/0.37 tff(143,plain,
% 0.14/0.37 ((~![X: $i] : (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X)))))))))) | (~((~((~ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))) | (~(ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_8(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))))))))),
% 0.14/0.37 inference(quant_inst,[status(thm)],[])).
% 0.14/0.37 tff(144,plain,
% 0.14/0.37 (~((~((~ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))) | (~(ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_8(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))))),
% 0.14/0.37 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.14/0.37 tff(145,plain,
% 0.14/0.37 (((~((~ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))) | (~(ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_8(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))))))) | ((~ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))),
% 0.14/0.37 inference(tautology,[status(thm)],[])).
% 0.14/0.37 tff(146,plain,
% 0.14/0.37 ((~ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))),
% 0.14/0.37 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.14/0.37 tff(147,plain,
% 0.14/0.37 (^[X: $i] : rewrite((~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))))) <=> (~((~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))))))))))),
% 0.14/0.37 inference(bind,[status(th)],[])).
% 0.14/0.37 tff(148,plain,
% 0.14/0.37 (![X: $i] : (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))))) <=> ![X: $i] : (~((~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))))))))),
% 0.14/0.37 inference(quant_intro,[status(thm)],[147])).
% 0.14/0.37 tff(149,plain,
% 0.14/0.37 (^[X: $i] : refl((~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))))) <=> (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))))))),
% 0.14/0.37 inference(bind,[status(th)],[])).
% 0.14/0.37 tff(150,plain,
% 0.14/0.37 (![X: $i] : (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))))) <=> ![X: $i] : (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y)))))))),
% 0.14/0.37 inference(quant_intro,[status(thm)],[149])).
% 0.14/0.37 tff(151,plain,
% 0.14/0.37 (^[X: $i] : rewrite((~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))))) <=> (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))))))),
% 0.14/0.37 inference(bind,[status(th)],[])).
% 0.14/0.37 tff(152,plain,
% 0.14/0.37 (![X: $i] : (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))))) <=> ![X: $i] : (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y)))))))),
% 0.14/0.37 inference(quant_intro,[status(thm)],[151])).
% 0.14/0.37 tff(153,plain,
% 0.14/0.37 (![X: $i] : (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))))) <=> ![X: $i] : (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y)))))))),
% 0.14/0.37 inference(transitivity,[status(thm)],[152, 150])).
% 0.14/0.37 tff(154,plain,
% 0.14/0.37 (^[X: $i] : trans(monotonicity(rewrite(((~ca_Ax2(X)) | (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X)) & rp(X, tptp_fun_Y_5(X)) & cowlThing(tptp_fun_Y_5(X)) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))) <=> ((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))), trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((rr(X, Y) & cowlThing(Y)) <=> (~((~rr(X, Y)) | (~cowlThing(Y))))), ((~(rr(X, Y) & cowlThing(Y))) <=> (~(~((~rr(X, Y)) | (~cowlThing(Y))))))), rewrite((~(~((~rr(X, Y)) | (~cowlThing(Y))))) <=> ((~rr(X, Y)) | (~cowlThing(Y)))), ((~(rr(X, Y) & cowlThing(Y))) <=> ((~rr(X, Y)) | (~cowlThing(Y)))))), (![Y: $i] : (~(rr(X, Y) & cowlThing(Y))) <=> ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))))), quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((rp(X, Y) & cowlThing(Y)) <=> (~((~rp(X, Y)) | (~cowlThing(Y))))), ((~(rp(X, Y) & cowlThing(Y))) <=> (~(~((~rp(X, Y)) | (~cowlThing(Y))))))), rewrite((~(~((~rp(X, Y)) | (~cowlThing(Y))))) <=> ((~rp(X, Y)) | (~cowlThing(Y)))), ((~(rp(X, Y) & cowlThing(Y))) <=> ((~rp(X, Y)) | (~cowlThing(Y)))))), (![Y: $i] : (~(rp(X, Y) & cowlThing(Y))) <=> ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))), ((ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))) | ![Y: $i] : (~(rp(X, Y) & cowlThing(Y))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X)))))) <=> (ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X)))))))), rewrite((ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X)))))) <=> (ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))), ((ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))) | ![Y: $i] : (~(rp(X, Y) & cowlThing(Y))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X)))))) <=> (ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y)))))), ((((~ca_Ax2(X)) | (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X)) & rp(X, tptp_fun_Y_5(X)) & cowlThing(tptp_fun_Y_5(X)) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))) & (ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))) | ![Y: $i] : (~(rp(X, Y) & cowlThing(Y))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))))) <=> (((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X)))))) & (ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))))), rewrite((((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X)))))) & (ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))) <=> (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y)))))))), ((((~ca_Ax2(X)) | (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X)) & rp(X, tptp_fun_Y_5(X)) & cowlThing(tptp_fun_Y_5(X)) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))) & (ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))) | ![Y: $i] : (~(rp(X, Y) & cowlThing(Y))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))))) <=> (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y)))))))))),
% 0.14/0.37 inference(bind,[status(th)],[])).
% 0.14/0.37 tff(155,plain,
% 0.14/0.37 (![X: $i] : (((~ca_Ax2(X)) | (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X)) & rp(X, tptp_fun_Y_5(X)) & cowlThing(tptp_fun_Y_5(X)) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))) & (ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))) | ![Y: $i] : (~(rp(X, Y) & cowlThing(Y))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))))) <=> ![X: $i] : (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y)))))))),
% 0.14/0.37 inference(quant_intro,[status(thm)],[154])).
% 0.14/0.37 tff(156,plain,
% 0.14/0.37 (^[X: $i] : rewrite((((~ca_Ax2(X)) | (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & (rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X))) & (rp(X, tptp_fun_Y_5(X)) & cowlThing(tptp_fun_Y_5(X))) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))) & (ca_Ax2(X) | ((~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))) | ![Y: $i] : (~(rp(X, Y) & cowlThing(Y))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X)))))))) <=> (((~ca_Ax2(X)) | (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X)) & rp(X, tptp_fun_Y_5(X)) & cowlThing(tptp_fun_Y_5(X)) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))) & (ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))) | ![Y: $i] : (~(rp(X, Y) & cowlThing(Y))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))))))),
% 0.14/0.37 inference(bind,[status(th)],[])).
% 0.14/0.37 tff(157,plain,
% 0.14/0.37 (![X: $i] : (((~ca_Ax2(X)) | (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & (rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X))) & (rp(X, tptp_fun_Y_5(X)) & cowlThing(tptp_fun_Y_5(X))) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))) & (ca_Ax2(X) | ((~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))) | ![Y: $i] : (~(rp(X, Y) & cowlThing(Y))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X)))))))) <=> ![X: $i] : (((~ca_Ax2(X)) | (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X)) & rp(X, tptp_fun_Y_5(X)) & cowlThing(tptp_fun_Y_5(X)) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))) & (ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))) | ![Y: $i] : (~(rp(X, Y) & cowlThing(Y))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X)))))))),
% 0.14/0.37 inference(quant_intro,[status(thm)],[156])).
% 0.14/0.38 tff(158,plain,
% 0.14/0.38 (![X: $i] : (ca_Ax2(X) <=> (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y)) & ?[Y: $i] : (rp(X, Y) & cowlThing(Y)) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))) <=> ![X: $i] : (ca_Ax2(X) <=> (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y)) & ?[Y: $i] : (rp(X, Y) & cowlThing(Y)) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(159,plain,
% 0.14/0.38 (^[X: $i] : rewrite((ca_Ax2(X) <=> (((((![Y: $i] : (rp(X, Y) => ca_Vx3(Y)) & ![Y: $i] : (rp(X, Y) => ca_Vx5(Y))) & ![Y: $i] : (rr(X, Y) => cc(Y))) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y))) & ?[Y: $i] : (rp(X, Y) & cowlThing(Y))) & ![Y: $i] : (rp(X, Y) => ca_Vx4(Y)))) <=> (ca_Ax2(X) <=> (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y)) & ?[Y: $i] : (rp(X, Y) & cowlThing(Y)) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(160,plain,
% 0.14/0.38 (![X: $i] : (ca_Ax2(X) <=> (((((![Y: $i] : (rp(X, Y) => ca_Vx3(Y)) & ![Y: $i] : (rp(X, Y) => ca_Vx5(Y))) & ![Y: $i] : (rr(X, Y) => cc(Y))) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y))) & ?[Y: $i] : (rp(X, Y) & cowlThing(Y))) & ![Y: $i] : (rp(X, Y) => ca_Vx4(Y)))) <=> ![X: $i] : (ca_Ax2(X) <=> (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y)) & ?[Y: $i] : (rp(X, Y) & cowlThing(Y)) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[159])).
% 0.14/0.38 tff(161,axiom,(![X: $i] : (ca_Ax2(X) <=> (((((![Y: $i] : (rp(X, Y) => ca_Vx3(Y)) & ![Y: $i] : (rp(X, Y) => ca_Vx5(Y))) & ![Y: $i] : (rr(X, Y) => cc(Y))) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y))) & ?[Y: $i] : (rp(X, Y) & cowlThing(Y))) & ![Y: $i] : (rp(X, Y) => ca_Vx4(Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_7')).
% 0.14/0.38 tff(162,plain,
% 0.14/0.38 (![X: $i] : (ca_Ax2(X) <=> (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y)) & ?[Y: $i] : (rp(X, Y) & cowlThing(Y)) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.14/0.38 tff(163,plain,
% 0.14/0.38 (![X: $i] : (ca_Ax2(X) <=> (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y)) & ?[Y: $i] : (rp(X, Y) & cowlThing(Y)) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.14/0.38 tff(164,plain,(
% 0.14/0.38 ![X: $i] : (((~ca_Ax2(X)) | (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & (rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X))) & (rp(X, tptp_fun_Y_5(X)) & cowlThing(tptp_fun_Y_5(X))) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))) & (ca_Ax2(X) | ((~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))) | ![Y: $i] : (~(rp(X, Y) & cowlThing(Y))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))))))),
% 0.14/0.38 inference(skolemize,[status(sab)],[163])).
% 0.14/0.38 tff(165,plain,
% 0.14/0.38 (![X: $i] : (((~ca_Ax2(X)) | (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X)) & rp(X, tptp_fun_Y_5(X)) & cowlThing(tptp_fun_Y_5(X)) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))) & (ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))) | ![Y: $i] : (~(rp(X, Y) & cowlThing(Y))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X)))))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[164, 157])).
% 0.14/0.38 tff(166,plain,
% 0.14/0.38 (![X: $i] : (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y)))))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[165, 155])).
% 0.14/0.38 tff(167,plain,
% 0.14/0.38 (![X: $i] : (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y)))))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[166, 153])).
% 0.14/0.38 tff(168,plain,
% 0.14/0.38 (![X: $i] : (~((~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))))))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[167, 148])).
% 0.14/0.38 tff(169,plain,
% 0.14/0.38 (((~![X: $i] : (~((~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))))))))) | (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(ca_Vx3(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx5(tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx4(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))))))))) <=> ((~![X: $i] : (~((~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))))))))) | (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(ca_Vx3(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx5(tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx4(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))))))))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(170,plain,
% 0.14/0.38 ((~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(ca_Vx3(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx5(tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx4(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | ![Y: $i] : ((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))))))))) <=> (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(ca_Vx3(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx5(tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx4(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))))))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(171,plain,
% 0.14/0.38 (((~![X: $i] : (~((~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))))))))) | (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(ca_Vx3(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx5(tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx4(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | ![Y: $i] : ((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))))))))) <=> ((~![X: $i] : (~((~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))))))))) | (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(ca_Vx3(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx5(tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx4(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))))))))))),
% 0.14/0.38 inference(monotonicity,[status(thm)],[170])).
% 0.14/0.38 tff(172,plain,
% 0.14/0.38 (((~![X: $i] : (~((~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))))))))) | (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(ca_Vx3(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx5(tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx4(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | ![Y: $i] : ((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))))))))) <=> ((~![X: $i] : (~((~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))))))))) | (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(ca_Vx3(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx5(tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx4(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))))))))))),
% 0.14/0.39 inference(transitivity,[status(thm)],[171, 169])).
% 0.14/0.39 tff(173,plain,
% 0.14/0.39 ((~![X: $i] : (~((~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))))))))) | (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(ca_Vx3(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx5(tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx4(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | ![Y: $i] : ((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))))))))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(174,plain,
% 0.14/0.39 ((~![X: $i] : (~((~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))))))))) | (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(ca_Vx3(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx5(tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx4(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))))))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.14/0.39 tff(175,plain,
% 0.14/0.39 (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(ca_Vx3(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx5(tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx4(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))))))))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[174, 168])).
% 0.14/0.39 tff(176,plain,
% 0.14/0.39 (((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(ca_Vx3(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx5(tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx4(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))))))) | ((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))))))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(177,plain,
% 0.14/0.39 ((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.14/0.39 tff(178,plain,
% 0.14/0.39 (^[X: $i] : refl(((~cUnsatisfiable(X)) | (~((~rs(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X)))))) <=> ((~cUnsatisfiable(X)) | (~((~rs(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X)))))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(179,plain,
% 0.14/0.39 (![X: $i] : ((~cUnsatisfiable(X)) | (~((~rs(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X)))))) <=> ![X: $i] : ((~cUnsatisfiable(X)) | (~((~rs(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[178])).
% 0.14/0.39 tff(180,plain,
% 0.14/0.39 (^[X: $i] : rewrite(((~cUnsatisfiable(X)) | (rs(X, tptp_fun_Y_0(X)) & ca_Ax2(tptp_fun_Y_0(X)))) <=> ((~cUnsatisfiable(X)) | (~((~rs(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X)))))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(181,plain,
% 0.14/0.39 (![X: $i] : ((~cUnsatisfiable(X)) | (rs(X, tptp_fun_Y_0(X)) & ca_Ax2(tptp_fun_Y_0(X)))) <=> ![X: $i] : ((~cUnsatisfiable(X)) | (~((~rs(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[180])).
% 0.14/0.39 tff(182,plain,
% 0.14/0.39 (![X: $i] : ((~cUnsatisfiable(X)) | ?[Y: $i] : (rs(X, Y) & ca_Ax2(Y))) <=> ![X: $i] : ((~cUnsatisfiable(X)) | ?[Y: $i] : (rs(X, Y) & ca_Ax2(Y)))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(183,plain,
% 0.14/0.39 (^[X: $i] : rewrite((cUnsatisfiable(X) => ?[Y: $i] : (rs(X, Y) & ca_Ax2(Y))) <=> ((~cUnsatisfiable(X)) | ?[Y: $i] : (rs(X, Y) & ca_Ax2(Y))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(184,plain,
% 0.14/0.39 (![X: $i] : (cUnsatisfiable(X) => ?[Y: $i] : (rs(X, Y) & ca_Ax2(Y))) <=> ![X: $i] : ((~cUnsatisfiable(X)) | ?[Y: $i] : (rs(X, Y) & ca_Ax2(Y)))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[183])).
% 0.14/0.39 tff(185,axiom,(![X: $i] : (cUnsatisfiable(X) => ?[Y: $i] : (rs(X, Y) & ca_Ax2(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_3')).
% 0.14/0.39 tff(186,plain,
% 0.14/0.39 (![X: $i] : ((~cUnsatisfiable(X)) | ?[Y: $i] : (rs(X, Y) & ca_Ax2(Y)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.14/0.39 tff(187,plain,
% 0.14/0.39 (![X: $i] : ((~cUnsatisfiable(X)) | ?[Y: $i] : (rs(X, Y) & ca_Ax2(Y)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[186, 182])).
% 0.14/0.39 tff(188,plain,(
% 0.14/0.39 ![X: $i] : ((~cUnsatisfiable(X)) | (rs(X, tptp_fun_Y_0(X)) & ca_Ax2(tptp_fun_Y_0(X))))),
% 0.14/0.39 inference(skolemize,[status(sab)],[187])).
% 0.14/0.39 tff(189,plain,
% 0.14/0.39 (![X: $i] : ((~cUnsatisfiable(X)) | (~((~rs(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[188, 181])).
% 0.14/0.39 tff(190,plain,
% 0.14/0.39 (![X: $i] : ((~cUnsatisfiable(X)) | (~((~rs(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[189, 179])).
% 0.14/0.39 tff(191,plain,
% 0.14/0.39 (((~![X: $i] : ((~cUnsatisfiable(X)) | (~((~rs(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | ((~cUnsatisfiable(i2003_11_14_17_21_33997)) | (~((~rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))) <=> ((~![X: $i] : ((~cUnsatisfiable(X)) | (~((~rs(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~cUnsatisfiable(i2003_11_14_17_21_33997)) | (~((~rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(192,plain,
% 0.14/0.39 ((~![X: $i] : ((~cUnsatisfiable(X)) | (~((~rs(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | ((~cUnsatisfiable(i2003_11_14_17_21_33997)) | (~((~rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(193,plain,
% 0.14/0.39 ((~![X: $i] : ((~cUnsatisfiable(X)) | (~((~rs(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~cUnsatisfiable(i2003_11_14_17_21_33997)) | (~((~rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.14/0.39 tff(194,plain,
% 0.14/0.39 (~((~rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[193, 190, 43])).
% 0.14/0.39 tff(195,plain,
% 0.14/0.39 (((~rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(196,plain,
% 0.14/0.39 (ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[195, 194])).
% 0.14/0.39 tff(197,plain,
% 0.14/0.39 ((~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))))))) | (~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(198,plain,
% 0.14/0.39 ((~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))))))) | (~((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[197, 196])).
% 0.14/0.39 tff(199,plain,
% 0.14/0.39 (~((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[198, 177])).
% 0.14/0.39 tff(200,plain,
% 0.14/0.39 (((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | ![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(201,plain,
% 0.14/0.39 (![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[200, 199])).
% 0.14/0.39 tff(202,plain,
% 0.14/0.39 (((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(203,plain,
% 0.14/0.39 (rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[202, 199])).
% 0.14/0.39 tff(204,plain,
% 0.14/0.39 (((~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) <=> ((~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(205,plain,
% 0.14/0.39 ((~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(206,plain,
% 0.14/0.39 ((~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.14/0.39 tff(207,plain,
% 0.14/0.39 (ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[206, 203, 201])).
% 0.14/0.39 tff(208,plain,
% 0.14/0.39 ((~((~ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))) | (~ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(209,plain,
% 0.14/0.39 ((~((~ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))) | ![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[208, 207])).
% 0.14/0.39 tff(210,plain,
% 0.14/0.39 (![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[209, 146])).
% 0.14/0.39 tff(211,plain,
% 0.14/0.39 (^[X: $i] : refl((~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))))))) <=> (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(212,plain,
% 0.14/0.40 (![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))))))) <=> ![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[211])).
% 0.14/0.40 tff(213,plain,
% 0.14/0.40 (^[X: $i] : rewrite((~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))))))) <=> (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(214,plain,
% 0.14/0.40 (![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))))))) <=> ![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[213])).
% 0.14/0.40 tff(215,plain,
% 0.14/0.40 (![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))))))) <=> ![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))),
% 0.14/0.40 inference(transitivity,[status(thm)],[214, 212])).
% 0.14/0.40 tff(216,plain,
% 0.14/0.40 (^[X: $i] : trans(monotonicity(rewrite(((~ca_Vx3(X)) | (rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X)))) <=> ((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))), rewrite((ca_Vx3(X) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y)))) <=> (ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))))), ((((~ca_Vx3(X)) | (rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X)))) & (ca_Vx3(X) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))))) <=> (((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X)))))) & (ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))))))), rewrite((((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X)))))) & (ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))))) <=> (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))), ((((~ca_Vx3(X)) | (rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X)))) & (ca_Vx3(X) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))))) <=> (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(217,plain,
% 0.14/0.40 (![X: $i] : (((~ca_Vx3(X)) | (rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X)))) & (ca_Vx3(X) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))))) <=> ![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[216])).
% 0.14/0.40 tff(218,plain,
% 0.14/0.40 (![X: $i] : (ca_Vx3(X) <=> ?[Y: $i] : (rr(X, Y) & cowlThing(Y))) <=> ![X: $i] : (ca_Vx3(X) <=> ?[Y: $i] : (rr(X, Y) & cowlThing(Y)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(219,axiom,(![X: $i] : (ca_Vx3(X) <=> ?[Y: $i] : (rr(X, Y) & cowlThing(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_8')).
% 0.14/0.40 tff(220,plain,
% 0.14/0.40 (![X: $i] : (ca_Vx3(X) <=> ?[Y: $i] : (rr(X, Y) & cowlThing(Y)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.14/0.40 tff(221,plain,(
% 0.14/0.40 ![X: $i] : (((~ca_Vx3(X)) | (rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X)))) & (ca_Vx3(X) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y)))))),
% 0.14/0.40 inference(skolemize,[status(sab)],[220])).
% 0.14/0.40 tff(222,plain,
% 0.14/0.40 (![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[221, 217])).
% 0.14/0.40 tff(223,plain,
% 0.14/0.40 (![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[222, 215])).
% 0.14/0.40 tff(224,plain,
% 0.14/0.40 (((~![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))) | (~((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~(ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))))))) <=> ((~![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))) | (~((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~(ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(225,plain,
% 0.14/0.40 ((~((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~(ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : ((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)) | (~cowlThing(Y))))))) <=> (~((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~(ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(226,plain,
% 0.14/0.40 (((~![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))) | (~((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~(ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : ((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)) | (~cowlThing(Y)))))))) <=> ((~![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))) | (~((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~(ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))))))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[225])).
% 0.14/0.40 tff(227,plain,
% 0.14/0.40 (((~![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))) | (~((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~(ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : ((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)) | (~cowlThing(Y)))))))) <=> ((~![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))) | (~((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~(ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))))))),
% 0.14/0.40 inference(transitivity,[status(thm)],[226, 224])).
% 0.14/0.40 tff(228,plain,
% 0.14/0.40 ((~![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))) | (~((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~(ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : ((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)) | (~cowlThing(Y)))))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(229,plain,
% 0.14/0.40 ((~![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))) | (~((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~(ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.14/0.40 tff(230,plain,
% 0.14/0.40 (~((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~(ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[229, 223])).
% 0.14/0.40 tff(231,plain,
% 0.14/0.40 (((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~(ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))))) | ((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(232,plain,
% 0.14/0.40 ((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[231, 230])).
% 0.14/0.40 tff(233,plain,
% 0.14/0.40 (((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | ![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(234,plain,
% 0.14/0.40 (![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[233, 199])).
% 0.14/0.40 tff(235,plain,
% 0.14/0.40 (((~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) <=> ((~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(236,plain,
% 0.14/0.40 ((~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(237,plain,
% 0.14/0.40 ((~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.14/0.40 tff(238,plain,
% 0.14/0.40 (ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[237, 203, 234])).
% 0.14/0.40 tff(239,plain,
% 0.14/0.40 ((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(240,plain,
% 0.14/0.40 ((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[239, 238])).
% 0.14/0.40 tff(241,plain,
% 0.14/0.40 (~((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[240, 232])).
% 0.14/0.40 tff(242,plain,
% 0.14/0.40 (((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(243,plain,
% 0.14/0.40 (rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[242, 241])).
% 0.14/0.40 tff(244,plain,
% 0.14/0.40 (((~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))) | (cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))) <=> ((~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))) | cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(245,plain,
% 0.14/0.40 ((~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))) | (cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(246,plain,
% 0.14/0.40 ((~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))) | cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.14/0.40 tff(247,plain,
% 0.14/0.40 (cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[246, 243, 210])).
% 0.14/0.40 tff(248,plain,
% 0.14/0.40 ((~((~cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y))))) | (~cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y)))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(249,plain,
% 0.14/0.40 ((~((~cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y))))) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[248, 247])).
% 0.14/0.40 tff(250,plain,
% 0.14/0.40 (![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[249, 126])).
% 0.14/0.40 tff(251,plain,
% 0.14/0.40 (^[X: $i, Y: $i] : refl((rinvR(X, Y) <=> rr(Y, X)) <=> (rinvR(X, Y) <=> rr(Y, X)))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(252,plain,
% 0.14/0.40 (![X: $i, Y: $i] : (rinvR(X, Y) <=> rr(Y, X)) <=> ![X: $i, Y: $i] : (rinvR(X, Y) <=> rr(Y, X))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[251])).
% 0.14/0.40 tff(253,plain,
% 0.14/0.40 (![X: $i, Y: $i] : (rinvR(X, Y) <=> rr(Y, X)) <=> ![X: $i, Y: $i] : (rinvR(X, Y) <=> rr(Y, X))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(254,axiom,(![X: $i, Y: $i] : (rinvR(X, Y) <=> rr(Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_14')).
% 0.14/0.40 tff(255,plain,
% 0.14/0.40 (![X: $i, Y: $i] : (rinvR(X, Y) <=> rr(Y, X))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.14/0.40 tff(256,plain,(
% 0.14/0.40 ![X: $i, Y: $i] : (rinvR(X, Y) <=> rr(Y, X))),
% 0.14/0.40 inference(skolemize,[status(sab)],[255])).
% 0.14/0.40 tff(257,plain,
% 0.14/0.40 (![X: $i, Y: $i] : (rinvR(X, Y) <=> rr(Y, X))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[256, 252])).
% 0.14/0.40 tff(258,plain,
% 0.14/0.40 ((~![X: $i, Y: $i] : (rinvR(X, Y) <=> rr(Y, X))) | (rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) <=> rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(259,plain,
% 0.14/0.40 (rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) <=> rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[258, 257])).
% 0.14/0.40 tff(260,plain,
% 0.14/0.40 ((~(rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) <=> rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(261,plain,
% 0.14/0.40 ((~(rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) <=> rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[260, 243])).
% 0.14/0.40 tff(262,plain,
% 0.14/0.40 (rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[261, 259])).
% 0.14/0.40 tff(263,plain,
% 0.14/0.40 (((~![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y)))) | (ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) <=> ((~![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y)))) | ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(264,plain,
% 0.14/0.40 ((~![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y)))) | (ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(265,plain,
% 0.14/0.40 ((~![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y)))) | ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.14/0.40 tff(266,plain,
% 0.14/0.40 (ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[265, 262, 250])).
% 0.14/0.40 tff(267,plain,
% 0.14/0.40 ((~((~ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))) | (~ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(268,plain,
% 0.14/0.40 ((~((~ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[267, 266])).
% 0.14/0.40 tff(269,plain,
% 0.14/0.40 (![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[268, 106])).
% 0.14/0.40 tff(270,plain,
% 0.14/0.40 (^[X: $i, Y: $i] : refl((rinvP(X, Y) <=> rp(Y, X)) <=> (rinvP(X, Y) <=> rp(Y, X)))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(271,plain,
% 0.14/0.40 (![X: $i, Y: $i] : (rinvP(X, Y) <=> rp(Y, X)) <=> ![X: $i, Y: $i] : (rinvP(X, Y) <=> rp(Y, X))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[270])).
% 0.14/0.40 tff(272,plain,
% 0.14/0.40 (![X: $i, Y: $i] : (rinvP(X, Y) <=> rp(Y, X)) <=> ![X: $i, Y: $i] : (rinvP(X, Y) <=> rp(Y, X))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(273,axiom,(![X: $i, Y: $i] : (rinvP(X, Y) <=> rp(Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_13')).
% 0.14/0.40 tff(274,plain,
% 0.14/0.40 (![X: $i, Y: $i] : (rinvP(X, Y) <=> rp(Y, X))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.14/0.40 tff(275,plain,(
% 0.14/0.40 ![X: $i, Y: $i] : (rinvP(X, Y) <=> rp(Y, X))),
% 0.14/0.40 inference(skolemize,[status(sab)],[274])).
% 0.14/0.40 tff(276,plain,
% 0.14/0.40 (![X: $i, Y: $i] : (rinvP(X, Y) <=> rp(Y, X))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[275, 271])).
% 0.14/0.40 tff(277,plain,
% 0.14/0.40 ((~![X: $i, Y: $i] : (rinvP(X, Y) <=> rp(Y, X))) | (rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_0(i2003_11_14_17_21_33997)) <=> rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(278,plain,
% 0.14/0.40 (rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_0(i2003_11_14_17_21_33997)) <=> rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[277, 276])).
% 0.14/0.40 tff(279,plain,
% 0.14/0.40 ((~(rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_0(i2003_11_14_17_21_33997)) <=> rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(280,plain,
% 0.14/0.40 ((~(rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_0(i2003_11_14_17_21_33997)) <=> rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_0(i2003_11_14_17_21_33997))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[279, 203])).
% 0.14/0.40 tff(281,plain,
% 0.14/0.40 (rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_0(i2003_11_14_17_21_33997))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[280, 278])).
% 0.14/0.40 tff(282,plain,
% 0.14/0.40 (((~![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))) | (ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_0(i2003_11_14_17_21_33997))))) <=> ((~![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))) | ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_0(i2003_11_14_17_21_33997))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(283,plain,
% 0.14/0.40 ((~![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))) | (ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_0(i2003_11_14_17_21_33997))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(284,plain,
% 0.14/0.40 ((~![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))) | ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_0(i2003_11_14_17_21_33997)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.14/0.41 tff(285,plain,
% 0.14/0.41 (ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[284, 281, 269])).
% 0.14/0.41 tff(286,plain,
% 0.14/0.41 ((~((~ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | (~ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(287,plain,
% 0.14/0.41 ((~((~ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | ![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[286, 285])).
% 0.14/0.41 tff(288,plain,
% 0.14/0.41 (![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[287, 86])).
% 0.14/0.41 tff(289,plain,
% 0.14/0.41 (^[X: $i, Y: $i] : refl((rinvS(X, Y) <=> rs(Y, X)) <=> (rinvS(X, Y) <=> rs(Y, X)))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(290,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (rinvS(X, Y) <=> rs(Y, X)) <=> ![X: $i, Y: $i] : (rinvS(X, Y) <=> rs(Y, X))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[289])).
% 0.14/0.41 tff(291,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (rinvS(X, Y) <=> rs(Y, X)) <=> ![X: $i, Y: $i] : (rinvS(X, Y) <=> rs(Y, X))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(292,axiom,(![X: $i, Y: $i] : (rinvS(X, Y) <=> rs(Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_15')).
% 0.14/0.41 tff(293,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (rinvS(X, Y) <=> rs(Y, X))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.14/0.41 tff(294,plain,(
% 0.14/0.41 ![X: $i, Y: $i] : (rinvS(X, Y) <=> rs(Y, X))),
% 0.14/0.41 inference(skolemize,[status(sab)],[293])).
% 0.14/0.41 tff(295,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (rinvS(X, Y) <=> rs(Y, X))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[294, 290])).
% 0.14/0.41 tff(296,plain,
% 0.14/0.41 ((~![X: $i, Y: $i] : (rinvS(X, Y) <=> rs(Y, X))) | (rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), i2003_11_14_17_21_33997) <=> rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997)))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(297,plain,
% 0.14/0.41 (rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), i2003_11_14_17_21_33997) <=> rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[296, 295])).
% 0.14/0.41 tff(298,plain,
% 0.14/0.41 (((~rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(299,plain,
% 0.14/0.41 (rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[298, 194])).
% 0.14/0.41 tff(300,plain,
% 0.14/0.41 ((~(rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), i2003_11_14_17_21_33997) <=> rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), i2003_11_14_17_21_33997) | (~rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997)))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(301,plain,
% 0.14/0.41 ((~(rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), i2003_11_14_17_21_33997) <=> rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), i2003_11_14_17_21_33997)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[300, 299])).
% 0.14/0.41 tff(302,plain,
% 0.14/0.41 (rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), i2003_11_14_17_21_33997)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[301, 297])).
% 0.14/0.41 tff(303,plain,
% 0.14/0.41 (((~![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (caxcomp(i2003_11_14_17_21_33997) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), i2003_11_14_17_21_33997)))) <=> ((~![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | caxcomp(i2003_11_14_17_21_33997) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), i2003_11_14_17_21_33997)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(304,plain,
% 0.14/0.41 ((~![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (caxcomp(i2003_11_14_17_21_33997) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), i2003_11_14_17_21_33997)))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(305,plain,
% 0.14/0.41 ((~![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | caxcomp(i2003_11_14_17_21_33997) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), i2003_11_14_17_21_33997))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.14/0.41 tff(306,plain,
% 0.14/0.41 ($false),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[305, 302, 288, 66])).
% 0.14/0.41 % SZS output end Proof
%------------------------------------------------------------------------------