0.00/0.02	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.04	% Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM
0.11/0.37	% Computer : n019.cluster.edu
0.11/0.37	% Model    : x86_64 x86_64
0.11/0.37	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.37	% Memory   : 8046.5625MB
0.11/0.37	% OS       : Linux 6.8.0-71-generic
0.11/0.37	% CPULimit : 1440
0.11/0.37	% WCLimit  : 180
0.11/0.37	% DateTime : Mon Jul 27 15:13:07 UTC 2026
0.11/0.38	% CPUTime  : 
0.11/0.38	Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM
0.11/0.41	Running higher-order theorem proving
0.11/0.46	Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p
11.88/2.23	% Version: 3.5.1-ho
11.88/2.23	% Preprocessing class: HSLMSMSSLLLCHSA.
11.88/2.23	% Scheduled 6 strats onto 8 cores with 180 seconds (1440 total)
11.88/2.23	% Starting lpo1_fix with 540s (3) cores
11.88/2.23	% Starting full_lambda_9 with 180s (1) cores
11.88/2.23	% Starting almost_fo_4 with 180s (1) cores
11.88/2.23	% Starting new_ho_9 with 180s (1) cores
11.88/2.23	% Starting pre_casc_4 with 180s (1) cores
11.88/2.23	% Starting ho_unfolding_6 with 180s (1) cores
11.88/2.23	% lpo1_fix with pid 2580685 completed with status 0
11.88/2.23	% Result found by lpo1_fix
11.88/2.23	% Preprocessing class: HSLMSMSSLLLCHSA.
11.88/2.23	% Scheduled 6 strats onto 8 cores with 180 seconds (1440 total)
11.88/2.23	% Starting lpo1_fix with 540s (3) cores
11.88/2.23	% (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
11.88/2.23	% No SInE strategy applied
11.88/2.23	% Search class: HGHSM-FSLM32-MHSMMSBN
11.88/2.23	% Scheduled 11 strats onto 3 cores with 540 seconds (540 total)
11.88/2.23	% Starting SubtermCWHack with 55s (1) cores
11.88/2.23	% Starting full_lambda_5 with 50s (1) cores
11.88/2.23	% Starting new_ho_6 with 50s (1) cores
11.88/2.23	% full_lambda_5 with pid 2580742 completed with status 0
11.88/2.23	% Result found by full_lambda_5
11.88/2.23	% Preprocessing class: HSLMSMSSLLLCHSA.
11.88/2.23	% Scheduled 6 strats onto 8 cores with 180 seconds (1440 total)
11.88/2.23	% Starting lpo1_fix with 540s (3) cores
11.88/2.23	% (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
11.88/2.23	% No SInE strategy applied
11.88/2.23	% Search class: HGHSM-FSLM32-MHSMMSBN
11.88/2.23	% Scheduled 11 strats onto 3 cores with 540 seconds (540 total)
11.88/2.23	% Starting SubtermCWHack with 55s (1) cores
11.88/2.23	% Starting full_lambda_5 with 50s (1) cores
11.88/2.23	% Preprocessing time       : 0.017 s
11.88/2.23	% Presaturation interreduction done
11.88/2.23	
11.88/2.23	% Proof found!
11.88/2.23	% SZS status Theorem
11.88/2.23	% SZS output start CNFRefutation
11.88/2.23	thf(decl_23, type, is_of: $i > ($i > $o) > $o).
11.88/2.23	thf(decl_24, type, all_of: ($i > $o) > ($i > $o) > $o).
11.88/2.23	thf(decl_26, type, in: $i > $i > $o).
11.88/2.23	thf(decl_28, type, emptyset: $i).
11.88/2.23	thf(decl_48, type, ordsucc: $i > $i).
11.88/2.23	thf(decl_62, type, imp: $o > $o > $o).
11.88/2.23	thf(decl_63, type, d_not: $o > $o).
11.88/2.23	thf(decl_66, type, l_ec: $o > $o > $o).
11.88/2.23	thf(decl_67, type, d_and: $o > $o > $o).
11.88/2.23	thf(decl_68, type, l_or: $o > $o > $o).
11.88/2.23	thf(decl_72, type, non: $i > ($i > $o) > $i > $o).
11.88/2.23	thf(decl_73, type, l_some: $i > ($i > $o) > $o).
11.88/2.23	thf(decl_75, type, and3: $o > $o > $o > $o).
11.88/2.23	thf(decl_76, type, ec3: $o > $o > $o > $o).
11.88/2.23	thf(decl_78, type, e_is: $i > $i > $i > $o).
11.88/2.23	thf(decl_124, type, nat: $i).
11.88/2.23	thf(decl_125, type, n_is: $i > $i > $o).
11.88/2.23	thf(decl_126, type, nis: $i > $i > $o).
11.88/2.23	thf(decl_128, type, n_some: ($i > $o) > $o).
11.88/2.23	thf(decl_131, type, n_1: $i).
11.88/2.23	thf(decl_143, type, n_pl: $i > $i > $i).
11.88/2.23	thf(decl_148, type, diffprop: $i > $i > $i > $o).
11.88/2.23	thf(decl_149, type, d_29_ii: $i > $i > $o).
11.88/2.23	thf(decl_150, type, iii: $i > $i > $o).
11.88/2.23	thf(decl_152, type, moreis: $i > $i > $o).
11.88/2.23	thf(decl_153, type, lessis: $i > $i > $o).
11.88/2.23	thf(decl_188, type, esk31_2: $i > $i > $i).
11.88/2.23	thf(decl_189, type, esk32_2: $i > $i > $i).
11.88/2.23	thf(decl_212, type, esk55_2: $i > $i > $i).
11.88/2.23	thf(decl_215, type, esk58_2: $i > $i > $i).
11.88/2.23	thf(decl_233, type, esk76_0: $i).
11.88/2.23	thf(decl_234, type, esk77_0: $i).
11.88/2.23	thf(decl_235, type, esk78_0: $i).
11.88/2.23	thf(decl_240, type, esk83_3: $i > $i > $i > $i).
11.88/2.23	thf(decl_247, type, esk90_2: $i > $i > $i).
11.88/2.23	thf(def_d_not, axiom, ((d_not)=(^[X36:$o]:((imp @ ((X36)) @ (~($true)))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', def_d_not)).
11.88/2.23	thf(def_imp, axiom, ((imp)=(^[X34:$o, X35:$o]:((((X34))=>((X35)))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', def_imp)).
11.88/2.23	thf(def_all_of, axiom, ((all_of)=(^[X3:$i > $o, X2:$i > $o]:(![X4:$i]:((((is_of @ X4 @ X3))=>((X2 @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', def_all_of)).
11.88/2.23	thf(def_is_of, axiom, ((is_of)=(^[X1:$i, X2:$i > $o]:((X2 @ X1)))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', def_is_of)).
11.88/2.23	thf(def_non, axiom, ((non)=(^[X1:$i, X2:$i > $o, X4:$i]:((d_not @ ((X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', def_non)).
11.88/2.23	thf(def_l_some, axiom, ((l_some)=(^[X1:$i, X2:$i > $o]:((d_not @ ((all_of @ (^[X4:$i]:((in @ X4 @ X1))) @ (non @ X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', def_l_some)).
11.88/2.23	thf(def_e_is, axiom, ((e_is)=(^[X1:$i, X60:$i, X61:$i]:(((X60)=(X61))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', def_e_is)).
11.88/2.23	thf(def_diffprop, axiom, ((diffprop)=(^[X1:$i, X183:$i, X4:$i]:((n_is @ X1 @ (n_pl @ X183 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', def_diffprop)).
11.88/2.23	thf(def_n_is, axiom, ((n_is)=(^[Z0:$i, Z1:$i]:(((Z0)=(Z1))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', def_n_is)).
11.88/2.23	thf(def_l_or, axiom, ((l_or)=(^[X42:$o]:(imp @ ((d_not @ ((X42))))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', def_l_or)).
11.88/2.23	thf(def_iii, axiom, ((iii)=(^[X1:$i, X185:$i]:((n_some @ (diffprop @ X185 @ X1))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', def_iii)).
11.88/2.23	thf(def_n_some, axiom, ((n_some)=(^[Z0:$i > $o]:(((((((![X505:$i]:((((((in @ X505 @ nat))))=>((((((((Z0 @ X505))))=>((~($true)))))))))))))=>((~($true)))))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', def_n_some)).
11.88/2.23	thf(def_lessis, axiom, ((lessis)=(^[X1:$i, X188:$i]:((l_or @ ((iii @ X1 @ X188)) @ ((n_is @ X1 @ X188)))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', def_lessis)).
11.88/2.23	thf(def_d_29_ii, axiom, ((d_29_ii)=(^[X1:$i, X184:$i]:((n_some @ (diffprop @ X1 @ X184))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', def_d_29_ii)).
11.88/2.23	thf(def_l_ec, axiom, ((l_ec)=(^[X38:$o, X39:$o]:((imp @ ((X38)) @ ((d_not @ ((X39)))))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', def_l_ec)).
11.88/2.23	thf(satz26, conjecture, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X295:$i]:((in @ X295 @ nat))) @ (^[X296:$i]:((((iii @ X296 @ (n_pl @ X1 @ n_1)))=>((lessis @ X296 @ X1))))))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', satz26)).
11.88/2.23	thf(def_d_and, axiom, ((d_and)=(^[X40:$o, X41:$o]:((d_not @ ((l_ec @ ((X40)) @ ((X41)))))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', def_d_and)).
11.88/2.23	thf(satz10k, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X201:$i]:((in @ X201 @ nat))) @ (^[X202:$i]:((((d_not @ ((lessis @ X1 @ X202))))=>((d_29_ii @ X1 @ X202))))))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', satz10k)).
11.88/2.23	thf(def_and3, axiom, ((and3)=(^[X51:$o, X52:$o, X53:$o]:((d_and @ ((X51)) @ ((d_and @ ((X52)) @ ((X53)))))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', def_and3)).
11.88/2.23	thf(def_moreis, axiom, ((moreis)=(^[X1:$i, X187:$i]:((l_or @ ((d_29_ii @ X1 @ X187)) @ ((n_is @ X1 @ X187)))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', def_moreis)).
11.88/2.23	thf(satz11, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X256:$i]:((in @ X256 @ nat))) @ (^[X257:$i]:((((d_29_ii @ X1 @ X257))=>((iii @ X257 @ X1))))))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', satz11)).
11.88/2.23	thf(def_ec3, axiom, ((ec3)=(^[X54:$o, X55:$o, X56:$o]:((and3 @ ((l_ec @ ((X54)) @ ((X55)))) @ ((l_ec @ ((X55)) @ ((X56)))) @ ((l_ec @ ((X56)) @ ((X54)))))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', def_ec3)).
11.88/2.23	thf(satz16a, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X307:$i]:((in @ X307 @ nat))) @ (^[X308:$i]:((all_of @ (^[X4:$i]:((in @ X4 @ nat))) @ (^[X4:$i]:((((((iii @ X1 @ X4))<=((iii @ X308 @ X4))))<=((lessis @ X1 @ X308)))))))))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', satz16a)).
11.88/2.23	thf(satz12, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X264:$i]:((in @ X264 @ nat))) @ (^[X265:$i]:((((d_29_ii @ X265 @ X1))<=((iii @ X1 @ X265))))))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', satz12)).
11.88/2.23	thf(def_nis, axiom, ((nis)=(^[X1:$i, X113:$i]:((d_not @ ((n_is @ X1 @ X113)))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', def_nis)).
11.88/2.23	thf(satz25a, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X321:$i]:((in @ X321 @ nat))) @ (^[X322:$i]:((((moreis @ X322 @ (ordsucc @ X1)))<=((d_29_ii @ X322 @ X1))))))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', satz25a)).
11.88/2.23	thf(satz9b, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X199:$i]:((in @ X199 @ nat))) @ (^[X200:$i]:((ec3 @ ((n_is @ X1 @ X200)) @ ((n_some @ (diffprop @ X1 @ X200))) @ ((n_some @ (diffprop @ X200 @ X1)))))))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', satz9b)).
11.88/2.23	thf(satz7, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X223:$i]:((in @ X223 @ nat))) @ (^[X224:$i]:((nis @ X224 @ (n_pl @ X1 @ X224)))))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', satz7)).
11.88/2.23	thf(satz6, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X189:$i]:((in @ X189 @ nat))) @ (^[X190:$i]:((n_is @ (n_pl @ X1 @ X190) @ (n_pl @ X190 @ X1)))))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', satz6)).
11.88/2.23	thf(def_n_1, axiom, ((n_1)=(ordsucc @ emptyset)), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', def_n_1)).
11.88/2.23	thf(suc_p, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((is_of @ (ordsucc @ X1) @ (^[X118:$i]:((in @ X118 @ nat))))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', suc_p)).
11.88/2.23	thf(satz4e, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((n_is @ (ordsucc @ X1) @ (n_pl @ X1 @ n_1))))), file('/export/starexec/sandbox/tmp/tmp.qQ1cn1LRpz/E---3.1_2580670.p', satz4e)).
11.88/2.23	thf(c_0_32, plain, ((d_not)=(^[Z0:$o]:((((((Z0)))=>((~($true)))))))), inference(fof_simplification,[status(thm)],[def_d_not])).
11.88/2.23	thf(c_0_33, plain, ((imp)=(^[Z0:$o, Z1:$o]:((((Z0))=>((Z1)))))), inference(fof_simplification,[status(thm)],[def_imp])).
11.88/2.23	thf(c_0_34, plain, ((all_of)=(^[Z0:$i > $o, Z1:$i > $o]:(![X4:$i]:(((((Z0 @ X4)))=>((Z1 @ X4))))))), inference(fof_simplification,[status(thm)],[def_all_of])).
11.88/2.23	thf(c_0_35, plain, ((is_of)=(^[Z0:$i, Z1:$i > $o]:((Z1 @ Z0)))), inference(fof_simplification,[status(thm)],[def_is_of])).
11.88/2.23	thf(c_0_36, plain, ((non)=(^[Z0:$i, Z1:$i > $o, Z2:$i]:(((((((Z1 @ Z2))))=>((~($true)))))))), inference(fof_simplification,[status(thm)],[def_non])).
11.88/2.23	thf(c_0_37, plain, ((d_not)=(^[Z0:$o]:((((((Z0)))=>((~($true)))))))), inference(apply_def,[status(thm)],[c_0_32, c_0_33])).
11.88/2.23	thf(c_0_38, plain, ((l_some)=(^[Z0:$i, Z1:$i > $o]:(((((((![X478:$i]:((((((in @ X478 @ Z0))))=>((((((((Z1 @ X478))))=>((~($true)))))))))))))=>((~($true)))))))), inference(fof_simplification,[status(thm)],[def_l_some])).
11.88/2.23	thf(c_0_39, plain, ((all_of)=(^[Z0:$i > $o, Z1:$i > $o]:(![X4:$i]:(((((Z0 @ X4)))=>((Z1 @ X4))))))), inference(apply_def,[status(thm)],[c_0_34, c_0_35])).
11.88/2.23	thf(c_0_40, plain, ((non)=(^[Z0:$i, Z1:$i > $o, Z2:$i]:(((((((Z1 @ Z2))))=>((~($true)))))))), inference(apply_def,[status(thm)],[c_0_36, c_0_37])).
11.88/2.23	thf(c_0_41, plain, ((e_is)=(^[Z0:$i, Z1:$i, Z2:$i]:(((Z1)=(Z2))))), inference(fof_simplification,[status(thm)],[def_e_is])).
11.88/2.23	thf(c_0_42, plain, ((l_some)=(^[Z0:$i, Z1:$i > $o]:(((((((![X478:$i]:((((((in @ X478 @ Z0))))=>((((((((Z1 @ X478))))=>((~($true)))))))))))))=>((~($true)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_38, c_0_39]), c_0_37]), c_0_40])).
11.88/2.23	thf(c_0_43, plain, ((diffprop)=(^[Z0:$i, Z1:$i, Z2:$i]:((((Z0)=(n_pl @ Z1 @ Z2)))))), inference(fof_simplification,[status(thm)],[def_diffprop])).
11.88/2.23	thf(c_0_44, axiom, ((n_is)=(^[Z0:$i, Z1:$i]:(((Z0)=(Z1))))), inference(apply_def,[status(thm)],[def_n_is, c_0_41])).
11.88/2.23	thf(c_0_45, plain, ((l_or)=(^[Z0:$o, Z1:$o]:((((((((((Z0))))=>((~($true)))))))=>((Z1)))))), inference(fof_simplification,[status(thm)],[def_l_or])).
11.88/2.23	thf(c_0_46, plain, ((iii)=(^[Z0:$i, Z1:$i]:(((((((![X517:$i]:((((((in @ X517 @ nat))))=>(((((((((((Z1)=(n_pl @ Z0 @ X517)))))))=>((~($true)))))))))))))=>((~($true)))))))), inference(fof_simplification,[status(thm)],[def_iii])).
11.88/2.23	thf(c_0_47, axiom, ((n_some)=(^[Z0:$i > $o]:(((((((![X505:$i]:((((((in @ X505 @ nat))))=>((((((((Z0 @ X505))))=>((~($true)))))))))))))=>((~($true)))))))), inference(apply_def,[status(thm)],[def_n_some, c_0_42])).
11.88/2.23	thf(c_0_48, plain, ((diffprop)=(^[Z0:$i, Z1:$i, Z2:$i]:((((Z0)=(n_pl @ Z1 @ Z2)))))), inference(apply_def,[status(thm)],[c_0_43, c_0_44])).
11.88/2.23	thf(c_0_49, plain, ((lessis)=(^[Z0:$i, Z1:$i]:(((((((((((((((((![X521:$i]:((((((in @ X521 @ nat))))=>(((((((((((Z1)=(n_pl @ Z0 @ X521)))))))=>((~($true)))))))))))))=>((~($true)))))))))=>((~($true)))))))=>(((((Z0)=(Z1)))))))))), inference(fof_simplification,[status(thm)],[def_lessis])).
11.88/2.23	thf(c_0_50, plain, ((l_or)=(^[Z0:$o, Z1:$o]:((((((((((Z0))))=>((~($true)))))))=>((Z1)))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_45, c_0_33]), c_0_37])).
11.88/2.23	thf(c_0_51, plain, ((iii)=(^[Z0:$i, Z1:$i]:(((((((![X517:$i]:((((((in @ X517 @ nat))))=>(((((((((((Z1)=(n_pl @ Z0 @ X517)))))))=>((~($true)))))))))))))=>((~($true)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_46, c_0_47]), c_0_48])).
11.88/2.23	thf(c_0_52, plain, ((d_29_ii)=(^[Z0:$i, Z1:$i]:(((((((![X516:$i]:((((((in @ X516 @ nat))))=>(((((((((((Z0)=(n_pl @ Z1 @ X516)))))))=>((~($true)))))))))))))=>((~($true)))))))), inference(fof_simplification,[status(thm)],[def_d_29_ii])).
11.88/2.23	thf(c_0_53, plain, ((l_ec)=(^[Z0:$o, Z1:$o]:((((((Z0)))=>((((((((Z1))))=>((~($true)))))))))))), inference(fof_simplification,[status(thm)],[def_l_ec])).
11.88/2.23	thf(c_0_54, negated_conjecture, ~((all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X295:$i]:((in @ X295 @ nat))) @ (^[X296:$i]:((((iii @ X296 @ (n_pl @ X1 @ n_1)))=>((lessis @ X296 @ X1)))))))))), inference(assume_negation,[status(cth)],[satz26])).
11.88/2.23	thf(c_0_55, plain, ((lessis)=(^[Z0:$i, Z1:$i]:(((((((((((((((((![X521:$i]:((((((in @ X521 @ nat))))=>(((((((((((Z1)=(n_pl @ Z0 @ X521)))))))=>((~($true)))))))))))))=>((~($true)))))))))=>((~($true)))))))=>(((((Z0)=(Z1)))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_49, c_0_50]), c_0_44]), c_0_51])).
11.88/2.23	thf(c_0_56, plain, ((d_29_ii)=(^[Z0:$i, Z1:$i]:(((((((![X516:$i]:((((((in @ X516 @ nat))))=>(((((((((((Z0)=(n_pl @ Z1 @ X516)))))))=>((~($true)))))))))))))=>((~($true)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_52, c_0_47]), c_0_48])).
11.88/2.23	thf(c_0_57, plain, ((d_and)=(^[Z0:$o, Z1:$o]:((((((((((((Z0))))=>(((((((((Z1)))))=>((~($true))))))))))))=>((~($true)))))))), inference(fof_simplification,[status(thm)],[def_d_and])).
11.88/2.23	thf(c_0_58, plain, ((l_ec)=(^[Z0:$o, Z1:$o]:((((((Z0)))=>((((((((Z1))))=>((~($true)))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_53, c_0_33]), c_0_37])).
11.88/2.23	thf(c_0_59, negated_conjecture, ~(![X856:$i]:(((in @ X856 @ nat)=>![X855:$i]:(((in @ X855 @ nat)=>((![X853:$i]:(((in @ X853 @ nat)=>(((n_pl @ X856 @ n_1)=(n_pl @ X855 @ X853))=>~($true))))=>~($true))=>(((![X854:$i]:(((in @ X854 @ nat)=>(((X856)=(n_pl @ X855 @ X854))=>~($true))))=>~($true))=>~($true))=>((X855)=(X856))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_54]), c_0_39]), c_0_51]), c_0_55])).
11.88/2.23	thf(c_0_60, plain, ![X627:$i]:(((in @ X627 @ nat)=>![X626:$i]:(((in @ X626 @ nat)=>(((((![X624:$i]:(((in @ X624 @ nat)=>(((X626)=(n_pl @ X627 @ X624))=>~($true))))=>~($true))=>~($true))=>((X627)=(X626)))=>~($true))=>(![X625:$i]:(((in @ X625 @ nat)=>(((X627)=(n_pl @ X626 @ X625))=>~($true))))=>~($true))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz10k]), c_0_39]), c_0_37]), c_0_56]), c_0_55])).
11.88/2.23	thf(c_0_61, plain, ((and3)=(^[Z0:$o, Z1:$o, Z2:$o]:(((((((((((((Z0)))))=>(((((((((((((((((((((Z1)))))=>((((((((((Z2))))))=>((~($true))))))))))))=>((~($true))))))))))=>((~($true))))))))))))=>((~($true)))))))), inference(fof_simplification,[status(thm)],[def_and3])).
11.88/2.23	thf(c_0_62, plain, ((d_and)=(^[Z0:$o, Z1:$o]:((((((((((((Z0))))=>(((((((((Z1)))))=>((~($true))))))))))))=>((~($true)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_57, c_0_37]), c_0_58])).
11.88/2.23	thf(c_0_63, plain, ((moreis)=(^[Z0:$i, Z1:$i]:(((((((((((((((((![X520:$i]:((((((in @ X520 @ nat))))=>(((((((((((Z0)=(n_pl @ Z1 @ X520)))))))=>((~($true)))))))))))))=>((~($true)))))))))=>((~($true)))))))=>(((((Z0)=(Z1)))))))))), inference(fof_simplification,[status(thm)],[def_moreis])).
11.88/2.23	thf(c_0_64, plain, ![X763:$i]:(((in @ X763 @ nat)=>![X762:$i]:(((in @ X762 @ nat)=>((![X760:$i]:(((in @ X760 @ nat)=>(((X763)=(n_pl @ X762 @ X760))=>~($true))))=>~($true))=>(![X761:$i]:(((in @ X761 @ nat)=>(((X763)=(n_pl @ X762 @ X761))=>~($true))))=>~($true))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz11]), c_0_39]), c_0_56]), c_0_51])).
11.88/2.23	thf(c_0_65, negated_conjecture, ![X1660:$i]:(((in @ esk76_0 @ nat)&((in @ esk77_0 @ nat)&((((in @ esk78_0 @ nat)|~($true))&((((n_pl @ esk76_0 @ n_1)=(n_pl @ esk77_0 @ esk78_0))|~($true))&(($true)|~($true))))&(((~(in @ X1660 @ nat)|(((esk76_0)!=(n_pl @ esk77_0 @ X1660))|~($true))|~($true))&(($true)|~($true)))&((esk77_0)!=(esk76_0))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])])])])])])).
11.88/2.23	thf(c_0_66, plain, ![X1416:$i, X1417:$i]:(((((((in @ (esk32_2 @ X1416 @ X1417) @ nat)|~($true)|((in @ (esk31_2 @ X1416 @ X1417) @ nat)|~($true)|((X1416)=(X1417)))|~(in @ X1417 @ nat)|~(in @ X1416 @ nat))&((((X1416)=(n_pl @ X1417 @ (esk32_2 @ X1416 @ X1417)))|~($true)|((in @ (esk31_2 @ X1416 @ X1417) @ nat)|~($true)|((X1416)=(X1417)))|~(in @ X1417 @ nat)|~(in @ X1416 @ nat))&(($true)|~($true)|((in @ (esk31_2 @ X1416 @ X1417) @ nat)|~($true)|((X1416)=(X1417)))|~(in @ X1417 @ nat)|~(in @ X1416 @ nat))))&((((in @ (esk32_2 @ X1416 @ X1417) @ nat)|~($true)|(((X1417)=(n_pl @ X1416 @ (esk31_2 @ X1416 @ X1417)))|~($true)|((X1416)=(X1417)))|~(in @ X1417 @ nat)|~(in @ X1416 @ nat))&((((X1416)=(n_pl @ X1417 @ (esk32_2 @ X1416 @ X1417)))|~($true)|(((X1417)=(n_pl @ X1416 @ (esk31_2 @ X1416 @ X1417)))|~($true)|((X1416)=(X1417)))|~(in @ X1417 @ nat)|~(in @ X1416 @ nat))&(($true)|~($true)|(((X1417)=(n_pl @ X1416 @ (esk31_2 @ X1416 @ X1417)))|~($true)|((X1416)=(X1417)))|~(in @ X1417 @ nat)|~(in @ X1416 @ nat))))&(((in @ (esk32_2 @ X1416 @ X1417) @ nat)|~($true)|(($true)|~($true)|((X1416)=(X1417)))|~(in @ X1417 @ nat)|~(in @ X1416 @ nat))&((((X1416)=(n_pl @ X1417 @ (esk32_2 @ X1416 @ X1417)))|~($true)|(($true)|~($true)|((X1416)=(X1417)))|~(in @ X1417 @ nat)|~(in @ X1416 @ nat))&(($true)|~($true)|(($true)|~($true)|((X1416)=(X1417)))|~(in @ X1417 @ nat)|~(in @ X1416 @ nat))))))&(((in @ (esk32_2 @ X1416 @ X1417) @ nat)|~($true)|(($true)|((X1416)=(X1417)))|~(in @ X1417 @ nat)|~(in @ X1416 @ nat))&((((X1416)=(n_pl @ X1417 @ (esk32_2 @ X1416 @ X1417)))|~($true)|(($true)|((X1416)=(X1417)))|~(in @ X1417 @ nat)|~(in @ X1416 @ nat))&(($true)|~($true)|(($true)|((X1416)=(X1417)))|~(in @ X1417 @ nat)|~(in @ X1416 @ nat)))))&(((in @ (esk32_2 @ X1416 @ X1417) @ nat)|~($true)|($true)|~(in @ X1417 @ nat)|~(in @ X1416 @ nat))&((((X1416)=(n_pl @ X1417 @ (esk32_2 @ X1416 @ X1417)))|~($true)|($true)|~(in @ X1417 @ nat)|~(in @ X1416 @ nat))&(($true)|~($true)|($true)|~(in @ X1417 @ nat)|~(in @ X1416 @ nat)))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_60])])])])])])).
11.88/2.23	thf(c_0_67, plain, ((ec3)=(^[Z0:$o, Z1:$o, Z2:$o]:(((((((((((((((((((Z0))))=>(((((((((Z1)))))=>((~($true))))))))))))))=>(((((((((((((((((((((((((((Z1))))=>(((((((((Z2)))))=>((~($true))))))))))))))=>((((((((((((((((Z2))))=>(((((((((Z0)))))=>((~($true)))))))))))))))=>((~($true))))))))))))=>((~($true))))))))))=>((~($true))))))))))))=>((~($true)))))))), inference(fof_simplification,[status(thm)],[def_ec3])).
11.88/2.23	thf(c_0_68, plain, ((and3)=(^[Z0:$o, Z1:$o, Z2:$o]:(((((((((((((Z0)))))=>(((((((((((((((((((((Z1)))))=>((((((((((Z2))))))=>((~($true))))))))))))=>((~($true))))))))))=>((~($true))))))))))))=>((~($true)))))))), inference(apply_def,[status(thm)],[c_0_61, c_0_62])).
11.88/2.23	thf(c_0_69, plain, ((moreis)=(^[Z0:$i, Z1:$i]:(((((((((((((((((![X520:$i]:((((((in @ X520 @ nat))))=>(((((((((((Z0)=(n_pl @ Z1 @ X520)))))))=>((~($true)))))))))))))=>((~($true)))))))))=>((~($true)))))))=>(((((Z0)=(Z1)))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_63, c_0_50]), c_0_44]), c_0_56])).
11.88/2.23	thf(c_0_70, plain, ![X888:$i]:(((in @ X888 @ nat)=>![X887:$i]:(((in @ X887 @ nat)=>![X886:$i]:(((in @ X886 @ nat)=>((((![X885:$i]:(((in @ X885 @ nat)=>(((X887)=(n_pl @ X888 @ X885))=>~($true))))=>~($true))=>~($true))=>((X888)=(X887)))=>((![X884:$i]:(((in @ X884 @ nat)=>(((X886)=(n_pl @ X887 @ X884))=>~($true))))=>~($true))=>(![X883:$i]:(((in @ X883 @ nat)=>(((X886)=(n_pl @ X888 @ X883))=>~($true))))=>~($true)))))))))), inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz16a]), c_0_39]), c_0_51]), c_0_55])])).
11.88/2.23	thf(c_0_71, plain, ![X1552:$i, X1553:$i, X1554:$i]:(((((in @ (esk55_2 @ X1552 @ X1553) @ nat)|~($true)|(~(in @ X1554 @ nat)|(((X1552)!=(n_pl @ X1553 @ X1554))|~($true)))|~(in @ X1553 @ nat)|~(in @ X1552 @ nat))&((((X1552)=(n_pl @ X1553 @ (esk55_2 @ X1552 @ X1553)))|~($true)|(~(in @ X1554 @ nat)|(((X1552)!=(n_pl @ X1553 @ X1554))|~($true)))|~(in @ X1553 @ nat)|~(in @ X1552 @ nat))&(($true)|~($true)|(~(in @ X1554 @ nat)|(((X1552)!=(n_pl @ X1553 @ X1554))|~($true)))|~(in @ X1553 @ nat)|~(in @ X1552 @ nat))))&(((in @ (esk55_2 @ X1552 @ X1553) @ nat)|~($true)|($true)|~(in @ X1553 @ nat)|~(in @ X1552 @ nat))&((((X1552)=(n_pl @ X1553 @ (esk55_2 @ X1552 @ X1553)))|~($true)|($true)|~(in @ X1553 @ nat)|~(in @ X1552 @ nat))&(($true)|~($true)|($true)|~(in @ X1553 @ nat)|~(in @ X1552 @ nat)))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])])])])])).
11.88/2.23	thf(c_0_72, negated_conjecture, ![X1:$i]:((~((in @ X1 @ nat))|((esk76_0)!=(n_pl @ esk77_0 @ X1))|~(($true))|~(($true)))), inference(split_conjunct,[status(thm)],[c_0_65])).
11.88/2.23	thf(c_0_73, plain, ![X4:$i, X1:$i]:((((X1)=(n_pl @ X4 @ (esk32_2 @ X1 @ X4)))|((X4)=(n_pl @ X1 @ (esk31_2 @ X1 @ X4)))|((X1)=(X4))|~(($true))|~(($true))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_66])).
11.88/2.23	thf(c_0_74, plain, ![X4:$i, X1:$i]:((((X1)=(n_pl @ X4 @ (esk32_2 @ X1 @ X4)))|(in @ (esk31_2 @ X1 @ X4) @ nat)|((X1)=(X4))|~(($true))|~(($true))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_66])).
11.88/2.23	thf(c_0_75, plain, ![X785:$i]:(((in @ X785 @ nat)=>![X784:$i]:(((in @ X784 @ nat)=>((![X783:$i]:(((in @ X783 @ nat)=>(((X784)=(n_pl @ X785 @ X783))=>~($true))))=>~($true))=>(![X782:$i]:(((in @ X782 @ nat)=>(((X784)=(n_pl @ X785 @ X782))=>~($true))))=>~($true))))))), inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz12]), c_0_39]), c_0_56]), c_0_51])])).
11.88/2.23	thf(c_0_76, plain, ((nis)=(^[Z0:$i, Z1:$i]:(((((((((Z0)=(Z1))))))=>((~($true)))))))), inference(fof_simplification,[status(thm)],[def_nis])).
11.88/2.23	thf(c_0_77, plain, ((ec3)=(^[Z0:$o, Z1:$o, Z2:$o]:(((((((((((((((((((Z0))))=>(((((((((Z1)))))=>((~($true))))))))))))))=>(((((((((((((((((((((((((((Z1))))=>(((((((((Z2)))))=>((~($true))))))))))))))=>((((((((((((((((Z2))))=>(((((((((Z0)))))=>((~($true)))))))))))))))=>((~($true))))))))))))=>((~($true))))))))))=>((~($true))))))))))))=>((~($true)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_67, c_0_58]), c_0_68])).
11.88/2.23	thf(c_0_78, plain, ![X919:$i]:(((in @ X919 @ nat)=>![X918:$i]:(((in @ X918 @ nat)=>((![X917:$i]:(((in @ X917 @ nat)=>(((X918)=(n_pl @ X919 @ X917))=>~($true))))=>~($true))=>(((![X916:$i]:(((in @ X916 @ nat)=>(((X918)=(n_pl @ (ordsucc @ X919) @ X916))=>~($true))))=>~($true))=>~($true))=>((X918)=(ordsucc @ X919)))))))), inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz25a]), c_0_39]), c_0_56]), c_0_69])])).
11.88/2.23	thf(c_0_79, plain, ![X1687:$i, X1688:$i, X1689:$i, X1690:$i, X1691:$i]:(((((((in @ (esk83_3 @ X1687 @ X1688 @ X1689) @ nat)|~($true)|(~(in @ X1691 @ nat)|(((X1689)!=(n_pl @ X1688 @ X1691))|~($true)))|(~(in @ X1690 @ nat)|(((X1688)!=(n_pl @ X1687 @ X1690))|~($true))|~($true))|~(in @ X1689 @ nat)|~(in @ X1688 @ nat)|~(in @ X1687 @ nat))&((((X1689)=(n_pl @ X1687 @ (esk83_3 @ X1687 @ X1688 @ X1689)))|~($true)|(~(in @ X1691 @ nat)|(((X1689)!=(n_pl @ X1688 @ X1691))|~($true)))|(~(in @ X1690 @ nat)|(((X1688)!=(n_pl @ X1687 @ X1690))|~($true))|~($true))|~(in @ X1689 @ nat)|~(in @ X1688 @ nat)|~(in @ X1687 @ nat))&(($true)|~($true)|(~(in @ X1691 @ nat)|(((X1689)!=(n_pl @ X1688 @ X1691))|~($true)))|(~(in @ X1690 @ nat)|(((X1688)!=(n_pl @ X1687 @ X1690))|~($true))|~($true))|~(in @ X1689 @ nat)|~(in @ X1688 @ nat)|~(in @ X1687 @ nat))))&(((in @ (esk83_3 @ X1687 @ X1688 @ X1689) @ nat)|~($true)|($true)|(~(in @ X1690 @ nat)|(((X1688)!=(n_pl @ X1687 @ X1690))|~($true))|~($true))|~(in @ X1689 @ nat)|~(in @ X1688 @ nat)|~(in @ X1687 @ nat))&((((X1689)=(n_pl @ X1687 @ (esk83_3 @ X1687 @ X1688 @ X1689)))|~($true)|($true)|(~(in @ X1690 @ nat)|(((X1688)!=(n_pl @ X1687 @ X1690))|~($true))|~($true))|~(in @ X1689 @ nat)|~(in @ X1688 @ nat)|~(in @ X1687 @ nat))&(($true)|~($true)|($true)|(~(in @ X1690 @ nat)|(((X1688)!=(n_pl @ X1687 @ X1690))|~($true))|~($true))|~(in @ X1689 @ nat)|~(in @ X1688 @ nat)|~(in @ X1687 @ nat)))))&((((in @ (esk83_3 @ X1687 @ X1688 @ X1689) @ nat)|~($true)|(~(in @ X1691 @ nat)|(((X1689)!=(n_pl @ X1688 @ X1691))|~($true)))|(($true)|~($true))|~(in @ X1689 @ nat)|~(in @ X1688 @ nat)|~(in @ X1687 @ nat))&((((X1689)=(n_pl @ X1687 @ (esk83_3 @ X1687 @ X1688 @ X1689)))|~($true)|(~(in @ X1691 @ nat)|(((X1689)!=(n_pl @ X1688 @ X1691))|~($true)))|(($true)|~($true))|~(in @ X1689 @ nat)|~(in @ X1688 @ nat)|~(in @ X1687 @ nat))&(($true)|~($true)|(~(in @ X1691 @ nat)|(((X1689)!=(n_pl @ X1688 @ X1691))|~($true)))|(($true)|~($true))|~(in @ X1689 @ nat)|~(in @ X1688 @ nat)|~(in @ X1687 @ nat))))&(((in @ (esk83_3 @ X1687 @ X1688 @ X1689) @ nat)|~($true)|($true)|(($true)|~($true))|~(in @ X1689 @ nat)|~(in @ X1688 @ nat)|~(in @ X1687 @ nat))&((((X1689)=(n_pl @ X1687 @ (esk83_3 @ X1687 @ X1688 @ X1689)))|~($true)|($true)|(($true)|~($true))|~(in @ X1689 @ nat)|~(in @ X1688 @ nat)|~(in @ X1687 @ nat))&(($true)|~($true)|($true)|(($true)|~($true))|~(in @ X1689 @ nat)|~(in @ X1688 @ nat)|~(in @ X1687 @ nat))))))&((((in @ (esk83_3 @ X1687 @ X1688 @ X1689) @ nat)|~($true)|(~(in @ X1691 @ nat)|(((X1689)!=(n_pl @ X1688 @ X1691))|~($true)))|((X1687)!=(X1688))|~(in @ X1689 @ nat)|~(in @ X1688 @ nat)|~(in @ X1687 @ nat))&((((X1689)=(n_pl @ X1687 @ (esk83_3 @ X1687 @ X1688 @ X1689)))|~($true)|(~(in @ X1691 @ nat)|(((X1689)!=(n_pl @ X1688 @ X1691))|~($true)))|((X1687)!=(X1688))|~(in @ X1689 @ nat)|~(in @ X1688 @ nat)|~(in @ X1687 @ nat))&(($true)|~($true)|(~(in @ X1691 @ nat)|(((X1689)!=(n_pl @ X1688 @ X1691))|~($true)))|((X1687)!=(X1688))|~(in @ X1689 @ nat)|~(in @ X1688 @ nat)|~(in @ X1687 @ nat))))&(((in @ (esk83_3 @ X1687 @ X1688 @ X1689) @ nat)|~($true)|($true)|((X1687)!=(X1688))|~(in @ X1689 @ nat)|~(in @ X1688 @ nat)|~(in @ X1687 @ nat))&((((X1689)=(n_pl @ X1687 @ (esk83_3 @ X1687 @ X1688 @ X1689)))|~($true)|($true)|((X1687)!=(X1688))|~(in @ X1689 @ nat)|~(in @ X1688 @ nat)|~(in @ X1687 @ nat))&(($true)|~($true)|($true)|((X1687)!=(X1688))|~(in @ X1689 @ nat)|~(in @ X1688 @ nat)|~(in @ X1687 @ nat))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_70])])])])])])).
11.88/2.23	thf(c_0_80, plain, ![X5:$i, X4:$i, X1:$i]:((((X1)=(n_pl @ X4 @ (esk55_2 @ X1 @ X4)))|~(($true))|~((in @ X5 @ nat))|((X1)!=(n_pl @ X4 @ X5))|~(($true))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_71])).
11.88/2.23	thf(c_0_81, negated_conjecture, ![X1:$i]:((((esk76_0)!=(n_pl @ esk77_0 @ X1))|~((in @ X1 @ nat)))), inference(cn,[status(thm)],[c_0_72])).
11.88/2.23	thf(c_0_82, plain, ![X4:$i, X1:$i]:((((X1)=(X4))|((X4)=(n_pl @ X1 @ (esk31_2 @ X1 @ X4)))|((X1)=(n_pl @ X4 @ (esk32_2 @ X1 @ X4)))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(cn,[status(thm)],[c_0_73])).
11.88/2.23	thf(c_0_83, negated_conjecture, (in @ esk77_0 @ nat), inference(split_conjunct,[status(thm)],[c_0_65])).
11.88/2.23	thf(c_0_84, negated_conjecture, (in @ esk76_0 @ nat), inference(split_conjunct,[status(thm)],[c_0_65])).
11.88/2.23	thf(c_0_85, negated_conjecture, ((esk77_0)!=(esk76_0)), inference(split_conjunct,[status(thm)],[c_0_65])).
11.88/2.23	thf(c_0_86, plain, ![X4:$i, X1:$i]:(((in @ (esk32_2 @ X1 @ X4) @ nat)|((X4)=(n_pl @ X1 @ (esk31_2 @ X1 @ X4)))|((X1)=(X4))|~(($true))|~(($true))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_66])).
11.88/2.23	thf(c_0_87, plain, ![X4:$i, X1:$i]:((((X1)=(X4))|((X1)=(n_pl @ X4 @ (esk32_2 @ X1 @ X4)))|(in @ (esk31_2 @ X1 @ X4) @ nat)|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(cn,[status(thm)],[c_0_74])).
11.88/2.23	thf(c_0_88, plain, ![X4:$i, X1:$i]:(((in @ (esk32_2 @ X1 @ X4) @ nat)|(in @ (esk31_2 @ X1 @ X4) @ nat)|((X1)=(X4))|~(($true))|~(($true))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_66])).
11.88/2.23	thf(c_0_89, plain, ![X5:$i, X4:$i, X1:$i]:(((in @ (esk55_2 @ X1 @ X4) @ nat)|~(($true))|~((in @ X5 @ nat))|((X1)!=(n_pl @ X4 @ X5))|~(($true))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_71])).
11.88/2.23	thf(c_0_90, plain, ![X1576:$i, X1577:$i, X1578:$i]:(((((in @ (esk58_2 @ X1576 @ X1577) @ nat)|~($true)|(~(in @ X1578 @ nat)|(((X1577)!=(n_pl @ X1576 @ X1578))|~($true)))|~(in @ X1577 @ nat)|~(in @ X1576 @ nat))&((((X1577)=(n_pl @ X1576 @ (esk58_2 @ X1576 @ X1577)))|~($true)|(~(in @ X1578 @ nat)|(((X1577)!=(n_pl @ X1576 @ X1578))|~($true)))|~(in @ X1577 @ nat)|~(in @ X1576 @ nat))&(($true)|~($true)|(~(in @ X1578 @ nat)|(((X1577)!=(n_pl @ X1576 @ X1578))|~($true)))|~(in @ X1577 @ nat)|~(in @ X1576 @ nat))))&(((in @ (esk58_2 @ X1576 @ X1577) @ nat)|~($true)|($true)|~(in @ X1577 @ nat)|~(in @ X1576 @ nat))&((((X1577)=(n_pl @ X1576 @ (esk58_2 @ X1576 @ X1577)))|~($true)|($true)|~(in @ X1577 @ nat)|~(in @ X1576 @ nat))&(($true)|~($true)|($true)|~(in @ X1577 @ nat)|~(in @ X1576 @ nat)))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_75])])])])])])).
11.88/2.23	thf(c_0_91, plain, ((nis)=(^[Z0:$i, Z1:$i]:(((((((((Z0)=(Z1))))))=>((~($true)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_76, c_0_37]), c_0_44])).
11.88/2.23	thf(c_0_92, plain, ![X623:$i]:(((in @ X623 @ nat)=>![X622:$i]:(((in @ X622 @ nat)=>(((((X623)=(X622))=>((![X620:$i]:(((in @ X620 @ nat)=>(((X623)=(n_pl @ X622 @ X620))=>~($true))))=>~($true))=>~($true)))=>(((((![X620:$i]:(((in @ X620 @ nat)=>(((X623)=(n_pl @ X622 @ X620))=>~($true))))=>~($true))=>((![X621:$i]:(((in @ X621 @ nat)=>(((X622)=(n_pl @ X623 @ X621))=>~($true))))=>~($true))=>~($true)))=>(((![X621:$i]:(((in @ X621 @ nat)=>(((X622)=(n_pl @ X623 @ X621))=>~($true))))=>~($true))=>(((X623)=(X622))=>~($true)))=>~($true)))=>~($true))=>~($true)))=>~($true)))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz9b]), c_0_39]), c_0_77]), c_0_44]), c_0_47]), c_0_48])).
11.88/2.23	thf(c_0_93, plain, ![X1720:$i, X1721:$i, X1722:$i]:((((((in @ (esk90_2 @ X1720 @ X1721) @ nat)|~($true)|((X1721)=(ordsucc @ X1720))|(~(in @ X1722 @ nat)|(((X1721)!=(n_pl @ X1720 @ X1722))|~($true)))|~(in @ X1721 @ nat)|~(in @ X1720 @ nat))&((((X1721)=(n_pl @ (ordsucc @ X1720) @ (esk90_2 @ X1720 @ X1721)))|~($true)|((X1721)=(ordsucc @ X1720))|(~(in @ X1722 @ nat)|(((X1721)!=(n_pl @ X1720 @ X1722))|~($true)))|~(in @ X1721 @ nat)|~(in @ X1720 @ nat))&(($true)|~($true)|((X1721)=(ordsucc @ X1720))|(~(in @ X1722 @ nat)|(((X1721)!=(n_pl @ X1720 @ X1722))|~($true)))|~(in @ X1721 @ nat)|~(in @ X1720 @ nat))))&(($true)|((X1721)=(ordsucc @ X1720))|(~(in @ X1722 @ nat)|(((X1721)!=(n_pl @ X1720 @ X1722))|~($true)))|~(in @ X1721 @ nat)|~(in @ X1720 @ nat)))&((((in @ (esk90_2 @ X1720 @ X1721) @ nat)|~($true)|((X1721)=(ordsucc @ X1720))|($true)|~(in @ X1721 @ nat)|~(in @ X1720 @ nat))&((((X1721)=(n_pl @ (ordsucc @ X1720) @ (esk90_2 @ X1720 @ X1721)))|~($true)|((X1721)=(ordsucc @ X1720))|($true)|~(in @ X1721 @ nat)|~(in @ X1720 @ nat))&(($true)|~($true)|((X1721)=(ordsucc @ X1720))|($true)|~(in @ X1721 @ nat)|~(in @ X1720 @ nat))))&(($true)|((X1721)=(ordsucc @ X1720))|($true)|~(in @ X1721 @ nat)|~(in @ X1720 @ nat))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_78])])])])])])).
11.88/2.23	thf(c_0_94, plain, ![X1:$i, X6:$i, X5:$i, X4:$i]:((((X1)=(n_pl @ X4 @ (esk83_3 @ X4 @ X5 @ X1)))|~(($true))|~((in @ X6 @ nat))|((X1)!=(n_pl @ X5 @ X6))|~(($true))|((X4)!=(X5))|~((in @ X1 @ nat))|~((in @ X5 @ nat))|~((in @ X4 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_79])).
11.88/2.23	thf(c_0_95, plain, ![X5:$i, X4:$i, X1:$i]:((((X1)=(n_pl @ X4 @ (esk55_2 @ X1 @ X4)))|((X1)!=(n_pl @ X4 @ X5))|~((in @ X5 @ nat))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(cn,[status(thm)],[c_0_80])).
11.88/2.23	thf(c_0_96, negated_conjecture, (((n_pl @ esk76_0 @ (esk31_2 @ esk76_0 @ esk77_0))=(esk77_0))|~((in @ (esk32_2 @ esk76_0 @ esk77_0) @ nat))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_82]), c_0_83])])]), c_0_84])]), c_0_85])).
11.88/2.23	thf(c_0_97, plain, ![X4:$i, X1:$i]:((((X1)=(X4))|((X4)=(n_pl @ X1 @ (esk31_2 @ X1 @ X4)))|(in @ (esk32_2 @ X1 @ X4) @ nat)|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(cn,[status(thm)],[c_0_86])).
11.88/2.23	thf(c_0_98, negated_conjecture, ((in @ (esk31_2 @ esk76_0 @ esk77_0) @ nat)|~((in @ (esk32_2 @ esk76_0 @ esk77_0) @ nat))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_87]), c_0_83])])]), c_0_84])]), c_0_85])).
11.88/2.23	thf(c_0_99, plain, ![X4:$i, X1:$i]:((((X1)=(X4))|(in @ (esk31_2 @ X1 @ X4) @ nat)|(in @ (esk32_2 @ X1 @ X4) @ nat)|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(cn,[status(thm)],[c_0_88])).
11.88/2.23	thf(c_0_100, plain, ![X5:$i, X4:$i, X1:$i]:(((in @ (esk55_2 @ X1 @ X4) @ nat)|((X1)!=(n_pl @ X4 @ X5))|~((in @ X5 @ nat))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(cn,[status(thm)],[c_0_89])).
11.88/2.23	thf(c_0_101, plain, ![X6:$i, X5:$i, X4:$i, X1:$i]:(((in @ (esk83_3 @ X1 @ X4 @ X5) @ nat)|~(($true))|~((in @ X6 @ nat))|((X5)!=(n_pl @ X4 @ X6))|~(($true))|((X1)!=(X4))|~((in @ X5 @ nat))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_79])).
11.88/2.23	thf(c_0_102, plain, ![X1:$i, X5:$i, X4:$i]:((((X1)=(n_pl @ X4 @ (esk58_2 @ X4 @ X1)))|~(($true))|~((in @ X5 @ nat))|((X1)!=(n_pl @ X4 @ X5))|~(($true))|~((in @ X1 @ nat))|~((in @ X4 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_90])).
11.88/2.23	thf(c_0_103, plain, ![X5:$i, X4:$i, X1:$i]:(((in @ (esk58_2 @ X1 @ X4) @ nat)|~(($true))|~((in @ X5 @ nat))|((X4)!=(n_pl @ X1 @ X5))|~(($true))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_90])).
11.88/2.23	thf(c_0_104, plain, ![X681:$i]:(((in @ X681 @ nat)=>![X680:$i]:(((in @ X680 @ nat)=>(((X680)=(n_pl @ X681 @ X680))=>~($true)))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz7]), c_0_39]), c_0_91])).
11.88/2.23	thf(c_0_105, plain, ![X1410:$i, X1411:$i, X1412:$i, X1413:$i, X1414:$i, X1415:$i]:((((~(in @ X1412 @ nat)|(((X1410)!=(n_pl @ X1411 @ X1412))|~($true))|~($true)|((X1410)!=(X1411))|~($true)|~(in @ X1411 @ nat)|~(in @ X1410 @ nat))&(($true)|~($true)|((X1410)!=(X1411))|~($true)|~(in @ X1411 @ nat)|~(in @ X1410 @ nat)))&(((((~(in @ X1414 @ nat)|(((X1411)!=(n_pl @ X1410 @ X1414))|~($true))|~($true)|(~(in @ X1413 @ nat)|(((X1410)!=(n_pl @ X1411 @ X1413))|~($true)))|~($true)|~($true)|~(in @ X1411 @ nat)|~(in @ X1410 @ nat))&(($true)|~($true)|(~(in @ X1413 @ nat)|(((X1410)!=(n_pl @ X1411 @ X1413))|~($true)))|~($true)|~($true)|~(in @ X1411 @ nat)|~(in @ X1410 @ nat)))&((~(in @ X1414 @ nat)|(((X1411)!=(n_pl @ X1410 @ X1414))|~($true))|~($true)|($true)|~($true)|~($true)|~(in @ X1411 @ nat)|~(in @ X1410 @ nat))&(($true)|~($true)|($true)|~($true)|~($true)|~(in @ X1411 @ nat)|~(in @ X1410 @ nat))))&(((~(in @ X1415 @ nat)|(((X1411)!=(n_pl @ X1410 @ X1415))|~($true))|(((X1410)!=(X1411))|~($true))|~($true)|~($true)|~(in @ X1411 @ nat)|~(in @ X1410 @ nat))&(($true)|(((X1410)!=(X1411))|~($true))|~($true)|~($true)|~(in @ X1411 @ nat)|~(in @ X1410 @ nat)))&(($true)|~($true)|~($true)|~(in @ X1411 @ nat)|~(in @ X1410 @ nat))))&(($true)|~($true)|~(in @ X1411 @ nat)|~(in @ X1410 @ nat))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_92])])])])])).
11.88/2.23	thf(c_0_106, plain, ![X1:$i, X5:$i, X4:$i]:((((X1)=(n_pl @ (ordsucc @ X4) @ (esk90_2 @ X4 @ X1)))|((X1)=(ordsucc @ X4))|~(($true))|~((in @ X5 @ nat))|((X1)!=(n_pl @ X4 @ X5))|~(($true))|~((in @ X1 @ nat))|~((in @ X4 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_93])).
11.88/2.23	thf(c_0_107, plain, ![X6:$i, X5:$i, X4:$i, X1:$i]:((((X1)=(n_pl @ X4 @ (esk83_3 @ X4 @ X5 @ X1)))|((X4)!=(X5))|((X1)!=(n_pl @ X5 @ X6))|~((in @ X6 @ nat))|~((in @ X5 @ nat))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(cn,[status(thm)],[c_0_94])).
11.88/2.23	thf(c_0_108, plain, ![X4:$i, X1:$i]:((((n_pl @ X1 @ (esk55_2 @ (n_pl @ X1 @ X4) @ X1))=(n_pl @ X1 @ X4))|~((in @ (n_pl @ X1 @ X4) @ nat))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(er,[status(thm)],[c_0_95])).
11.88/2.23	thf(c_0_109, negated_conjecture, ((n_pl @ esk76_0 @ (esk31_2 @ esk76_0 @ esk77_0))=(esk77_0)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96, c_0_97]), c_0_83]), c_0_84])]), c_0_85])).
11.88/2.23	thf(c_0_110, negated_conjecture, (in @ (esk31_2 @ esk76_0 @ esk77_0) @ nat), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98, c_0_99]), c_0_83]), c_0_84])]), c_0_85])).
11.88/2.23	thf(c_0_111, plain, ![X4:$i, X1:$i]:(((in @ (esk55_2 @ (n_pl @ X1 @ X4) @ X1) @ nat)|~((in @ (n_pl @ X1 @ X4) @ nat))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(er,[status(thm)],[c_0_100])).
11.88/2.23	thf(c_0_112, plain, ![X6:$i, X5:$i, X4:$i, X1:$i]:(((in @ (esk83_3 @ X1 @ X4 @ X5) @ nat)|((X1)!=(X4))|((X5)!=(n_pl @ X4 @ X6))|~((in @ X6 @ nat))|~((in @ X5 @ nat))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(cn,[status(thm)],[c_0_101])).
11.88/2.23	thf(c_0_113, plain, ![X5:$i, X4:$i, X1:$i]:(((in @ (esk90_2 @ X1 @ X4) @ nat)|((X4)=(ordsucc @ X1))|~(($true))|~((in @ X5 @ nat))|((X4)!=(n_pl @ X1 @ X5))|~(($true))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_93])).
11.88/2.23	thf(c_0_114, plain, ![X5:$i, X4:$i, X1:$i]:((((X1)=(n_pl @ X4 @ (esk58_2 @ X4 @ X1)))|((X1)!=(n_pl @ X4 @ X5))|~((in @ X5 @ nat))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(cn,[status(thm)],[c_0_102])).
11.88/2.23	thf(c_0_115, plain, ![X5:$i, X4:$i, X1:$i]:(((in @ (esk58_2 @ X1 @ X4) @ nat)|((X4)!=(n_pl @ X1 @ X5))|~((in @ X5 @ nat))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(cn,[status(thm)],[c_0_103])).
11.88/2.23	thf(c_0_116, plain, ![X1472:$i, X1473:$i]:((~(in @ X1472 @ nat)|(~(in @ X1473 @ nat)|(((X1473)!=(n_pl @ X1472 @ X1473))|~($true))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_104])])])])).
11.88/2.23	thf(c_0_117, plain, ![X604:$i]:(((in @ X604 @ nat)=>![X603:$i]:(((in @ X603 @ nat)=>((n_pl @ X604 @ X603)=(n_pl @ X603 @ X604)))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz6]), c_0_39]), c_0_44])).
11.88/2.23	thf(c_0_118, plain, ![X1:$i, X4:$i, X6:$i, X5:$i]:((~((in @ X1 @ nat))|((X4)!=(n_pl @ X5 @ X1))|~(($true))|~(($true))|~((in @ X6 @ nat))|((X5)!=(n_pl @ X4 @ X6))|~(($true))|~(($true))|~(($true))|~((in @ X4 @ nat))|~((in @ X5 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_105])).
11.88/2.23	thf(c_0_119, plain, ![X5:$i, X4:$i, X1:$i]:((((X1)=(ordsucc @ X4))|((X1)=(n_pl @ (ordsucc @ X4) @ (esk90_2 @ X4 @ X1)))|((X1)!=(n_pl @ X4 @ X5))|~((in @ X5 @ nat))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(cn,[status(thm)],[c_0_106])).
11.88/2.23	thf(c_0_120, plain, ![X4:$i, X1:$i]:((((n_pl @ X1 @ (esk83_3 @ X1 @ X1 @ (n_pl @ X1 @ X4)))=(n_pl @ X1 @ X4))|~((in @ (n_pl @ X1 @ X4) @ nat))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_107])])).
11.88/2.23	thf(c_0_121, negated_conjecture, ((n_pl @ esk76_0 @ (esk55_2 @ esk77_0 @ esk76_0))=(esk77_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108, c_0_109]), c_0_83]), c_0_110]), c_0_84])])).
11.88/2.23	thf(c_0_122, negated_conjecture, (in @ (esk55_2 @ esk77_0 @ esk76_0) @ nat), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111, c_0_109]), c_0_83]), c_0_110]), c_0_84])])).
11.88/2.23	thf(c_0_123, plain, ![X4:$i, X1:$i]:(((in @ (esk83_3 @ X1 @ X1 @ (n_pl @ X1 @ X4)) @ nat)|~((in @ (n_pl @ X1 @ X4) @ nat))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_112])])).
11.88/2.23	thf(c_0_124, plain, ![X5:$i, X4:$i, X1:$i]:((((X4)=(ordsucc @ X1))|(in @ (esk90_2 @ X1 @ X4) @ nat)|((X4)!=(n_pl @ X1 @ X5))|~((in @ X5 @ nat))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(cn,[status(thm)],[c_0_113])).
11.88/2.23	thf(c_0_125, plain, ![X4:$i, X1:$i]:((((n_pl @ X1 @ (esk58_2 @ X1 @ (n_pl @ X1 @ X4)))=(n_pl @ X1 @ X4))|~((in @ (n_pl @ X1 @ X4) @ nat))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(er,[status(thm)],[c_0_114])).
11.88/2.23	thf(c_0_126, plain, ![X4:$i, X1:$i]:(((in @ (esk58_2 @ X1 @ (n_pl @ X1 @ X4)) @ nat)|~((in @ (n_pl @ X1 @ X4) @ nat))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(er,[status(thm)],[c_0_115])).
11.88/2.23	thf(c_0_127, plain, ![X1:$i, X4:$i]:((~((in @ X1 @ nat))|~((in @ X4 @ nat))|((X4)!=(n_pl @ X1 @ X4))|~(($true)))), inference(split_conjunct,[status(thm)],[c_0_116])).
11.88/2.23	thf(c_0_128, plain, ![X1393:$i, X1394:$i]:((~(in @ X1393 @ nat)|(~(in @ X1394 @ nat)|((n_pl @ X1393 @ X1394)=(n_pl @ X1394 @ X1393))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_117])])])])).
11.88/2.23	thf(c_0_129, negated_conjecture, (((n_pl @ esk76_0 @ n_1)=(n_pl @ esk77_0 @ esk78_0))|~(($true))), inference(split_conjunct,[status(thm)],[c_0_65])).
11.88/2.23	thf(c_0_130, plain, ![X6:$i, X5:$i, X4:$i, X1:$i]:((((X5)!=(n_pl @ X4 @ X6))|((X4)!=(n_pl @ X5 @ X1))|~((in @ X6 @ nat))|~((in @ X5 @ nat))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(cn,[status(thm)],[c_0_118])).
11.88/2.23	thf(c_0_131, plain, ![X4:$i, X1:$i]:((((n_pl @ (ordsucc @ X1) @ (esk90_2 @ X1 @ (n_pl @ X1 @ X4)))=(n_pl @ X1 @ X4))|((n_pl @ X1 @ X4)=(ordsucc @ X1))|~((in @ (n_pl @ X1 @ X4) @ nat))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(er,[status(thm)],[c_0_119])).
11.88/2.23	thf(c_0_132, negated_conjecture, ((n_pl @ esk76_0 @ (esk83_3 @ esk76_0 @ esk76_0 @ esk77_0))=(esk77_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120, c_0_121]), c_0_83]), c_0_122]), c_0_84])])).
11.88/2.23	thf(c_0_133, negated_conjecture, (in @ (esk83_3 @ esk76_0 @ esk76_0 @ esk77_0) @ nat), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123, c_0_109]), c_0_83]), c_0_110]), c_0_84])])).
11.88/2.23	thf(c_0_134, plain, ![X4:$i, X1:$i]:((((n_pl @ X1 @ X4)=(ordsucc @ X1))|(in @ (esk90_2 @ X1 @ (n_pl @ X1 @ X4)) @ nat)|~((in @ (n_pl @ X1 @ X4) @ nat))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(er,[status(thm)],[c_0_124])).
11.88/2.23	thf(c_0_135, negated_conjecture, ((n_pl @ esk76_0 @ (esk58_2 @ esk76_0 @ esk77_0))=(esk77_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125, c_0_109]), c_0_83]), c_0_110]), c_0_84])])).
11.88/2.23	thf(c_0_136, negated_conjecture, (in @ (esk58_2 @ esk76_0 @ esk77_0) @ nat), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126, c_0_109]), c_0_83]), c_0_110]), c_0_84])])).
11.88/2.23	thf(c_0_137, plain, ![X4:$i, X1:$i]:((((X4)!=(n_pl @ X1 @ X4))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(cn,[status(thm)],[c_0_127])).
11.88/2.23	thf(c_0_138, plain, ![X1:$i, X4:$i]:((((n_pl @ X1 @ X4)=(n_pl @ X4 @ X1))|~((in @ X1 @ nat))|~((in @ X4 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_128])).
11.88/2.23	thf(c_0_139, negated_conjecture, ((n_pl @ esk77_0 @ esk78_0)=(n_pl @ esk76_0 @ n_1)), inference(cn,[status(thm)],[c_0_129])).
11.88/2.23	thf(c_0_140, plain, ((n_1)=(ordsucc @ emptyset)), inference(split_conjunct,[status(thm)],[def_n_1])).
11.88/2.23	thf(c_0_141, negated_conjecture, ((in @ esk78_0 @ nat)|~(($true))), inference(split_conjunct,[status(thm)],[c_0_65])).
11.88/2.23	thf(c_0_142, plain, ![X1:$i, X4:$i, X5:$i]:((((n_pl @ (n_pl @ X1 @ X4) @ X5)!=(X1))|~((in @ (n_pl @ X1 @ X4) @ nat))|~((in @ X4 @ nat))|~((in @ X1 @ nat))|~((in @ X5 @ nat)))), inference(er,[status(thm)],[c_0_130])).
11.88/2.23	thf(c_0_143, negated_conjecture, (((n_pl @ (ordsucc @ esk76_0) @ (esk90_2 @ esk76_0 @ esk77_0))=(esk77_0))|((esk77_0)=(ordsucc @ esk76_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131, c_0_132]), c_0_83]), c_0_133]), c_0_84])])).
11.88/2.23	thf(c_0_144, negated_conjecture, (((esk77_0)=(ordsucc @ esk76_0))|(in @ (esk90_2 @ esk76_0 @ esk77_0) @ nat)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134, c_0_135]), c_0_83]), c_0_136]), c_0_84])])).
11.88/2.23	thf(c_0_145, plain, ![X1:$i, X4:$i]:((((n_pl @ X1 @ X4)!=(X1))|~((in @ X1 @ nat))|~((in @ X4 @ nat)))), inference(spm,[status(thm)],[c_0_137, c_0_138])).
11.88/2.23	thf(c_0_146, negated_conjecture, ((n_pl @ esk77_0 @ esk78_0)=(n_pl @ esk76_0 @ (ordsucc @ emptyset))), inference(rw,[status(thm)],[c_0_139, c_0_140])).
11.88/2.23	thf(c_0_147, negated_conjecture, (in @ esk78_0 @ nat), inference(cn,[status(thm)],[c_0_141])).
11.88/2.23	thf(c_0_148, negated_conjecture, ![X1:$i]:((((esk77_0)=(ordsucc @ esk76_0))|((n_pl @ esk77_0 @ X1)!=(ordsucc @ esk76_0))|~((in @ (ordsucc @ esk76_0) @ nat))|~((in @ X1 @ nat)))), inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142, c_0_143]), c_0_83])]), c_0_144])).
11.88/2.23	thf(c_0_149, plain, ![X534:$i]:(((in @ X534 @ nat)=>(in @ (ordsucc @ X534) @ nat))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[suc_p]), c_0_35]), c_0_39])).
11.88/2.23	thf(c_0_150, plain, ![X639:$i]:(((in @ X639 @ nat)=>((ordsucc @ X639)=(n_pl @ X639 @ n_1)))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz4e]), c_0_39]), c_0_44])).
11.88/2.23	thf(c_0_151, negated_conjecture, ((esk77_0)!=(n_pl @ esk76_0 @ (ordsucc @ emptyset))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145, c_0_146]), c_0_83]), c_0_147])])).
11.88/2.23	thf(c_0_152, negated_conjecture, (((esk77_0)=(ordsucc @ esk76_0))|((ordsucc @ esk76_0)!=(n_pl @ esk76_0 @ (ordsucc @ emptyset)))|~((in @ (ordsucc @ esk76_0) @ nat))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148, c_0_146]), c_0_147])])).
11.88/2.23	thf(c_0_153, plain, ![X1178:$i]:((~(in @ X1178 @ nat)|(in @ (ordsucc @ X1178) @ nat))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_149])])])).
11.88/2.23	thf(c_0_154, plain, ![X1431:$i]:((~(in @ X1431 @ nat)|((ordsucc @ X1431)=(n_pl @ X1431 @ n_1)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_150])])])).
11.88/2.23	thf(c_0_155, negated_conjecture, (((ordsucc @ esk76_0)!=(n_pl @ esk76_0 @ (ordsucc @ emptyset)))|~((in @ (ordsucc @ esk76_0) @ nat))), inference(spm,[status(thm)],[c_0_151, c_0_152])).
11.88/2.23	thf(c_0_156, plain, ![X1:$i]:(((in @ (ordsucc @ X1) @ nat)|~((in @ X1 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_153])).
11.88/2.23	thf(c_0_157, plain, ![X1:$i]:((((ordsucc @ X1)=(n_pl @ X1 @ n_1))|~((in @ X1 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_154])).
11.88/2.23	thf(c_0_158, negated_conjecture, ((ordsucc @ esk76_0)!=(n_pl @ esk76_0 @ (ordsucc @ emptyset))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155, c_0_156]), c_0_84])])).
11.88/2.23	thf(c_0_159, plain, ![X1:$i]:((((ordsucc @ X1)=(n_pl @ X1 @ (ordsucc @ emptyset)))|~((in @ X1 @ nat)))), inference(rw,[status(thm)],[c_0_157, c_0_140])).
11.88/2.23	thf(c_0_160, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158, c_0_159]), c_0_84])]), ['proof']).
11.88/2.23	% SZS output end CNFRefutation
11.88/2.23	% Parsed axioms                        : 405
11.88/2.23	% Removed by relevancy pruning/SinE    : 0
11.88/2.23	% Initial clauses                      : 1208
11.88/2.23	% Removed in clause preprocessing      : 745
11.88/2.23	% Initial clauses in saturation        : 463
11.88/2.23	% Processed clauses                    : 2472
11.88/2.23	% ...of these trivial                  : 161
11.88/2.23	% ...subsumed                          : 611
11.88/2.23	% ...remaining for further processing  : 1700
11.88/2.23	% Other redundant clauses eliminated   : 1037
11.88/2.23	% Clauses deleted for lack of memory   : 0
11.88/2.23	% Backward-subsumed                    : 34
11.88/2.23	% Backward-rewritten                   : 159
11.88/2.23	% Generated clauses                    : 37007
11.88/2.23	% ...of the previous two non-redundant : 35342
11.88/2.23	% ...aggressively subsumed             : 0
11.88/2.23	% Contextual simplify-reflections      : 18
11.88/2.23	% Paramodulations                      : 35708
11.88/2.23	% Factorizations                       : 2
11.88/2.23	% NegExts                              : 25
11.88/2.23	% Equation resolutions                 : 1049
11.88/2.23	% Disequality decompositions           : 0
11.88/2.23	% Total rewrite steps                  : 19472
11.88/2.23	% ...of those cached                   : 18947
11.88/2.23	% Propositional unsat checks           : 0
11.88/2.23	%    Propositional check models        : 0
11.88/2.23	%    Propositional check unsatisfiable : 0
11.88/2.23	%    Propositional clauses             : 0
11.88/2.23	%    Propositional clauses after purity: 0
11.88/2.23	%    Propositional unsat core size     : 0
11.88/2.23	%    Propositional preprocessing time  : 0.000
11.88/2.23	%    Propositional encoding time       : 0.000
11.88/2.23	%    Propositional solver time         : 0.000
11.88/2.23	%    Success case prop preproc time    : 0.000
11.88/2.23	%    Success case prop encoding time   : 0.000
11.88/2.23	%    Success case prop solver time     : 0.000
11.88/2.23	% Current number of processed clauses  : 948
11.88/2.23	%    Positive orientable unit clauses  : 196
11.88/2.23	%    Positive unorientable unit clauses: 7
11.88/2.23	%    Negative unit clauses             : 219
11.88/2.23	%    Non-unit-clauses                  : 526
11.88/2.23	% Current number of unprocessed clauses: 33500
11.88/2.23	% ...number of literals in the above   : 200219
11.88/2.23	% Current number of archived formulas  : 0
11.88/2.23	% Current number of archived clauses   : 618
11.88/2.23	% Clause-clause subsumption calls (NU) : 199852
11.88/2.23	% Rec. Clause-clause subsumption calls : 26961
11.88/2.23	% Non-unit clause-clause subsumptions  : 360
11.88/2.23	% Unit Clause-clause subsumption calls : 25009
11.88/2.23	% Rewrite failures with RHS unbound    : 0
11.88/2.23	% BW rewrite match attempts            : 151
11.88/2.23	% BW rewrite match successes           : 65
11.88/2.23	% Condensation attempts                : 0
11.88/2.23	% Condensation successes               : 0
11.88/2.23	% Termbank termtop insertions          : 1181903
11.88/2.23	% Search garbage collected termcells   : 49895
11.88/2.23	
11.88/2.23	% -------------------------------------------------
11.88/2.23	% User time                : 1.528 s
11.88/2.23	% System time              : 0.075 s
11.88/2.23	% Total time               : 1.602 s
11.88/2.23	% Maximum resident set size: 10716 pages
11.88/2.23	
11.88/2.23	% -------------------------------------------------
11.88/2.23	% User time                : 4.572 s
11.88/2.23	% System time              : 0.212 s
11.88/2.23	% Total time               : 4.785 s
11.88/2.23	% Maximum resident set size: 5376 pages
11.88/2.23	% E exiting
11.88/2.24	EOF