TSTP Solution File: KRS155+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS155+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 17:45:00 EDT 2022
% Result : Theorem 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KRS155+1 : TPTP v8.1.0. Released v3.1.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 09:49:43 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 tff(cC8_type, type, (
% 0.19/0.44 cC8: $i > $o)).
% 0.19/0.44 tff(iV8467_type, type, (
% 0.19/0.44 iV8467: $i)).
% 0.19/0.44 tff(cC4_type, type, (
% 0.19/0.44 cC4: $i > $o)).
% 0.19/0.44 tff(cC10_type, type, (
% 0.19/0.44 cC10: $i > $o)).
% 0.19/0.44 tff(rR1_type, type, (
% 0.19/0.44 rR1: ( $i * $i ) > $o)).
% 0.19/0.44 tff(cC6xcomp_type, type, (
% 0.19/0.44 cC6xcomp: $i > $o)).
% 0.19/0.44 tff(tptp_fun_Y_56_type, type, (
% 0.19/0.44 tptp_fun_Y_56: $i > $i)).
% 0.19/0.44 tff(iV8469_type, type, (
% 0.19/0.44 iV8469: $i)).
% 0.19/0.44 tff(cC2xcomp_type, type, (
% 0.19/0.44 cC2xcomp: $i > $o)).
% 0.19/0.44 tff(tptp_fun_Y_9_type, type, (
% 0.19/0.44 tptp_fun_Y_9: $i > $i)).
% 0.19/0.44 tff(iV8468_type, type, (
% 0.19/0.44 iV8468: $i)).
% 0.19/0.44 tff(cC60_type, type, (
% 0.19/0.44 cC60: $i > $o)).
% 0.19/0.44 tff(iV8472_type, type, (
% 0.19/0.44 iV8472: $i)).
% 0.19/0.44 tff(cC58_type, type, (
% 0.19/0.44 cC58: $i > $o)).
% 0.19/0.44 tff(cC2_type, type, (
% 0.19/0.44 cC2: $i > $o)).
% 0.19/0.44 tff(tptp_fun_Y_18_type, type, (
% 0.19/0.44 tptp_fun_Y_18: $i > $i)).
% 0.19/0.44 tff(iV8476_type, type, (
% 0.19/0.44 iV8476: $i)).
% 0.19/0.44 tff(cC48_type, type, (
% 0.19/0.44 cC48: $i > $o)).
% 0.19/0.44 tff(cC20_type, type, (
% 0.19/0.44 cC20: $i > $o)).
% 0.19/0.44 tff(cC34_type, type, (
% 0.19/0.44 cC34: $i > $o)).
% 0.19/0.44 tff(cC32xcomp_type, type, (
% 0.19/0.44 cC32xcomp: $i > $o)).
% 0.19/0.44 tff(tptp_fun_Y_22_type, type, (
% 0.19/0.44 tptp_fun_Y_22: $i > $i)).
% 0.19/0.44 tff(iV8474_type, type, (
% 0.19/0.44 iV8474: $i)).
% 0.19/0.44 tff(cC14_type, type, (
% 0.19/0.44 cC14: $i > $o)).
% 0.19/0.44 tff(cTOP_type, type, (
% 0.19/0.44 cTOP: $i > $o)).
% 0.19/0.44 tff(tptp_fun_Y_2_type, type, (
% 0.19/0.44 tptp_fun_Y_2: $i > $i)).
% 0.19/0.44 tff(iV8470_type, type, (
% 0.19/0.44 iV8470: $i)).
% 0.19/0.44 tff(cC62_type, type, (
% 0.19/0.44 cC62: $i > $o)).
% 0.19/0.44 tff(tptp_fun_Y_44_type, type, (
% 0.19/0.44 tptp_fun_Y_44: $i > $i)).
% 0.19/0.44 tff(cC82_type, type, (
% 0.19/0.44 cC82: $i > $o)).
% 0.19/0.44 tff(cC80_type, type, (
% 0.19/0.44 cC80: $i > $o)).
% 0.19/0.44 tff(tptp_fun_Y_58_type, type, (
% 0.19/0.44 tptp_fun_Y_58: $i > $i)).
% 0.19/0.44 tff(iV8471_type, type, (
% 0.19/0.44 iV8471: $i)).
% 0.19/0.44 tff(cC78xcomp_type, type, (
% 0.19/0.44 cC78xcomp: $i > $o)).
% 0.19/0.44 tff(cowlThing_type, type, (
% 0.19/0.44 cowlThing: $i > $o)).
% 0.19/0.44 tff(xsd_integer_type, type, (
% 0.19/0.44 xsd_integer: $i > $o)).
% 0.19/0.44 tff(xsd_string_type, type, (
% 0.19/0.44 xsd_string: $i > $o)).
% 0.19/0.44 tff(cowlNothing_type, type, (
% 0.19/0.44 cowlNothing: $i > $o)).
% 0.19/0.44 tff(1,assumption,((~((~cC8(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_56(iV8467))) | (~cC6xcomp(tptp_fun_Y_56(iV8467))))))) | (~(cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y)))))), introduced(assumption)).
% 0.19/0.44 tff(2,plain,
% 0.19/0.44 (^[X: $i] : refl((~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(3,plain,
% 0.19/0.44 (![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.44 tff(4,plain,
% 0.19/0.44 (^[X: $i] : rewrite((~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(5,plain,
% 0.19/0.44 (![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.44 tff(6,plain,
% 0.19/0.44 (![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[5, 3])).
% 0.19/0.44 tff(7,plain,
% 0.19/0.44 (^[X: $i] : trans(monotonicity(rewrite(((~cC8(X)) | (rR1(X, tptp_fun_Y_56(X)) & cC6xcomp(tptp_fun_Y_56(X)))) <=> ((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))), rewrite((cC8(X) | ![Y: $i] : (~(rR1(X, Y) & cC6xcomp(Y)))) <=> (cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y))))), ((((~cC8(X)) | (rR1(X, tptp_fun_Y_56(X)) & cC6xcomp(tptp_fun_Y_56(X)))) & (cC8(X) | ![Y: $i] : (~(rR1(X, Y) & cC6xcomp(Y))))) <=> (((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X)))))) & (cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y))))))), rewrite((((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X)))))) & (cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y))))) <=> (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y)))))))), ((((~cC8(X)) | (rR1(X, tptp_fun_Y_56(X)) & cC6xcomp(tptp_fun_Y_56(X)))) & (cC8(X) | ![Y: $i] : (~(rR1(X, Y) & cC6xcomp(Y))))) <=> (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y)))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(8,plain,
% 0.19/0.44 (![X: $i] : (((~cC8(X)) | (rR1(X, tptp_fun_Y_56(X)) & cC6xcomp(tptp_fun_Y_56(X)))) & (cC8(X) | ![Y: $i] : (~(rR1(X, Y) & cC6xcomp(Y))))) <=> ![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[7])).
% 0.19/0.44 tff(9,plain,
% 0.19/0.44 (![X: $i] : (cC8(X) <=> ?[Y: $i] : (rR1(X, Y) & cC6xcomp(Y))) <=> ![X: $i] : (cC8(X) <=> ?[Y: $i] : (rR1(X, Y) & cC6xcomp(Y)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(10,axiom,(![X: $i] : (cC8(X) <=> ?[Y: $i] : (rR1(X, Y) & cC6xcomp(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_79')).
% 0.19/0.44 tff(11,plain,
% 0.19/0.44 (![X: $i] : (cC8(X) <=> ?[Y: $i] : (rR1(X, Y) & cC6xcomp(Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.19/0.44 tff(12,plain,(
% 0.19/0.44 ![X: $i] : (((~cC8(X)) | (rR1(X, tptp_fun_Y_56(X)) & cC6xcomp(tptp_fun_Y_56(X)))) & (cC8(X) | ![Y: $i] : (~(rR1(X, Y) & cC6xcomp(Y)))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[11])).
% 0.19/0.44 tff(13,plain,
% 0.19/0.44 (![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.19/0.44 tff(14,plain,
% 0.19/0.44 (![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.19/0.44 tff(15,plain,
% 0.19/0.44 ((~![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC8(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_56(iV8467))) | (~cC6xcomp(tptp_fun_Y_56(iV8467))))))) | (~(cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y)))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(16,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[15, 14, 1])).
% 0.19/0.44 tff(17,plain,(~((~((~cC8(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_56(iV8467))) | (~cC6xcomp(tptp_fun_Y_56(iV8467))))))) | (~(cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(18,plain,
% 0.19/0.44 (((~((~cC8(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_56(iV8467))) | (~cC6xcomp(tptp_fun_Y_56(iV8467))))))) | (~(cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y)))))) | (cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(19,plain,
% 0.19/0.44 (cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.19/0.44 tff(20,assumption,(![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y)))), introduced(assumption)).
% 0.19/0.44 tff(21,plain,
% 0.19/0.44 (cC6xcomp(iV8469) <=> cC6xcomp(iV8469)),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(22,axiom,(cC6xcomp(iV8469)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_113')).
% 0.19/0.44 tff(23,plain,
% 0.19/0.44 (cC6xcomp(iV8469)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.45 tff(24,plain,
% 0.19/0.45 (rR1(iV8467, iV8469) <=> rR1(iV8467, iV8469)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(25,axiom,(rR1(iV8467, iV8469)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_105')).
% 0.19/0.45 tff(26,plain,
% 0.19/0.45 (rR1(iV8467, iV8469)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.45 tff(27,plain,
% 0.19/0.45 (((~![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y)))) | ((~cC6xcomp(iV8469)) | (~rR1(iV8467, iV8469)))) <=> ((~![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y)))) | (~cC6xcomp(iV8469)) | (~rR1(iV8467, iV8469)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(28,plain,
% 0.19/0.45 ((~![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y)))) | ((~cC6xcomp(iV8469)) | (~rR1(iV8467, iV8469)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(29,plain,
% 0.19/0.45 ((~![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y)))) | (~cC6xcomp(iV8469)) | (~rR1(iV8467, iV8469))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.45 tff(30,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[29, 26, 23, 20])).
% 0.19/0.45 tff(31,plain,(~![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(32,plain,
% 0.19/0.45 ((~(cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y))))) | cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(33,plain,
% 0.19/0.45 ((~(cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y))))) | cC8(iV8467)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.19/0.45 tff(34,plain,
% 0.19/0.45 (cC8(iV8467)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[33, 19])).
% 0.19/0.45 tff(35,assumption,((~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC4(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467)))))))), introduced(assumption)).
% 0.19/0.45 tff(36,plain,
% 0.19/0.45 (^[X: $i] : refl((~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(37,plain,
% 0.19/0.45 (![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.45 tff(38,plain,
% 0.19/0.45 (^[X: $i] : rewrite((~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(39,plain,
% 0.19/0.45 (![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.45 tff(40,plain,
% 0.19/0.45 (![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[39, 37])).
% 0.19/0.45 tff(41,plain,
% 0.19/0.45 (^[X: $i] : trans(monotonicity(rewrite(((~cC4(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) <=> ((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))), rewrite((cC4(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y)))) <=> (cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))), ((((~cC4(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) & (cC4(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y))))) <=> (((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X)))))) & (cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))), rewrite((((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X)))))) & (cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))) <=> (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))), ((((~cC4(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) & (cC4(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y))))) <=> (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(42,plain,
% 0.19/0.45 (![X: $i] : (((~cC4(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) & (cC4(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y))))) <=> ![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[41])).
% 0.19/0.45 tff(43,plain,
% 0.19/0.45 (![X: $i] : (cC4(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2xcomp(Y))) <=> ![X: $i] : (cC4(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2xcomp(Y)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(44,axiom,(![X: $i] : (cC4(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2xcomp(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_35')).
% 0.19/0.45 tff(45,plain,
% 0.19/0.45 (![X: $i] : (cC4(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2xcomp(Y)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.45 tff(46,plain,(
% 0.19/0.45 ![X: $i] : (((~cC4(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) & (cC4(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y)))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[45])).
% 0.19/0.45 tff(47,plain,
% 0.19/0.45 (![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.19/0.45 tff(48,plain,
% 0.19/0.45 (![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.19/0.45 tff(49,plain,
% 0.19/0.45 (((~![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC4(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467)))))))))) <=> ((~![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC4(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(50,plain,
% 0.19/0.45 ((~((~((~cC4(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))) | (~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))))) <=> (~((~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC4(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467)))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(51,plain,
% 0.19/0.45 (((~![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC4(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))) | (~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC4(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[50])).
% 0.19/0.45 tff(52,plain,
% 0.19/0.45 (((~![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC4(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))) | (~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC4(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[51, 49])).
% 0.19/0.45 tff(53,plain,
% 0.19/0.45 ((~![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC4(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))) | (~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(54,plain,
% 0.19/0.45 ((~![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC4(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467)))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.45 tff(55,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[54, 48, 35])).
% 0.19/0.45 tff(56,plain,(~((~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC4(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(57,plain,
% 0.19/0.45 (((~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC4(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467)))))))) | (cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(58,plain,
% 0.19/0.45 (cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.19/0.45 tff(59,assumption,(![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))), introduced(assumption)).
% 0.19/0.45 tff(60,plain,
% 0.19/0.45 (cC2xcomp(iV8468) <=> cC2xcomp(iV8468)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(61,axiom,(cC2xcomp(iV8468)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_111')).
% 0.19/0.45 tff(62,plain,
% 0.19/0.45 (cC2xcomp(iV8468)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.19/0.45 tff(63,plain,
% 0.19/0.45 (rR1(iV8467, iV8468) <=> rR1(iV8467, iV8468)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(64,axiom,(rR1(iV8467, iV8468)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_107')).
% 0.19/0.45 tff(65,plain,
% 0.19/0.45 (rR1(iV8467, iV8468)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.45 tff(66,plain,
% 0.19/0.45 (((~![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))) | ((~cC2xcomp(iV8468)) | (~rR1(iV8467, iV8468)))) <=> ((~![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))) | (~cC2xcomp(iV8468)) | (~rR1(iV8467, iV8468)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(67,plain,
% 0.19/0.45 ((~![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))) | ((~cC2xcomp(iV8468)) | (~rR1(iV8467, iV8468)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(68,plain,
% 0.19/0.45 ((~![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))) | (~cC2xcomp(iV8468)) | (~rR1(iV8467, iV8468))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.45 tff(69,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[68, 65, 62, 59])).
% 0.19/0.45 tff(70,plain,(~![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(71,plain,
% 0.19/0.45 ((~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(72,plain,
% 0.19/0.45 ((~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | cC4(iV8467)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.19/0.45 tff(73,plain,
% 0.19/0.45 (cC4(iV8467)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[72, 58])).
% 0.19/0.45 tff(74,plain,
% 0.19/0.45 ((~((~cC4(iV8467)) | (~cC8(iV8467)))) | (~cC4(iV8467)) | (~cC8(iV8467))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(75,plain,
% 0.19/0.45 (~((~cC4(iV8467)) | (~cC8(iV8467)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[74, 73, 34])).
% 0.19/0.45 tff(76,assumption,((~((~cC58(iV8472)) | (~((~rR1(iV8472, tptp_fun_Y_18(iV8472))) | (~cC2(tptp_fun_Y_18(iV8472))))))) | (~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))))), introduced(assumption)).
% 0.19/0.45 tff(77,plain,
% 0.19/0.45 (^[X: $i] : refl((~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(78,plain,
% 0.19/0.45 (![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[77])).
% 0.19/0.45 tff(79,plain,
% 0.19/0.45 (^[X: $i] : rewrite((~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(80,plain,
% 0.19/0.45 (![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.45 tff(81,plain,
% 0.19/0.45 (![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[80, 78])).
% 0.19/0.45 tff(82,plain,
% 0.19/0.45 (^[X: $i] : trans(monotonicity(rewrite(((~cC58(X)) | (rR1(X, tptp_fun_Y_18(X)) & cC2(tptp_fun_Y_18(X)))) <=> ((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))), rewrite((cC58(X) | ![Y: $i] : (~(rR1(X, Y) & cC2(Y)))) <=> (cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))), ((((~cC58(X)) | (rR1(X, tptp_fun_Y_18(X)) & cC2(tptp_fun_Y_18(X)))) & (cC58(X) | ![Y: $i] : (~(rR1(X, Y) & cC2(Y))))) <=> (((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X)))))) & (cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))), rewrite((((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X)))))) & (cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))) <=> (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))), ((((~cC58(X)) | (rR1(X, tptp_fun_Y_18(X)) & cC2(tptp_fun_Y_18(X)))) & (cC58(X) | ![Y: $i] : (~(rR1(X, Y) & cC2(Y))))) <=> (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(83,plain,
% 0.19/0.45 (![X: $i] : (((~cC58(X)) | (rR1(X, tptp_fun_Y_18(X)) & cC2(tptp_fun_Y_18(X)))) & (cC58(X) | ![Y: $i] : (~(rR1(X, Y) & cC2(Y))))) <=> ![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[82])).
% 0.19/0.46 tff(84,plain,
% 0.19/0.46 (![X: $i] : (cC58(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2(Y))) <=> ![X: $i] : (cC58(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2(Y)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(85,axiom,(![X: $i] : (cC58(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_57')).
% 0.19/0.46 tff(86,plain,
% 0.19/0.46 (![X: $i] : (cC58(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2(Y)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.46 tff(87,plain,(
% 0.19/0.46 ![X: $i] : (((~cC58(X)) | (rR1(X, tptp_fun_Y_18(X)) & cC2(tptp_fun_Y_18(X)))) & (cC58(X) | ![Y: $i] : (~(rR1(X, Y) & cC2(Y)))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[86])).
% 0.19/0.46 tff(88,plain,
% 0.19/0.46 (![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.19/0.46 tff(89,plain,
% 0.19/0.46 (![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.19/0.46 tff(90,plain,
% 0.19/0.46 ((~![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC58(iV8472)) | (~((~rR1(iV8472, tptp_fun_Y_18(iV8472))) | (~cC2(tptp_fun_Y_18(iV8472))))))) | (~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(91,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[90, 89, 76])).
% 0.19/0.46 tff(92,plain,(~((~((~cC58(iV8472)) | (~((~rR1(iV8472, tptp_fun_Y_18(iV8472))) | (~cC2(tptp_fun_Y_18(iV8472))))))) | (~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(93,plain,
% 0.19/0.46 (((~((~cC58(iV8472)) | (~((~rR1(iV8472, tptp_fun_Y_18(iV8472))) | (~cC2(tptp_fun_Y_18(iV8472))))))) | (~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))))) | (cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(94,plain,
% 0.19/0.46 (cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.19/0.46 tff(95,assumption,(![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))), introduced(assumption)).
% 0.19/0.46 tff(96,plain,
% 0.19/0.46 (cC2(iV8476) <=> cC2(iV8476)),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(97,axiom,(cC2(iV8476)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_132')).
% 0.19/0.46 tff(98,plain,
% 0.19/0.46 (cC2(iV8476)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.19/0.46 tff(99,plain,
% 0.19/0.46 (rR1(iV8472, iV8476) <=> rR1(iV8472, iV8476)),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(100,axiom,(rR1(iV8472, iV8476)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_124')).
% 0.19/0.46 tff(101,plain,
% 0.19/0.46 (rR1(iV8472, iV8476)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.19/0.46 tff(102,plain,
% 0.19/0.46 (((~![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))) | ((~cC2(iV8476)) | (~rR1(iV8472, iV8476)))) <=> ((~![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))) | (~cC2(iV8476)) | (~rR1(iV8472, iV8476)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(103,plain,
% 0.19/0.46 ((~![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))) | ((~cC2(iV8476)) | (~rR1(iV8472, iV8476)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(104,plain,
% 0.19/0.46 ((~![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))) | (~cC2(iV8476)) | (~rR1(iV8472, iV8476))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.46 tff(105,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[104, 101, 98, 95])).
% 0.19/0.46 tff(106,plain,(~![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(107,plain,
% 0.19/0.46 ((~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))) | cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(108,plain,
% 0.19/0.46 ((~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))) | cC58(iV8472)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.19/0.46 tff(109,plain,
% 0.19/0.46 (cC58(iV8472)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[108, 94])).
% 0.19/0.46 tff(110,plain,
% 0.19/0.46 (cC2xcomp(iV8472) <=> cC2xcomp(iV8472)),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(111,axiom,(cC2xcomp(iV8472)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_122')).
% 0.19/0.46 tff(112,plain,
% 0.19/0.46 (cC2xcomp(iV8472)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.19/0.46 tff(113,plain,
% 0.19/0.46 ((~((~cC2xcomp(iV8472)) | (~cC58(iV8472)))) | (~cC2xcomp(iV8472)) | (~cC58(iV8472))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(114,plain,
% 0.19/0.46 ((~((~cC2xcomp(iV8472)) | (~cC58(iV8472)))) | (~cC58(iV8472))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.19/0.46 tff(115,plain,
% 0.19/0.46 (~((~cC2xcomp(iV8472)) | (~cC58(iV8472)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[114, 109])).
% 0.19/0.46 tff(116,plain,
% 0.19/0.46 (^[X: $i] : refl((cC60(X) <=> (~((~cC2xcomp(X)) | (~cC58(X))))) <=> (cC60(X) <=> (~((~cC2xcomp(X)) | (~cC58(X))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(117,plain,
% 0.19/0.46 (![X: $i] : (cC60(X) <=> (~((~cC2xcomp(X)) | (~cC58(X))))) <=> ![X: $i] : (cC60(X) <=> (~((~cC2xcomp(X)) | (~cC58(X)))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[116])).
% 0.19/0.46 tff(118,plain,
% 0.19/0.46 (^[X: $i] : rewrite((cC60(X) <=> (cC2xcomp(X) & cC58(X))) <=> (cC60(X) <=> (~((~cC2xcomp(X)) | (~cC58(X))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(119,plain,
% 0.19/0.46 (![X: $i] : (cC60(X) <=> (cC2xcomp(X) & cC58(X))) <=> ![X: $i] : (cC60(X) <=> (~((~cC2xcomp(X)) | (~cC58(X)))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[118])).
% 0.19/0.46 tff(120,plain,
% 0.19/0.46 (![X: $i] : (cC60(X) <=> (cC2xcomp(X) & cC58(X))) <=> ![X: $i] : (cC60(X) <=> (cC2xcomp(X) & cC58(X)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(121,axiom,(![X: $i] : (cC60(X) <=> (cC2xcomp(X) & cC58(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_61')).
% 0.19/0.46 tff(122,plain,
% 0.19/0.46 (![X: $i] : (cC60(X) <=> (cC2xcomp(X) & cC58(X)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.19/0.46 tff(123,plain,(
% 0.19/0.46 ![X: $i] : (cC60(X) <=> (cC2xcomp(X) & cC58(X)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[122])).
% 0.19/0.46 tff(124,plain,
% 0.19/0.46 (![X: $i] : (cC60(X) <=> (~((~cC2xcomp(X)) | (~cC58(X)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.19/0.46 tff(125,plain,
% 0.19/0.46 (![X: $i] : (cC60(X) <=> (~((~cC2xcomp(X)) | (~cC58(X)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.19/0.46 tff(126,plain,
% 0.19/0.46 ((~![X: $i] : (cC60(X) <=> (~((~cC2xcomp(X)) | (~cC58(X)))))) | (cC60(iV8472) <=> (~((~cC2xcomp(iV8472)) | (~cC58(iV8472)))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(127,plain,
% 0.19/0.46 (cC60(iV8472) <=> (~((~cC2xcomp(iV8472)) | (~cC58(iV8472))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.19/0.46 tff(128,plain,
% 0.19/0.46 ((~(cC60(iV8472) <=> (~((~cC2xcomp(iV8472)) | (~cC58(iV8472)))))) | cC60(iV8472) | ((~cC2xcomp(iV8472)) | (~cC58(iV8472)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(129,plain,
% 0.19/0.46 (cC60(iV8472) | ((~cC2xcomp(iV8472)) | (~cC58(iV8472)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.19/0.46 tff(130,plain,
% 0.19/0.46 (cC60(iV8472)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[129, 115])).
% 0.19/0.46 tff(131,assumption,((~((~cC48(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))) | (~(cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))), introduced(assumption)).
% 0.19/0.46 tff(132,plain,
% 0.19/0.46 (^[X: $i] : refl((~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(133,plain,
% 0.19/0.46 (![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[132])).
% 0.19/0.46 tff(134,plain,
% 0.19/0.46 (^[X: $i] : rewrite((~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(135,plain,
% 0.19/0.46 (![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[134])).
% 0.19/0.46 tff(136,plain,
% 0.19/0.46 (![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[135, 133])).
% 0.19/0.46 tff(137,plain,
% 0.19/0.46 (^[X: $i] : trans(monotonicity(rewrite(((~cC48(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) <=> ((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))), rewrite((cC48(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y)))) <=> (cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))), ((((~cC48(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) & (cC48(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y))))) <=> (((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X)))))) & (cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))), rewrite((((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X)))))) & (cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))) <=> (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))), ((((~cC48(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) & (cC48(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y))))) <=> (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(138,plain,
% 0.19/0.46 (![X: $i] : (((~cC48(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) & (cC48(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y))))) <=> ![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[137])).
% 0.19/0.46 tff(139,plain,
% 0.19/0.46 (![X: $i] : (cC48(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2xcomp(Y))) <=> ![X: $i] : (cC48(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2xcomp(Y)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(140,axiom,(![X: $i] : (cC48(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2xcomp(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_44')).
% 0.19/0.46 tff(141,plain,
% 0.19/0.46 (![X: $i] : (cC48(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2xcomp(Y)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.19/0.46 tff(142,plain,(
% 0.19/0.46 ![X: $i] : (((~cC48(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) & (cC48(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y)))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[141])).
% 0.19/0.46 tff(143,plain,
% 0.19/0.46 (![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[142, 138])).
% 0.19/0.46 tff(144,plain,
% 0.19/0.46 (![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[143, 136])).
% 0.19/0.46 tff(145,plain,
% 0.19/0.46 ((~![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC48(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))) | (~(cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(146,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[145, 144, 131])).
% 0.19/0.46 tff(147,plain,(~((~((~cC48(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))) | (~(cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(148,plain,
% 0.19/0.46 (((~((~cC48(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))) | (~(cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))) | (cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(149,plain,
% 0.19/0.46 (cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.19/0.46 tff(150,plain,
% 0.19/0.46 ((~(cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(151,plain,
% 0.19/0.46 ((~(cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | cC48(iV8467)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[150, 70])).
% 0.19/0.46 tff(152,plain,
% 0.19/0.46 (cC48(iV8467)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[151, 149])).
% 0.19/0.46 tff(153,assumption,((~((~cC20(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))) | (~(cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))), introduced(assumption)).
% 0.19/0.46 tff(154,plain,
% 0.19/0.46 (^[X: $i] : refl((~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(155,plain,
% 0.19/0.46 (![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[154])).
% 0.19/0.46 tff(156,plain,
% 0.19/0.46 (^[X: $i] : rewrite((~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(157,plain,
% 0.19/0.46 (![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[156])).
% 0.19/0.46 tff(158,plain,
% 0.19/0.46 (![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[157, 155])).
% 0.19/0.46 tff(159,plain,
% 0.19/0.46 (^[X: $i] : trans(monotonicity(rewrite(((~cC20(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) <=> ((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))), rewrite((cC20(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y)))) <=> (cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))), ((((~cC20(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) & (cC20(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y))))) <=> (((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X)))))) & (cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))), rewrite((((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X)))))) & (cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))) <=> (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))), ((((~cC20(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) & (cC20(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y))))) <=> (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(160,plain,
% 0.19/0.46 (![X: $i] : (((~cC20(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) & (cC20(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y))))) <=> ![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[159])).
% 0.19/0.46 tff(161,plain,
% 0.19/0.46 (![X: $i] : (cC20(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2xcomp(Y))) <=> ![X: $i] : (cC20(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2xcomp(Y)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(162,axiom,(![X: $i] : (cC20(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2xcomp(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_13')).
% 0.19/0.46 tff(163,plain,
% 0.19/0.46 (![X: $i] : (cC20(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2xcomp(Y)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.19/0.46 tff(164,plain,(
% 0.19/0.46 ![X: $i] : (((~cC20(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) & (cC20(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y)))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[163])).
% 0.19/0.46 tff(165,plain,
% 0.19/0.46 (![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[164, 160])).
% 0.19/0.46 tff(166,plain,
% 0.19/0.46 (![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[165, 158])).
% 0.19/0.46 tff(167,plain,
% 0.19/0.46 ((~![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC20(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))) | (~(cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(168,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[167, 166, 153])).
% 0.19/0.46 tff(169,plain,(~((~((~cC20(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))) | (~(cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(170,plain,
% 0.19/0.46 (((~((~cC20(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))) | (~(cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))) | (cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(171,plain,
% 0.19/0.46 (cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[170, 169])).
% 0.19/0.46 tff(172,plain,
% 0.19/0.46 ((~(cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(173,plain,
% 0.19/0.46 ((~(cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | cC20(iV8467)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[172, 70])).
% 0.19/0.46 tff(174,plain,
% 0.19/0.46 (cC20(iV8467)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[173, 171])).
% 0.19/0.46 tff(175,assumption,((~((~cC34(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_22(iV8467))) | (~cC32xcomp(tptp_fun_Y_22(iV8467))))))) | (~(cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))))), introduced(assumption)).
% 0.19/0.46 tff(176,plain,
% 0.19/0.46 (^[X: $i] : refl((~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(177,plain,
% 0.19/0.46 (![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[176])).
% 0.19/0.46 tff(178,plain,
% 0.19/0.46 (^[X: $i] : rewrite((~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(179,plain,
% 0.19/0.46 (![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[178])).
% 0.19/0.46 tff(180,plain,
% 0.19/0.46 (![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[179, 177])).
% 0.19/0.46 tff(181,plain,
% 0.19/0.46 (^[X: $i] : trans(monotonicity(rewrite(((~cC34(X)) | (rR1(X, tptp_fun_Y_22(X)) & cC32xcomp(tptp_fun_Y_22(X)))) <=> ((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))), rewrite((cC34(X) | ![Y: $i] : (~(rR1(X, Y) & cC32xcomp(Y)))) <=> (cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y))))), ((((~cC34(X)) | (rR1(X, tptp_fun_Y_22(X)) & cC32xcomp(tptp_fun_Y_22(X)))) & (cC34(X) | ![Y: $i] : (~(rR1(X, Y) & cC32xcomp(Y))))) <=> (((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X)))))) & (cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y))))))), rewrite((((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X)))))) & (cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y))))) <=> (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y)))))))), ((((~cC34(X)) | (rR1(X, tptp_fun_Y_22(X)) & cC32xcomp(tptp_fun_Y_22(X)))) & (cC34(X) | ![Y: $i] : (~(rR1(X, Y) & cC32xcomp(Y))))) <=> (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y)))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(182,plain,
% 0.19/0.46 (![X: $i] : (((~cC34(X)) | (rR1(X, tptp_fun_Y_22(X)) & cC32xcomp(tptp_fun_Y_22(X)))) & (cC34(X) | ![Y: $i] : (~(rR1(X, Y) & cC32xcomp(Y))))) <=> ![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[181])).
% 0.19/0.46 tff(183,plain,
% 0.19/0.46 (![X: $i] : (cC34(X) <=> ?[Y: $i] : (rR1(X, Y) & cC32xcomp(Y))) <=> ![X: $i] : (cC34(X) <=> ?[Y: $i] : (rR1(X, Y) & cC32xcomp(Y)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(184,axiom,(![X: $i] : (cC34(X) <=> ?[Y: $i] : (rR1(X, Y) & cC32xcomp(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_29')).
% 0.19/0.46 tff(185,plain,
% 0.19/0.46 (![X: $i] : (cC34(X) <=> ?[Y: $i] : (rR1(X, Y) & cC32xcomp(Y)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.19/0.46 tff(186,plain,(
% 0.19/0.46 ![X: $i] : (((~cC34(X)) | (rR1(X, tptp_fun_Y_22(X)) & cC32xcomp(tptp_fun_Y_22(X)))) & (cC34(X) | ![Y: $i] : (~(rR1(X, Y) & cC32xcomp(Y)))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[185])).
% 0.19/0.47 tff(187,plain,
% 0.19/0.47 (![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[186, 182])).
% 0.19/0.47 tff(188,plain,
% 0.19/0.47 (![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[187, 180])).
% 0.19/0.47 tff(189,plain,
% 0.19/0.47 ((~![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC34(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_22(iV8467))) | (~cC32xcomp(tptp_fun_Y_22(iV8467))))))) | (~(cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(190,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[189, 188, 175])).
% 0.19/0.47 tff(191,plain,(~((~((~cC34(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_22(iV8467))) | (~cC32xcomp(tptp_fun_Y_22(iV8467))))))) | (~(cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(192,plain,
% 0.19/0.47 (((~((~cC34(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_22(iV8467))) | (~cC32xcomp(tptp_fun_Y_22(iV8467))))))) | (~(cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))))) | (cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(193,plain,
% 0.19/0.47 (cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[192, 191])).
% 0.19/0.47 tff(194,assumption,(![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))), introduced(assumption)).
% 0.19/0.47 tff(195,plain,
% 0.19/0.47 (cC32xcomp(iV8474) <=> cC32xcomp(iV8474)),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(196,axiom,(cC32xcomp(iV8474)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_127')).
% 0.19/0.47 tff(197,plain,
% 0.19/0.47 (cC32xcomp(iV8474)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.19/0.47 tff(198,plain,
% 0.19/0.47 (rR1(iV8467, iV8474) <=> rR1(iV8467, iV8474)),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(199,axiom,(rR1(iV8467, iV8474)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_106')).
% 0.19/0.47 tff(200,plain,
% 0.19/0.47 (rR1(iV8467, iV8474)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.19/0.47 tff(201,plain,
% 0.19/0.47 (((~![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))) | ((~cC32xcomp(iV8474)) | (~rR1(iV8467, iV8474)))) <=> ((~![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))) | (~cC32xcomp(iV8474)) | (~rR1(iV8467, iV8474)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(202,plain,
% 0.19/0.47 ((~![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))) | ((~cC32xcomp(iV8474)) | (~rR1(iV8467, iV8474)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(203,plain,
% 0.19/0.47 ((~![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))) | (~cC32xcomp(iV8474)) | (~rR1(iV8467, iV8474))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.19/0.47 tff(204,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[203, 200, 197, 194])).
% 0.19/0.47 tff(205,plain,(~![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(206,plain,
% 0.19/0.47 ((~(cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y))))) | cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(207,plain,
% 0.19/0.47 ((~(cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y))))) | cC34(iV8467)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[206, 205])).
% 0.19/0.47 tff(208,plain,
% 0.19/0.47 (cC34(iV8467)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[207, 193])).
% 0.19/0.47 tff(209,assumption,((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | (~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_2(iV8467))) | (~cTOP(tptp_fun_Y_2(iV8467)))))))), introduced(assumption)).
% 0.19/0.47 tff(210,plain,
% 0.19/0.47 (^[X: $i] : refl((~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))) <=> (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(211,plain,
% 0.19/0.47 (![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))) <=> ![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[210])).
% 0.19/0.47 tff(212,plain,
% 0.19/0.47 (^[X: $i] : rewrite((~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))) <=> (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(213,plain,
% 0.19/0.47 (![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))) <=> ![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[212])).
% 0.19/0.47 tff(214,plain,
% 0.19/0.47 (![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))) <=> ![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[213, 211])).
% 0.19/0.47 tff(215,plain,
% 0.19/0.47 (^[X: $i] : trans(monotonicity(rewrite(((~cC14(X)) | (rR1(X, tptp_fun_Y_2(X)) & cTOP(tptp_fun_Y_2(X)))) <=> ((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))), rewrite((cC14(X) | ![Y: $i] : (~(rR1(X, Y) & cTOP(Y)))) <=> (cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))), ((((~cC14(X)) | (rR1(X, tptp_fun_Y_2(X)) & cTOP(tptp_fun_Y_2(X)))) & (cC14(X) | ![Y: $i] : (~(rR1(X, Y) & cTOP(Y))))) <=> (((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X)))))) & (cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))), rewrite((((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X)))))) & (cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))) <=> (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))), ((((~cC14(X)) | (rR1(X, tptp_fun_Y_2(X)) & cTOP(tptp_fun_Y_2(X)))) & (cC14(X) | ![Y: $i] : (~(rR1(X, Y) & cTOP(Y))))) <=> (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(216,plain,
% 0.19/0.47 (![X: $i] : (((~cC14(X)) | (rR1(X, tptp_fun_Y_2(X)) & cTOP(tptp_fun_Y_2(X)))) & (cC14(X) | ![Y: $i] : (~(rR1(X, Y) & cTOP(Y))))) <=> ![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[215])).
% 0.19/0.47 tff(217,plain,
% 0.19/0.47 (![X: $i] : (cC14(X) <=> ?[Y: $i] : (rR1(X, Y) & cTOP(Y))) <=> ![X: $i] : (cC14(X) <=> ?[Y: $i] : (rR1(X, Y) & cTOP(Y)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(218,axiom,(![X: $i] : (cC14(X) <=> ?[Y: $i] : (rR1(X, Y) & cTOP(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_5')).
% 0.19/0.47 tff(219,plain,
% 0.19/0.47 (![X: $i] : (cC14(X) <=> ?[Y: $i] : (rR1(X, Y) & cTOP(Y)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.19/0.47 tff(220,plain,(
% 0.19/0.47 ![X: $i] : (((~cC14(X)) | (rR1(X, tptp_fun_Y_2(X)) & cTOP(tptp_fun_Y_2(X)))) & (cC14(X) | ![Y: $i] : (~(rR1(X, Y) & cTOP(Y)))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[219])).
% 0.19/0.47 tff(221,plain,
% 0.19/0.47 (![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[220, 216])).
% 0.19/0.47 tff(222,plain,
% 0.19/0.47 (![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[221, 214])).
% 0.19/0.48 tff(223,plain,
% 0.19/0.48 (((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | (~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_2(iV8467))) | (~cTOP(tptp_fun_Y_2(iV8467)))))))))) <=> ((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | (~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_2(iV8467))) | (~cTOP(tptp_fun_Y_2(iV8467))))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(224,plain,
% 0.19/0.48 ((~((~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_2(iV8467))) | (~cTOP(tptp_fun_Y_2(iV8467))))))) | (~(cC14(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cTOP(Y))))))) <=> (~((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | (~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_2(iV8467))) | (~cTOP(tptp_fun_Y_2(iV8467)))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(225,plain,
% 0.19/0.48 (((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_2(iV8467))) | (~cTOP(tptp_fun_Y_2(iV8467))))))) | (~(cC14(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cTOP(Y)))))))) <=> ((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | (~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_2(iV8467))) | (~cTOP(tptp_fun_Y_2(iV8467))))))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[224])).
% 0.19/0.48 tff(226,plain,
% 0.19/0.48 (((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_2(iV8467))) | (~cTOP(tptp_fun_Y_2(iV8467))))))) | (~(cC14(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cTOP(Y)))))))) <=> ((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | (~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_2(iV8467))) | (~cTOP(tptp_fun_Y_2(iV8467))))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[225, 223])).
% 0.19/0.48 tff(227,plain,
% 0.19/0.48 ((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_2(iV8467))) | (~cTOP(tptp_fun_Y_2(iV8467))))))) | (~(cC14(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cTOP(Y)))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(228,plain,
% 0.19/0.48 ((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | (~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_2(iV8467))) | (~cTOP(tptp_fun_Y_2(iV8467)))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.19/0.48 tff(229,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[228, 222, 209])).
% 0.19/0.48 tff(230,plain,(~((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | (~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_2(iV8467))) | (~cTOP(tptp_fun_Y_2(iV8467))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(231,plain,
% 0.19/0.48 (((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | (~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_2(iV8467))) | (~cTOP(tptp_fun_Y_2(iV8467)))))))) | (cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(232,plain,
% 0.19/0.48 (cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[231, 230])).
% 0.19/0.48 tff(233,assumption,(![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))), introduced(assumption)).
% 0.19/0.48 tff(234,plain,
% 0.19/0.48 (cTOP(iV8470) <=> cTOP(iV8470)),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(235,axiom,(cTOP(iV8470)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_116')).
% 0.19/0.48 tff(236,plain,
% 0.19/0.48 (cTOP(iV8470)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.19/0.48 tff(237,plain,
% 0.19/0.48 (rR1(iV8467, iV8470) <=> rR1(iV8467, iV8470)),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(238,axiom,(rR1(iV8467, iV8470)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_104')).
% 0.19/0.48 tff(239,plain,
% 0.19/0.48 (rR1(iV8467, iV8470)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.19/0.48 tff(240,plain,
% 0.19/0.48 (((~![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))) | ((~cTOP(iV8470)) | (~rR1(iV8467, iV8470)))) <=> ((~![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))) | (~cTOP(iV8470)) | (~rR1(iV8467, iV8470)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(241,plain,
% 0.19/0.48 ((~![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))) | ((~cTOP(iV8470)) | (~rR1(iV8467, iV8470)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(242,plain,
% 0.19/0.48 ((~![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))) | (~cTOP(iV8470)) | (~rR1(iV8467, iV8470))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.19/0.48 tff(243,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[242, 239, 236, 233])).
% 0.19/0.48 tff(244,plain,(~![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(245,plain,
% 0.19/0.48 ((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(246,plain,
% 0.19/0.48 ((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | cC14(iV8467)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[245, 244])).
% 0.19/0.48 tff(247,plain,
% 0.19/0.48 (cC14(iV8467)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[246, 232])).
% 0.19/0.48 tff(248,assumption,((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_44(iV8467))) | (~cC60(tptp_fun_Y_44(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))))), introduced(assumption)).
% 0.19/0.48 tff(249,plain,
% 0.19/0.48 (^[X: $i] : refl((~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))) <=> (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(250,plain,
% 0.19/0.48 (![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))) <=> ![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[249])).
% 0.19/0.48 tff(251,plain,
% 0.19/0.48 (^[X: $i] : rewrite((~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))) <=> (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(252,plain,
% 0.19/0.48 (![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))) <=> ![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[251])).
% 0.19/0.48 tff(253,plain,
% 0.19/0.48 (![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))) <=> ![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[252, 250])).
% 0.19/0.48 tff(254,plain,
% 0.19/0.48 (^[X: $i] : trans(monotonicity(rewrite(((~cC62(X)) | (rR1(X, tptp_fun_Y_44(X)) & cC60(tptp_fun_Y_44(X)))) <=> ((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))), rewrite((cC62(X) | ![Y: $i] : (~(rR1(X, Y) & cC60(Y)))) <=> (cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))), ((((~cC62(X)) | (rR1(X, tptp_fun_Y_44(X)) & cC60(tptp_fun_Y_44(X)))) & (cC62(X) | ![Y: $i] : (~(rR1(X, Y) & cC60(Y))))) <=> (((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X)))))) & (cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))), rewrite((((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X)))))) & (cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))) <=> (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))), ((((~cC62(X)) | (rR1(X, tptp_fun_Y_44(X)) & cC60(tptp_fun_Y_44(X)))) & (cC62(X) | ![Y: $i] : (~(rR1(X, Y) & cC60(Y))))) <=> (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(255,plain,
% 0.19/0.48 (![X: $i] : (((~cC62(X)) | (rR1(X, tptp_fun_Y_44(X)) & cC60(tptp_fun_Y_44(X)))) & (cC62(X) | ![Y: $i] : (~(rR1(X, Y) & cC60(Y))))) <=> ![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[254])).
% 0.19/0.48 tff(256,plain,
% 0.19/0.48 (![X: $i] : (cC62(X) <=> ?[Y: $i] : (rR1(X, Y) & cC60(Y))) <=> ![X: $i] : (cC62(X) <=> ?[Y: $i] : (rR1(X, Y) & cC60(Y)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(257,axiom,(![X: $i] : (cC62(X) <=> ?[Y: $i] : (rR1(X, Y) & cC60(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_62')).
% 0.19/0.48 tff(258,plain,
% 0.19/0.48 (![X: $i] : (cC62(X) <=> ?[Y: $i] : (rR1(X, Y) & cC60(Y)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.19/0.48 tff(259,plain,(
% 0.19/0.48 ![X: $i] : (((~cC62(X)) | (rR1(X, tptp_fun_Y_44(X)) & cC60(tptp_fun_Y_44(X)))) & (cC62(X) | ![Y: $i] : (~(rR1(X, Y) & cC60(Y)))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[258])).
% 0.19/0.48 tff(260,plain,
% 0.19/0.48 (![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[259, 255])).
% 0.19/0.48 tff(261,plain,
% 0.19/0.48 (![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[260, 253])).
% 0.19/0.48 tff(262,plain,
% 0.19/0.48 (((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_44(iV8467))) | (~cC60(tptp_fun_Y_44(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_44(iV8467))) | (~cC60(tptp_fun_Y_44(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(263,plain,
% 0.19/0.48 ((~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_44(iV8467))) | (~cC60(tptp_fun_Y_44(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC60(Y))))))) <=> (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_44(iV8467))) | (~cC60(tptp_fun_Y_44(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(264,plain,
% 0.19/0.48 (((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_44(iV8467))) | (~cC60(tptp_fun_Y_44(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC60(Y)))))))) <=> ((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_44(iV8467))) | (~cC60(tptp_fun_Y_44(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[263])).
% 0.19/0.48 tff(265,plain,
% 0.19/0.48 (((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_44(iV8467))) | (~cC60(tptp_fun_Y_44(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC60(Y)))))))) <=> ((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_44(iV8467))) | (~cC60(tptp_fun_Y_44(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[264, 262])).
% 0.19/0.48 tff(266,plain,
% 0.19/0.48 ((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_44(iV8467))) | (~cC60(tptp_fun_Y_44(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC60(Y)))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(267,plain,
% 0.19/0.48 ((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_44(iV8467))) | (~cC60(tptp_fun_Y_44(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.19/0.48 tff(268,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[267, 261, 248])).
% 0.19/0.48 tff(269,plain,(~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_44(iV8467))) | (~cC60(tptp_fun_Y_44(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(270,plain,
% 0.19/0.48 (((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_44(iV8467))) | (~cC60(tptp_fun_Y_44(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))))) | (cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(271,plain,
% 0.19/0.48 (cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[270, 269])).
% 0.19/0.48 tff(272,assumption,(![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))), introduced(assumption)).
% 0.19/0.48 tff(273,plain,
% 0.19/0.48 (rR1(iV8467, iV8472) <=> rR1(iV8467, iV8472)),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(274,axiom,(rR1(iV8467, iV8472)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_110')).
% 0.19/0.48 tff(275,plain,
% 0.19/0.48 (rR1(iV8467, iV8472)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.19/0.48 tff(276,plain,
% 0.19/0.48 (((~![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))) | ((~cC60(iV8472)) | (~rR1(iV8467, iV8472)))) <=> ((~![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))) | (~cC60(iV8472)) | (~rR1(iV8467, iV8472)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(277,plain,
% 0.19/0.48 ((~![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))) | ((~cC60(iV8472)) | (~rR1(iV8467, iV8472)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(278,plain,
% 0.19/0.48 ((~![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))) | (~cC60(iV8472)) | (~rR1(iV8467, iV8472))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.19/0.48 tff(279,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[278, 275, 130, 272])).
% 0.19/0.48 tff(280,plain,(~![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(281,plain,
% 0.19/0.48 ((~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))) | cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(282,plain,
% 0.19/0.49 ((~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))) | cC62(iV8467)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[281, 280])).
% 0.19/0.49 tff(283,plain,
% 0.19/0.49 (cC62(iV8467)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[282, 271])).
% 0.19/0.49 tff(284,assumption,((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | (~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_58(iV8467))) | (~cC80(tptp_fun_Y_58(iV8467)))))))), introduced(assumption)).
% 0.19/0.49 tff(285,plain,
% 0.19/0.49 (^[X: $i] : refl((~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))) <=> (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(286,plain,
% 0.19/0.49 (![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))) <=> ![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[285])).
% 0.19/0.49 tff(287,plain,
% 0.19/0.49 (^[X: $i] : rewrite((~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))) <=> (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(288,plain,
% 0.19/0.49 (![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))) <=> ![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[287])).
% 0.19/0.49 tff(289,plain,
% 0.19/0.49 (![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))) <=> ![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[288, 286])).
% 0.19/0.49 tff(290,plain,
% 0.19/0.49 (^[X: $i] : trans(monotonicity(rewrite(((~cC82(X)) | (rR1(X, tptp_fun_Y_58(X)) & cC80(tptp_fun_Y_58(X)))) <=> ((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))), rewrite((cC82(X) | ![Y: $i] : (~(rR1(X, Y) & cC80(Y)))) <=> (cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))), ((((~cC82(X)) | (rR1(X, tptp_fun_Y_58(X)) & cC80(tptp_fun_Y_58(X)))) & (cC82(X) | ![Y: $i] : (~(rR1(X, Y) & cC80(Y))))) <=> (((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X)))))) & (cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))), rewrite((((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X)))))) & (cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))) <=> (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))), ((((~cC82(X)) | (rR1(X, tptp_fun_Y_58(X)) & cC80(tptp_fun_Y_58(X)))) & (cC82(X) | ![Y: $i] : (~(rR1(X, Y) & cC80(Y))))) <=> (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(291,plain,
% 0.19/0.49 (![X: $i] : (((~cC82(X)) | (rR1(X, tptp_fun_Y_58(X)) & cC80(tptp_fun_Y_58(X)))) & (cC82(X) | ![Y: $i] : (~(rR1(X, Y) & cC80(Y))))) <=> ![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[290])).
% 0.19/0.49 tff(292,plain,
% 0.19/0.49 (![X: $i] : (cC82(X) <=> ?[Y: $i] : (rR1(X, Y) & cC80(Y))) <=> ![X: $i] : (cC82(X) <=> ?[Y: $i] : (rR1(X, Y) & cC80(Y)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(293,axiom,(![X: $i] : (cC82(X) <=> ?[Y: $i] : (rR1(X, Y) & cC80(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_82')).
% 0.19/0.49 tff(294,plain,
% 0.19/0.49 (![X: $i] : (cC82(X) <=> ?[Y: $i] : (rR1(X, Y) & cC80(Y)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.19/0.49 tff(295,plain,(
% 0.19/0.49 ![X: $i] : (((~cC82(X)) | (rR1(X, tptp_fun_Y_58(X)) & cC80(tptp_fun_Y_58(X)))) & (cC82(X) | ![Y: $i] : (~(rR1(X, Y) & cC80(Y)))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[294])).
% 0.19/0.49 tff(296,plain,
% 0.19/0.49 (![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[295, 291])).
% 0.19/0.49 tff(297,plain,
% 0.19/0.49 (![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[296, 289])).
% 0.19/0.49 tff(298,plain,
% 0.19/0.49 (((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | (~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_58(iV8467))) | (~cC80(tptp_fun_Y_58(iV8467)))))))))) <=> ((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | (~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_58(iV8467))) | (~cC80(tptp_fun_Y_58(iV8467))))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(299,plain,
% 0.19/0.49 ((~((~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_58(iV8467))) | (~cC80(tptp_fun_Y_58(iV8467))))))) | (~(cC82(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC80(Y))))))) <=> (~((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | (~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_58(iV8467))) | (~cC80(tptp_fun_Y_58(iV8467)))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(300,plain,
% 0.19/0.49 (((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_58(iV8467))) | (~cC80(tptp_fun_Y_58(iV8467))))))) | (~(cC82(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC80(Y)))))))) <=> ((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | (~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_58(iV8467))) | (~cC80(tptp_fun_Y_58(iV8467))))))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[299])).
% 0.19/0.49 tff(301,plain,
% 0.19/0.49 (((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_58(iV8467))) | (~cC80(tptp_fun_Y_58(iV8467))))))) | (~(cC82(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC80(Y)))))))) <=> ((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | (~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_58(iV8467))) | (~cC80(tptp_fun_Y_58(iV8467))))))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[300, 298])).
% 0.19/0.49 tff(302,plain,
% 0.19/0.49 ((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_58(iV8467))) | (~cC80(tptp_fun_Y_58(iV8467))))))) | (~(cC82(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC80(Y)))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(303,plain,
% 0.19/0.49 ((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | (~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_58(iV8467))) | (~cC80(tptp_fun_Y_58(iV8467)))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.19/0.49 tff(304,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[303, 297, 284])).
% 0.19/0.49 tff(305,plain,(~((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | (~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_58(iV8467))) | (~cC80(tptp_fun_Y_58(iV8467))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(306,plain,
% 0.19/0.49 (((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | (~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_58(iV8467))) | (~cC80(tptp_fun_Y_58(iV8467)))))))) | (cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(307,plain,
% 0.19/0.49 (cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[306, 305])).
% 0.19/0.49 tff(308,assumption,(![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))), introduced(assumption)).
% 0.19/0.49 tff(309,plain,
% 0.19/0.49 (^[X: $i] : refl((cC80(X) <=> (~((~cC2xcomp(X)) | (~cC78xcomp(X))))) <=> (cC80(X) <=> (~((~cC2xcomp(X)) | (~cC78xcomp(X))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(310,plain,
% 0.19/0.49 (![X: $i] : (cC80(X) <=> (~((~cC2xcomp(X)) | (~cC78xcomp(X))))) <=> ![X: $i] : (cC80(X) <=> (~((~cC2xcomp(X)) | (~cC78xcomp(X)))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[309])).
% 0.19/0.49 tff(311,plain,
% 0.19/0.49 (^[X: $i] : rewrite((cC80(X) <=> (cC78xcomp(X) & cC2xcomp(X))) <=> (cC80(X) <=> (~((~cC2xcomp(X)) | (~cC78xcomp(X))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(312,plain,
% 0.19/0.49 (![X: $i] : (cC80(X) <=> (cC78xcomp(X) & cC2xcomp(X))) <=> ![X: $i] : (cC80(X) <=> (~((~cC2xcomp(X)) | (~cC78xcomp(X)))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[311])).
% 0.19/0.49 tff(313,plain,
% 0.19/0.49 (![X: $i] : (cC80(X) <=> (cC78xcomp(X) & cC2xcomp(X))) <=> ![X: $i] : (cC80(X) <=> (cC78xcomp(X) & cC2xcomp(X)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(314,axiom,(![X: $i] : (cC80(X) <=> (cC78xcomp(X) & cC2xcomp(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_80')).
% 0.19/0.49 tff(315,plain,
% 0.19/0.49 (![X: $i] : (cC80(X) <=> (cC78xcomp(X) & cC2xcomp(X)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[314, 313])).
% 0.19/0.49 tff(316,plain,(
% 0.19/0.49 ![X: $i] : (cC80(X) <=> (cC78xcomp(X) & cC2xcomp(X)))),
% 0.19/0.49 inference(skolemize,[status(sab)],[315])).
% 0.19/0.49 tff(317,plain,
% 0.19/0.49 (![X: $i] : (cC80(X) <=> (~((~cC2xcomp(X)) | (~cC78xcomp(X)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[316, 312])).
% 0.19/0.49 tff(318,plain,
% 0.19/0.49 (![X: $i] : (cC80(X) <=> (~((~cC2xcomp(X)) | (~cC78xcomp(X)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[317, 310])).
% 0.19/0.49 tff(319,plain,
% 0.19/0.49 ((~![X: $i] : (cC80(X) <=> (~((~cC2xcomp(X)) | (~cC78xcomp(X)))))) | (cC80(iV8471) <=> (~((~cC2xcomp(iV8471)) | (~cC78xcomp(iV8471)))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(320,plain,
% 0.19/0.49 (cC80(iV8471) <=> (~((~cC2xcomp(iV8471)) | (~cC78xcomp(iV8471))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[319, 318])).
% 0.19/0.49 tff(321,plain,
% 0.19/0.49 (cC2xcomp(iV8471) <=> cC2xcomp(iV8471)),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(322,axiom,(cC2xcomp(iV8471)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_119')).
% 0.19/0.49 tff(323,plain,
% 0.19/0.49 (cC2xcomp(iV8471)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.19/0.49 tff(324,plain,
% 0.19/0.49 (cC78xcomp(iV8471) <=> cC78xcomp(iV8471)),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(325,axiom,(cC78xcomp(iV8471)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_118')).
% 0.19/0.49 tff(326,plain,
% 0.19/0.49 (cC78xcomp(iV8471)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.19/0.49 tff(327,plain,
% 0.19/0.49 ((~((~cC2xcomp(iV8471)) | (~cC78xcomp(iV8471)))) | (~cC2xcomp(iV8471)) | (~cC78xcomp(iV8471))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(328,plain,
% 0.19/0.49 (~((~cC2xcomp(iV8471)) | (~cC78xcomp(iV8471)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[327, 326, 323])).
% 0.19/0.49 tff(329,plain,
% 0.19/0.49 ((~(cC80(iV8471) <=> (~((~cC2xcomp(iV8471)) | (~cC78xcomp(iV8471)))))) | cC80(iV8471) | ((~cC2xcomp(iV8471)) | (~cC78xcomp(iV8471)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(330,plain,
% 0.19/0.50 ((~(cC80(iV8471) <=> (~((~cC2xcomp(iV8471)) | (~cC78xcomp(iV8471)))))) | cC80(iV8471)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[329, 328])).
% 0.19/0.50 tff(331,plain,
% 0.19/0.50 (cC80(iV8471)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[330, 320])).
% 0.19/0.50 tff(332,plain,
% 0.19/0.50 (rR1(iV8467, iV8471) <=> rR1(iV8467, iV8471)),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(333,axiom,(rR1(iV8467, iV8471)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_103')).
% 0.19/0.50 tff(334,plain,
% 0.19/0.50 (rR1(iV8467, iV8471)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[333, 332])).
% 0.19/0.50 tff(335,plain,
% 0.19/0.50 (((~![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))) | ((~cC80(iV8471)) | (~rR1(iV8467, iV8471)))) <=> ((~![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))) | (~cC80(iV8471)) | (~rR1(iV8467, iV8471)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(336,plain,
% 0.19/0.50 ((~![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))) | ((~cC80(iV8471)) | (~rR1(iV8467, iV8471)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(337,plain,
% 0.19/0.50 ((~![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))) | (~cC80(iV8471)) | (~rR1(iV8467, iV8471))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.19/0.50 tff(338,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[337, 334, 331, 308])).
% 0.19/0.50 tff(339,plain,(~![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(340,plain,
% 0.19/0.50 ((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(341,plain,
% 0.19/0.50 ((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | cC82(iV8467)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[340, 339])).
% 0.19/0.50 tff(342,plain,
% 0.19/0.50 (cC82(iV8467)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[341, 307])).
% 0.19/0.50 tff(343,plain,
% 0.19/0.50 ((~(~((~cC20(iV8467)) | (~cC4(iV8467)) | (~cC8(iV8467)) | (~cC82(iV8467)) | (~cC62(iV8467)) | (~cC14(iV8467)) | (~cC34(iV8467)) | (~cC10(iV8467)) | (~cC48(iV8467)) | (~cC80(iV8471)) | (~cC58(iV8472)) | (~cC60(iV8472))))) <=> ((~cC20(iV8467)) | (~cC4(iV8467)) | (~cC8(iV8467)) | (~cC82(iV8467)) | (~cC62(iV8467)) | (~cC14(iV8467)) | (~cC34(iV8467)) | (~cC10(iV8467)) | (~cC48(iV8467)) | (~cC80(iV8471)) | (~cC58(iV8472)) | (~cC60(iV8472)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(344,plain,
% 0.19/0.50 ((cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cC48(iV8467) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472)) <=> (~((~cC20(iV8467)) | (~cC4(iV8467)) | (~cC8(iV8467)) | (~cC82(iV8467)) | (~cC62(iV8467)) | (~cC14(iV8467)) | (~cC34(iV8467)) | (~cC10(iV8467)) | (~cC48(iV8467)) | (~cC80(iV8471)) | (~cC58(iV8472)) | (~cC60(iV8472))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(345,plain,
% 0.19/0.50 ((~(cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cC48(iV8467) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472))) <=> (~(~((~cC20(iV8467)) | (~cC4(iV8467)) | (~cC8(iV8467)) | (~cC82(iV8467)) | (~cC62(iV8467)) | (~cC14(iV8467)) | (~cC34(iV8467)) | (~cC10(iV8467)) | (~cC48(iV8467)) | (~cC80(iV8471)) | (~cC58(iV8472)) | (~cC60(iV8472)))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[344])).
% 0.19/0.50 tff(346,plain,
% 0.19/0.50 ((~(cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cC48(iV8467) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472))) <=> ((~cC20(iV8467)) | (~cC4(iV8467)) | (~cC8(iV8467)) | (~cC82(iV8467)) | (~cC62(iV8467)) | (~cC14(iV8467)) | (~cC34(iV8467)) | (~cC10(iV8467)) | (~cC48(iV8467)) | (~cC80(iV8471)) | (~cC58(iV8472)) | (~cC60(iV8472)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[345, 343])).
% 0.19/0.50 tff(347,plain,
% 0.19/0.50 ((~(cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cC48(iV8467) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472))) <=> (~(cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cC48(iV8467) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(348,plain,
% 0.19/0.50 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cowlThing(iV8467) & cC48(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472) & cowlThing(iV8472))) <=> (~(cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cC48(iV8467) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(349,plain,
% 0.19/0.50 ((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cowlThing(iV8467) & cC48(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472) & cowlThing(iV8472)) <=> (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cowlThing(iV8467) & cC48(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472) & cowlThing(iV8472))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(350,plain,
% 0.19/0.50 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cowlThing(iV8467) & cC48(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472) & cowlThing(iV8472))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cowlThing(iV8467) & cC48(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472) & cowlThing(iV8472)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[349])).
% 0.19/0.50 tff(351,plain,
% 0.19/0.50 ((~((((((((((((((((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & cC20(iV8467)) & cC4(iV8467)) & cC8(iV8467)) & cC82(iV8467)) & cC62(iV8467)) & cC14(iV8467)) & cC34(iV8467)) & cC10(iV8467)) & cowlThing(iV8467)) & cC48(iV8467)) & cowlThing(iV8471)) & cC80(iV8471)) & cC58(iV8472)) & cC60(iV8472)) & cowlThing(iV8472))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cowlThing(iV8467) & cC48(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472) & cowlThing(iV8472)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(352,axiom,(~((((((((((((((((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & cC20(iV8467)) & cC4(iV8467)) & cC8(iV8467)) & cC82(iV8467)) & cC62(iV8467)) & cC14(iV8467)) & cC34(iV8467)) & cC10(iV8467)) & cowlThing(iV8467)) & cC48(iV8467)) & cowlThing(iV8471)) & cC80(iV8471)) & cC58(iV8472)) & cC60(iV8472)) & cowlThing(iV8472))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','the_axiom')).
% 0.19/0.50 tff(353,plain,
% 0.19/0.50 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cowlThing(iV8467) & cC48(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472) & cowlThing(iV8472))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.19/0.50 tff(354,plain,
% 0.19/0.50 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cowlThing(iV8467) & cC48(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472) & cowlThing(iV8472))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[353, 350])).
% 0.19/0.51 tff(355,plain,
% 0.19/0.51 (~(cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cC48(iV8467) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[354, 348])).
% 0.19/0.51 tff(356,plain,
% 0.19/0.51 (~(cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cC48(iV8467) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[355, 347])).
% 0.19/0.51 tff(357,plain,
% 0.19/0.51 ((~cC20(iV8467)) | (~cC4(iV8467)) | (~cC8(iV8467)) | (~cC82(iV8467)) | (~cC62(iV8467)) | (~cC14(iV8467)) | (~cC34(iV8467)) | (~cC10(iV8467)) | (~cC48(iV8467)) | (~cC80(iV8471)) | (~cC58(iV8472)) | (~cC60(iV8472))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[356, 346])).
% 0.19/0.51 tff(358,plain,
% 0.19/0.51 ((~cC20(iV8467)) | (~cC4(iV8467)) | (~cC8(iV8467)) | (~cC82(iV8467)) | (~cC62(iV8467)) | (~cC14(iV8467)) | (~cC34(iV8467)) | (~cC10(iV8467)) | (~cC48(iV8467)) | (~cC58(iV8472)) | (~cC60(iV8472))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[357, 331])).
% 0.19/0.51 tff(359,plain,
% 0.19/0.51 (~cC10(iV8467)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[358, 73, 34, 342, 283, 247, 208, 174, 152, 109, 130])).
% 0.19/0.51 tff(360,plain,
% 0.19/0.51 ((~(cC10(iV8467) <=> (~((~cC4(iV8467)) | (~cC8(iV8467)))))) | cC10(iV8467) | ((~cC4(iV8467)) | (~cC8(iV8467)))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(361,plain,
% 0.19/0.51 (~(cC10(iV8467) <=> (~((~cC4(iV8467)) | (~cC8(iV8467)))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[360, 359, 75])).
% 0.19/0.51 tff(362,plain,
% 0.19/0.51 (^[X: $i] : refl((cC10(X) <=> (~((~cC4(X)) | (~cC8(X))))) <=> (cC10(X) <=> (~((~cC4(X)) | (~cC8(X))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(363,plain,
% 0.19/0.51 (![X: $i] : (cC10(X) <=> (~((~cC4(X)) | (~cC8(X))))) <=> ![X: $i] : (cC10(X) <=> (~((~cC4(X)) | (~cC8(X)))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[362])).
% 0.19/0.51 tff(364,plain,
% 0.19/0.51 (^[X: $i] : rewrite((cC10(X) <=> (cC4(X) & cC8(X))) <=> (cC10(X) <=> (~((~cC4(X)) | (~cC8(X))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(365,plain,
% 0.19/0.51 (![X: $i] : (cC10(X) <=> (cC4(X) & cC8(X))) <=> ![X: $i] : (cC10(X) <=> (~((~cC4(X)) | (~cC8(X)))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[364])).
% 0.19/0.51 tff(366,plain,
% 0.19/0.51 (![X: $i] : (cC10(X) <=> (cC4(X) & cC8(X))) <=> ![X: $i] : (cC10(X) <=> (cC4(X) & cC8(X)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(367,axiom,(![X: $i] : (cC10(X) <=> (cC4(X) & cC8(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_2')).
% 0.19/0.51 tff(368,plain,
% 0.19/0.51 (![X: $i] : (cC10(X) <=> (cC4(X) & cC8(X)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[367, 366])).
% 0.19/0.51 tff(369,plain,(
% 0.19/0.51 ![X: $i] : (cC10(X) <=> (cC4(X) & cC8(X)))),
% 0.19/0.51 inference(skolemize,[status(sab)],[368])).
% 0.19/0.51 tff(370,plain,
% 0.19/0.51 (![X: $i] : (cC10(X) <=> (~((~cC4(X)) | (~cC8(X)))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[369, 365])).
% 0.19/0.51 tff(371,plain,
% 0.19/0.51 (![X: $i] : (cC10(X) <=> (~((~cC4(X)) | (~cC8(X)))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[370, 363])).
% 0.19/0.51 tff(372,plain,
% 0.19/0.51 ((~![X: $i] : (cC10(X) <=> (~((~cC4(X)) | (~cC8(X)))))) | (cC10(iV8467) <=> (~((~cC4(iV8467)) | (~cC8(iV8467)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(373,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[372, 371, 361])).
% 0.19/0.51 % SZS output end Proof
%------------------------------------------------------------------------------