TSTP Solution File: KRS147+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS147+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 17:44:58 EDT 2022
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KRS147+1 : TPTP v8.1.0. Released v3.1.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 09:50:30 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(rR1_type, type, (
% 0.12/0.38 rR1: ( $i * $i ) > $o)).
% 0.12/0.38 tff(iV8467_type, type, (
% 0.12/0.38 iV8467: $i)).
% 0.12/0.38 tff(cC80_type, type, (
% 0.12/0.38 cC80: $i > $o)).
% 0.12/0.38 tff(cC82_type, type, (
% 0.12/0.38 cC82: $i > $o)).
% 0.12/0.38 tff(tptp_fun_Y_17_type, type, (
% 0.12/0.38 tptp_fun_Y_17: $i > $i)).
% 0.12/0.38 tff(cC58_type, type, (
% 0.12/0.38 cC58: $i > $o)).
% 0.12/0.38 tff(iV8472_type, type, (
% 0.12/0.38 iV8472: $i)).
% 0.12/0.38 tff(cC2_type, type, (
% 0.12/0.38 cC2: $i > $o)).
% 0.12/0.38 tff(tptp_fun_Y_6_type, type, (
% 0.12/0.38 tptp_fun_Y_6: $i > $i)).
% 0.12/0.38 tff(iV8476_type, type, (
% 0.12/0.38 iV8476: $i)).
% 0.12/0.38 tff(cC60_type, type, (
% 0.12/0.38 cC60: $i > $o)).
% 0.12/0.38 tff(cC34_type, type, (
% 0.12/0.38 cC34: $i > $o)).
% 0.12/0.38 tff(cC32_type, type, (
% 0.12/0.38 cC32: $i > $o)).
% 0.12/0.38 tff(tptp_fun_Y_7_type, type, (
% 0.12/0.38 tptp_fun_Y_7: $i > $i)).
% 0.12/0.38 tff(iV8474_type, type, (
% 0.12/0.38 iV8474: $i)).
% 0.12/0.38 tff(cC62_type, type, (
% 0.12/0.38 cC62: $i > $o)).
% 0.12/0.38 tff(tptp_fun_Y_12_type, type, (
% 0.12/0.38 tptp_fun_Y_12: $i > $i)).
% 0.12/0.38 tff(cC14_type, type, (
% 0.12/0.38 cC14: $i > $o)).
% 0.12/0.38 tff(cTOP_type, type, (
% 0.12/0.38 cTOP: $i > $o)).
% 0.12/0.38 tff(tptp_fun_Y_1_type, type, (
% 0.12/0.38 tptp_fun_Y_1: $i > $i)).
% 0.12/0.38 tff(iV8470_type, type, (
% 0.12/0.38 iV8470: $i)).
% 0.12/0.38 tff(cC8_type, type, (
% 0.12/0.38 cC8: $i > $o)).
% 0.12/0.38 tff(cC6_type, type, (
% 0.12/0.38 cC6: $i > $o)).
% 0.12/0.38 tff(tptp_fun_Y_16_type, type, (
% 0.12/0.38 tptp_fun_Y_16: $i > $i)).
% 0.12/0.38 tff(iV8469_type, type, (
% 0.12/0.38 iV8469: $i)).
% 0.12/0.38 tff(cC48_type, type, (
% 0.12/0.38 cC48: $i > $o)).
% 0.12/0.38 tff(tptp_fun_Y_3_type, type, (
% 0.12/0.38 tptp_fun_Y_3: $i > $i)).
% 0.12/0.38 tff(iV8468_type, type, (
% 0.12/0.38 iV8468: $i)).
% 0.12/0.38 tff(cC10_type, type, (
% 0.12/0.38 cC10: $i > $o)).
% 0.12/0.38 tff(cC4_type, type, (
% 0.12/0.38 cC4: $i > $o)).
% 0.12/0.38 tff(cC20_type, type, (
% 0.12/0.38 cC20: $i > $o)).
% 0.12/0.38 tff(iV8471_type, type, (
% 0.12/0.38 iV8471: $i)).
% 0.12/0.38 tff(cC78_type, type, (
% 0.12/0.38 cC78: $i > $o)).
% 0.12/0.38 tff(cowlThing_type, type, (
% 0.12/0.38 cowlThing: $i > $o)).
% 0.12/0.38 tff(xsd_integer_type, type, (
% 0.12/0.38 xsd_integer: $i > $o)).
% 0.12/0.38 tff(xsd_string_type, type, (
% 0.12/0.38 xsd_string: $i > $o)).
% 0.12/0.38 tff(cowlNothing_type, type, (
% 0.12/0.38 cowlNothing: $i > $o)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[X: $i] : refl((~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))) <=> (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))) <=> ![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (^[X: $i] : rewrite((~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))) <=> (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))) <=> ![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))) <=> ![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[4, 2])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (^[X: $i] : trans(monotonicity(rewrite(((~cC82(X)) | (rR1(X, tptp_fun_Y_17(X)) & cC80(tptp_fun_Y_17(X)))) <=> ((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(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_17(X)) & cC80(tptp_fun_Y_17(X)))) & (cC82(X) | ![Y: $i] : (~(rR1(X, Y) & cC80(Y))))) <=> (((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X)))))) & (cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))), rewrite((((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X)))))) & (cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))) <=> (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))), ((((~cC82(X)) | (rR1(X, tptp_fun_Y_17(X)) & cC80(tptp_fun_Y_17(X)))) & (cC82(X) | ![Y: $i] : (~(rR1(X, Y) & cC80(Y))))) <=> (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![X: $i] : (((~cC82(X)) | (rR1(X, tptp_fun_Y_17(X)) & cC80(tptp_fun_Y_17(X)))) & (cC82(X) | ![Y: $i] : (~(rR1(X, Y) & cC80(Y))))) <=> ![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (![X: $i] : (cC82(X) <=> ?[Y: $i] : (rR1(X, Y) & cC80(Y))) <=> ![X: $i] : (cC82(X) <=> ?[Y: $i] : (rR1(X, Y) & cC80(Y)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(9,axiom,(![X: $i] : (cC82(X) <=> ?[Y: $i] : (rR1(X, Y) & cC80(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_41')).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (![X: $i] : (cC82(X) <=> ?[Y: $i] : (rR1(X, Y) & cC80(Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.19/0.39 tff(11,plain,(
% 0.19/0.39 ![X: $i] : (((~cC82(X)) | (rR1(X, tptp_fun_Y_17(X)) & cC80(tptp_fun_Y_17(X)))) & (cC82(X) | ![Y: $i] : (~(rR1(X, Y) & cC80(Y)))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[10])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_17(iV8467))) | (~cC80(tptp_fun_Y_17(iV8467))))))) | (~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_17(iV8467))) | (~cC80(tptp_fun_Y_17(iV8467))))))) | (~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 ((~((~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_17(iV8467))) | (~cC80(tptp_fun_Y_17(iV8467))))))) | (~(cC82(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC80(Y))))))) <=> (~((~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_17(iV8467))) | (~cC80(tptp_fun_Y_17(iV8467))))))) | (~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_17(iV8467))) | (~cC80(tptp_fun_Y_17(iV8467))))))) | (~(cC82(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC80(Y)))))))) <=> ((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_17(iV8467))) | (~cC80(tptp_fun_Y_17(iV8467))))))) | (~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[15])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_17(iV8467))) | (~cC80(tptp_fun_Y_17(iV8467))))))) | (~(cC82(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC80(Y)))))))) <=> ((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_17(iV8467))) | (~cC80(tptp_fun_Y_17(iV8467))))))) | (~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[16, 14])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 ((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_17(iV8467))) | (~cC80(tptp_fun_Y_17(iV8467))))))) | (~(cC82(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC80(Y)))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 ((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_17(iV8467))) | (~cC80(tptp_fun_Y_17(iV8467))))))) | (~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (~((~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_17(iV8467))) | (~cC80(tptp_fun_Y_17(iV8467))))))) | (~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[19, 13])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (((~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_17(iV8467))) | (~cC80(tptp_fun_Y_17(iV8467))))))) | (~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))))) | (cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.19/0.39 tff(23,assumption,((~((~cC58(iV8472)) | (~((~cC2(tptp_fun_Y_6(iV8472))) | (~rR1(iV8472, tptp_fun_Y_6(iV8472))))))) | (~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))))), introduced(assumption)).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (^[X: $i] : refl((~((~((~cC58(X)) | (~((~cC2(tptp_fun_Y_6(X))) | (~rR1(X, tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC58(X)) | (~((~cC2(tptp_fun_Y_6(X))) | (~rR1(X, tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (![X: $i] : (~((~((~cC58(X)) | (~((~cC2(tptp_fun_Y_6(X))) | (~rR1(X, tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC58(X)) | (~((~cC2(tptp_fun_Y_6(X))) | (~rR1(X, tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (^[X: $i] : rewrite((~((~((~cC58(X)) | (~((~cC2(tptp_fun_Y_6(X))) | (~rR1(X, tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC58(X)) | (~((~cC2(tptp_fun_Y_6(X))) | (~rR1(X, tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (![X: $i] : (~((~((~cC58(X)) | (~((~cC2(tptp_fun_Y_6(X))) | (~rR1(X, tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC58(X)) | (~((~cC2(tptp_fun_Y_6(X))) | (~rR1(X, tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![X: $i] : (~((~((~cC58(X)) | (~((~cC2(tptp_fun_Y_6(X))) | (~rR1(X, tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC58(X)) | (~((~cC2(tptp_fun_Y_6(X))) | (~rR1(X, tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[27, 25])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (^[X: $i] : trans(monotonicity(rewrite(((~cC58(X)) | (rR1(X, tptp_fun_Y_6(X)) & cC2(tptp_fun_Y_6(X)))) <=> ((~cC58(X)) | (~((~cC2(tptp_fun_Y_6(X))) | (~rR1(X, tptp_fun_Y_6(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_6(X)) & cC2(tptp_fun_Y_6(X)))) & (cC58(X) | ![Y: $i] : (~(rR1(X, Y) & cC2(Y))))) <=> (((~cC58(X)) | (~((~cC2(tptp_fun_Y_6(X))) | (~rR1(X, tptp_fun_Y_6(X)))))) & (cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))), rewrite((((~cC58(X)) | (~((~cC2(tptp_fun_Y_6(X))) | (~rR1(X, tptp_fun_Y_6(X)))))) & (cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))) <=> (~((~((~cC58(X)) | (~((~cC2(tptp_fun_Y_6(X))) | (~rR1(X, tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))), ((((~cC58(X)) | (rR1(X, tptp_fun_Y_6(X)) & cC2(tptp_fun_Y_6(X)))) & (cC58(X) | ![Y: $i] : (~(rR1(X, Y) & cC2(Y))))) <=> (~((~((~cC58(X)) | (~((~cC2(tptp_fun_Y_6(X))) | (~rR1(X, tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (![X: $i] : (((~cC58(X)) | (rR1(X, tptp_fun_Y_6(X)) & cC2(tptp_fun_Y_6(X)))) & (cC58(X) | ![Y: $i] : (~(rR1(X, Y) & cC2(Y))))) <=> ![X: $i] : (~((~((~cC58(X)) | (~((~cC2(tptp_fun_Y_6(X))) | (~rR1(X, tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (![X: $i] : (cC58(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2(Y))) <=> ![X: $i] : (cC58(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2(Y)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(32,axiom,(![X: $i] : (cC58(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_27')).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (![X: $i] : (cC58(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2(Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.39 tff(34,plain,(
% 0.19/0.39 ![X: $i] : (((~cC58(X)) | (rR1(X, tptp_fun_Y_6(X)) & cC2(tptp_fun_Y_6(X)))) & (cC58(X) | ![Y: $i] : (~(rR1(X, Y) & cC2(Y)))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[33])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (![X: $i] : (~((~((~cC58(X)) | (~((~cC2(tptp_fun_Y_6(X))) | (~rR1(X, tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (![X: $i] : (~((~((~cC58(X)) | (~((~cC2(tptp_fun_Y_6(X))) | (~rR1(X, tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 ((~![X: $i] : (~((~((~cC58(X)) | (~((~cC2(tptp_fun_Y_6(X))) | (~rR1(X, tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC58(iV8472)) | (~((~cC2(tptp_fun_Y_6(iV8472))) | (~rR1(iV8472, tptp_fun_Y_6(iV8472))))))) | (~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[37, 36, 23])).
% 0.19/0.39 tff(39,plain,(~((~((~cC58(iV8472)) | (~((~cC2(tptp_fun_Y_6(iV8472))) | (~rR1(iV8472, tptp_fun_Y_6(iV8472))))))) | (~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (((~((~cC58(iV8472)) | (~((~cC2(tptp_fun_Y_6(iV8472))) | (~rR1(iV8472, tptp_fun_Y_6(iV8472))))))) | (~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))))) | (cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.19/0.39 tff(42,assumption,(![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))), introduced(assumption)).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (cC2(iV8476) <=> cC2(iV8476)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(44,axiom,(cC2(iV8476)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_84')).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (cC2(iV8476)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (rR1(iV8472, iV8476) <=> rR1(iV8472, iV8476)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(47,axiom,(rR1(iV8472, iV8476)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_76')).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (rR1(iV8472, iV8476)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 (((~![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))) | ((~cC2(iV8476)) | (~rR1(iV8472, iV8476)))) <=> ((~![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))) | (~cC2(iV8476)) | (~rR1(iV8472, iV8476)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 ((~![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))) | ((~cC2(iV8476)) | (~rR1(iV8472, iV8476)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 ((~![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))) | (~cC2(iV8476)) | (~rR1(iV8472, iV8476))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[51, 48, 45, 42])).
% 0.19/0.39 tff(53,plain,(~![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 ((~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))) | cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 ((~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))) | cC58(iV8472)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (cC58(iV8472)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[55, 41])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 ((~cC2(iV8472)) <=> (~cC2(iV8472))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(58,axiom,(~cC2(iV8472)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_74')).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (~cC2(iV8472)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 ((~(cC2(iV8472) | (~cC58(iV8472)))) | cC2(iV8472) | (~cC58(iV8472))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 ((~(cC2(iV8472) | (~cC58(iV8472)))) | (~cC58(iV8472))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (~(cC2(iV8472) | (~cC58(iV8472)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[61, 56])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (^[X: $i] : refl((cC60(X) <=> (~(cC2(X) | (~cC58(X))))) <=> (cC60(X) <=> (~(cC2(X) | (~cC58(X))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 (![X: $i] : (cC60(X) <=> (~(cC2(X) | (~cC58(X))))) <=> ![X: $i] : (cC60(X) <=> (~(cC2(X) | (~cC58(X)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[63])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 (^[X: $i] : rewrite((cC60(X) <=> (cC58(X) & (~cC2(X)))) <=> (cC60(X) <=> (~(cC2(X) | (~cC58(X))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 (![X: $i] : (cC60(X) <=> (cC58(X) & (~cC2(X)))) <=> ![X: $i] : (cC60(X) <=> (~(cC2(X) | (~cC58(X)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 (![X: $i] : (cC60(X) <=> (cC58(X) & (~cC2(X)))) <=> ![X: $i] : (cC60(X) <=> (cC58(X) & (~cC2(X))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(68,axiom,(![X: $i] : (cC60(X) <=> (cC58(X) & (~cC2(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_29')).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 (![X: $i] : (cC60(X) <=> (cC58(X) & (~cC2(X))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.19/0.39 tff(70,plain,(
% 0.19/0.39 ![X: $i] : (cC60(X) <=> (cC58(X) & (~cC2(X))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[69])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 (![X: $i] : (cC60(X) <=> (~(cC2(X) | (~cC58(X)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 (![X: $i] : (cC60(X) <=> (~(cC2(X) | (~cC58(X)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.19/0.39 tff(73,plain,
% 0.19/0.39 ((~![X: $i] : (cC60(X) <=> (~(cC2(X) | (~cC58(X)))))) | (cC60(iV8472) <=> (~(cC2(iV8472) | (~cC58(iV8472)))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(74,plain,
% 0.19/0.39 (cC60(iV8472) <=> (~(cC2(iV8472) | (~cC58(iV8472))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.19/0.39 tff(75,plain,
% 0.19/0.39 ((~(cC60(iV8472) <=> (~(cC2(iV8472) | (~cC58(iV8472)))))) | cC60(iV8472) | (cC2(iV8472) | (~cC58(iV8472)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(76,plain,
% 0.19/0.39 (cC60(iV8472) | (cC2(iV8472) | (~cC58(iV8472)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.19/0.39 tff(77,plain,
% 0.19/0.39 (cC60(iV8472)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[76, 62])).
% 0.19/0.39 tff(78,assumption,((~((~cC34(iV8467)) | (~(cC32(tptp_fun_Y_7(iV8467)) | (~rR1(iV8467, tptp_fun_Y_7(iV8467))))))) | (~(cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y)))))), introduced(assumption)).
% 0.19/0.39 tff(79,plain,
% 0.19/0.39 (^[X: $i] : refl((~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y))))))) <=> (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(80,plain,
% 0.19/0.39 (![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.39 tff(81,plain,
% 0.19/0.39 (^[X: $i] : rewrite((~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y))))))) <=> (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(82,plain,
% 0.19/0.39 (![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[81])).
% 0.19/0.39 tff(83,plain,
% 0.19/0.39 (![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[82, 80])).
% 0.19/0.39 tff(84,plain,
% 0.19/0.39 (^[X: $i] : trans(monotonicity(rewrite(((~cC34(X)) | (rR1(X, tptp_fun_Y_7(X)) & (~cC32(tptp_fun_Y_7(X))))) <=> ((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))), rewrite((cC34(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC32(Y))))) <=> (cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y))))), ((((~cC34(X)) | (rR1(X, tptp_fun_Y_7(X)) & (~cC32(tptp_fun_Y_7(X))))) & (cC34(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC32(Y)))))) <=> (((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X)))))) & (cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y))))))), rewrite((((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X)))))) & (cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y))))) <=> (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y)))))))), ((((~cC34(X)) | (rR1(X, tptp_fun_Y_7(X)) & (~cC32(tptp_fun_Y_7(X))))) & (cC34(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC32(Y)))))) <=> (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(85,plain,
% 0.19/0.39 (![X: $i] : (((~cC34(X)) | (rR1(X, tptp_fun_Y_7(X)) & (~cC32(tptp_fun_Y_7(X))))) & (cC34(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC32(Y)))))) <=> ![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[84])).
% 0.19/0.39 tff(86,plain,
% 0.19/0.39 (![X: $i] : (cC34(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC32(Y)))) <=> ![X: $i] : (cC34(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC32(Y))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(87,axiom,(![X: $i] : (cC34(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC32(Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_14')).
% 0.19/0.39 tff(88,plain,
% 0.19/0.39 (![X: $i] : (cC34(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC32(Y))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.39 tff(89,plain,(
% 0.19/0.39 ![X: $i] : (((~cC34(X)) | (rR1(X, tptp_fun_Y_7(X)) & (~cC32(tptp_fun_Y_7(X))))) & (cC34(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC32(Y))))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[88])).
% 0.19/0.39 tff(90,plain,
% 0.19/0.39 (![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.19/0.39 tff(91,plain,
% 0.19/0.39 (![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.19/0.39 tff(92,plain,
% 0.19/0.39 ((~![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y)))))))) | (~((~((~cC34(iV8467)) | (~(cC32(tptp_fun_Y_7(iV8467)) | (~rR1(iV8467, tptp_fun_Y_7(iV8467))))))) | (~(cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y)))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(93,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[92, 91, 78])).
% 0.19/0.39 tff(94,plain,(~((~((~cC34(iV8467)) | (~(cC32(tptp_fun_Y_7(iV8467)) | (~rR1(iV8467, tptp_fun_Y_7(iV8467))))))) | (~(cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(95,plain,
% 0.19/0.39 (((~((~cC34(iV8467)) | (~(cC32(tptp_fun_Y_7(iV8467)) | (~rR1(iV8467, tptp_fun_Y_7(iV8467))))))) | (~(cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y)))))) | (cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(96,plain,
% 0.19/0.39 (cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.19/0.39 tff(97,assumption,(![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y)))), introduced(assumption)).
% 0.19/0.39 tff(98,plain,
% 0.19/0.39 ((~cC32(iV8474)) <=> (~cC32(iV8474))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(99,axiom,(~cC32(iV8474)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_80')).
% 0.19/0.39 tff(100,plain,
% 0.19/0.39 (~cC32(iV8474)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.19/0.39 tff(101,plain,
% 0.19/0.39 (rR1(iV8467, iV8474) <=> rR1(iV8467, iV8474)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(102,axiom,(rR1(iV8467, iV8474)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_61')).
% 0.19/0.39 tff(103,plain,
% 0.19/0.39 (rR1(iV8467, iV8474)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.19/0.39 tff(104,plain,
% 0.19/0.39 (((~![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y)))) | (cC32(iV8474) | (~rR1(iV8467, iV8474)))) <=> ((~![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y)))) | cC32(iV8474) | (~rR1(iV8467, iV8474)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(105,plain,
% 0.19/0.39 ((~![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y)))) | (cC32(iV8474) | (~rR1(iV8467, iV8474)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(106,plain,
% 0.19/0.39 ((~![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y)))) | cC32(iV8474) | (~rR1(iV8467, iV8474))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.19/0.39 tff(107,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[106, 103, 100, 97])).
% 0.19/0.39 tff(108,plain,(~![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(109,plain,
% 0.19/0.39 ((~(cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y))))) | cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(110,plain,
% 0.19/0.39 ((~(cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y))))) | cC34(iV8467)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.19/0.39 tff(111,plain,
% 0.19/0.39 (cC34(iV8467)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[110, 96])).
% 0.19/0.39 tff(112,assumption,((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_12(iV8467))) | (~cC60(tptp_fun_Y_12(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))))), introduced(assumption)).
% 0.19/0.39 tff(113,plain,
% 0.19/0.39 (^[X: $i] : refl((~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))) <=> (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(114,plain,
% 0.19/0.39 (![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))) <=> ![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[113])).
% 0.19/0.39 tff(115,plain,
% 0.19/0.39 (^[X: $i] : rewrite((~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))) <=> (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(116,plain,
% 0.19/0.39 (![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))) <=> ![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[115])).
% 0.19/0.39 tff(117,plain,
% 0.19/0.39 (![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))) <=> ![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[116, 114])).
% 0.19/0.39 tff(118,plain,
% 0.19/0.39 (^[X: $i] : trans(monotonicity(rewrite(((~cC62(X)) | (rR1(X, tptp_fun_Y_12(X)) & cC60(tptp_fun_Y_12(X)))) <=> ((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(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_12(X)) & cC60(tptp_fun_Y_12(X)))) & (cC62(X) | ![Y: $i] : (~(rR1(X, Y) & cC60(Y))))) <=> (((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X)))))) & (cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))), rewrite((((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X)))))) & (cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))) <=> (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))), ((((~cC62(X)) | (rR1(X, tptp_fun_Y_12(X)) & cC60(tptp_fun_Y_12(X)))) & (cC62(X) | ![Y: $i] : (~(rR1(X, Y) & cC60(Y))))) <=> (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(119,plain,
% 0.19/0.39 (![X: $i] : (((~cC62(X)) | (rR1(X, tptp_fun_Y_12(X)) & cC60(tptp_fun_Y_12(X)))) & (cC62(X) | ![Y: $i] : (~(rR1(X, Y) & cC60(Y))))) <=> ![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[118])).
% 0.19/0.39 tff(120,plain,
% 0.19/0.39 (![X: $i] : (cC62(X) <=> ?[Y: $i] : (rR1(X, Y) & cC60(Y))) <=> ![X: $i] : (cC62(X) <=> ?[Y: $i] : (rR1(X, Y) & cC60(Y)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(121,axiom,(![X: $i] : (cC62(X) <=> ?[Y: $i] : (rR1(X, Y) & cC60(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_30')).
% 0.19/0.39 tff(122,plain,
% 0.19/0.39 (![X: $i] : (cC62(X) <=> ?[Y: $i] : (rR1(X, Y) & cC60(Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.19/0.39 tff(123,plain,(
% 0.19/0.39 ![X: $i] : (((~cC62(X)) | (rR1(X, tptp_fun_Y_12(X)) & cC60(tptp_fun_Y_12(X)))) & (cC62(X) | ![Y: $i] : (~(rR1(X, Y) & cC60(Y)))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[122])).
% 0.19/0.39 tff(124,plain,
% 0.19/0.39 (![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.19/0.39 tff(125,plain,
% 0.19/0.39 (![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.19/0.39 tff(126,plain,
% 0.19/0.39 (((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_12(iV8467))) | (~cC60(tptp_fun_Y_12(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_12(iV8467))) | (~cC60(tptp_fun_Y_12(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(127,plain,
% 0.19/0.39 ((~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_12(iV8467))) | (~cC60(tptp_fun_Y_12(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC60(Y))))))) <=> (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_12(iV8467))) | (~cC60(tptp_fun_Y_12(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(128,plain,
% 0.19/0.39 (((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_12(iV8467))) | (~cC60(tptp_fun_Y_12(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC60(Y)))))))) <=> ((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_12(iV8467))) | (~cC60(tptp_fun_Y_12(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[127])).
% 0.19/0.39 tff(129,plain,
% 0.19/0.39 (((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_12(iV8467))) | (~cC60(tptp_fun_Y_12(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC60(Y)))))))) <=> ((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_12(iV8467))) | (~cC60(tptp_fun_Y_12(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[128, 126])).
% 0.19/0.39 tff(130,plain,
% 0.19/0.39 ((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_12(iV8467))) | (~cC60(tptp_fun_Y_12(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC60(Y)))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(131,plain,
% 0.19/0.39 ((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_12(iV8467))) | (~cC60(tptp_fun_Y_12(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.19/0.39 tff(132,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[131, 125, 112])).
% 0.19/0.39 tff(133,plain,(~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_12(iV8467))) | (~cC60(tptp_fun_Y_12(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(134,plain,
% 0.19/0.39 (((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_12(iV8467))) | (~cC60(tptp_fun_Y_12(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))))) | (cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(135,plain,
% 0.19/0.40 (cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.19/0.40 tff(136,assumption,(![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))), introduced(assumption)).
% 0.19/0.40 tff(137,plain,
% 0.19/0.40 (rR1(iV8467, iV8472) <=> rR1(iV8467, iV8472)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(138,axiom,(rR1(iV8467, iV8472)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_60')).
% 0.19/0.40 tff(139,plain,
% 0.19/0.40 (rR1(iV8467, iV8472)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.19/0.40 tff(140,plain,
% 0.19/0.40 (((~![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))) | ((~cC60(iV8472)) | (~rR1(iV8467, iV8472)))) <=> ((~![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))) | (~cC60(iV8472)) | (~rR1(iV8467, iV8472)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(141,plain,
% 0.19/0.40 ((~![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))) | ((~cC60(iV8472)) | (~rR1(iV8467, iV8472)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(142,plain,
% 0.19/0.40 ((~![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))) | (~cC60(iV8472)) | (~rR1(iV8467, iV8472))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.19/0.40 tff(143,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[142, 139, 77, 136])).
% 0.19/0.40 tff(144,plain,(~![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(145,plain,
% 0.19/0.40 ((~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))) | cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(146,plain,
% 0.19/0.40 ((~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))) | cC62(iV8467)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.19/0.40 tff(147,plain,
% 0.19/0.40 (cC62(iV8467)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[146, 135])).
% 0.19/0.40 tff(148,assumption,((~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_1(iV8467))) | (~cTOP(tptp_fun_Y_1(iV8467))))))) | (~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))))), introduced(assumption)).
% 0.19/0.40 tff(149,plain,
% 0.19/0.40 (^[X: $i] : refl((~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))) <=> (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(150,plain,
% 0.19/0.40 (![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))) <=> ![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[149])).
% 0.19/0.40 tff(151,plain,
% 0.19/0.40 (^[X: $i] : rewrite((~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))) <=> (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(152,plain,
% 0.19/0.40 (![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))) <=> ![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[151])).
% 0.19/0.40 tff(153,plain,
% 0.19/0.40 (![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))) <=> ![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[152, 150])).
% 0.19/0.40 tff(154,plain,
% 0.19/0.40 (^[X: $i] : trans(monotonicity(rewrite(((~cC14(X)) | (rR1(X, tptp_fun_Y_1(X)) & cTOP(tptp_fun_Y_1(X)))) <=> ((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(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_1(X)) & cTOP(tptp_fun_Y_1(X)))) & (cC14(X) | ![Y: $i] : (~(rR1(X, Y) & cTOP(Y))))) <=> (((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X)))))) & (cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))), rewrite((((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X)))))) & (cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))) <=> (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))), ((((~cC14(X)) | (rR1(X, tptp_fun_Y_1(X)) & cTOP(tptp_fun_Y_1(X)))) & (cC14(X) | ![Y: $i] : (~(rR1(X, Y) & cTOP(Y))))) <=> (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(155,plain,
% 0.19/0.40 (![X: $i] : (((~cC14(X)) | (rR1(X, tptp_fun_Y_1(X)) & cTOP(tptp_fun_Y_1(X)))) & (cC14(X) | ![Y: $i] : (~(rR1(X, Y) & cTOP(Y))))) <=> ![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[154])).
% 0.19/0.40 tff(156,plain,
% 0.19/0.40 (![X: $i] : (cC14(X) <=> ?[Y: $i] : (rR1(X, Y) & cTOP(Y))) <=> ![X: $i] : (cC14(X) <=> ?[Y: $i] : (rR1(X, Y) & cTOP(Y)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(157,axiom,(![X: $i] : (cC14(X) <=> ?[Y: $i] : (rR1(X, Y) & cTOP(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_4')).
% 0.19/0.40 tff(158,plain,
% 0.19/0.40 (![X: $i] : (cC14(X) <=> ?[Y: $i] : (rR1(X, Y) & cTOP(Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.19/0.40 tff(159,plain,(
% 0.19/0.40 ![X: $i] : (((~cC14(X)) | (rR1(X, tptp_fun_Y_1(X)) & cTOP(tptp_fun_Y_1(X)))) & (cC14(X) | ![Y: $i] : (~(rR1(X, Y) & cTOP(Y)))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[158])).
% 0.19/0.40 tff(160,plain,
% 0.19/0.40 (![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[159, 155])).
% 0.19/0.40 tff(161,plain,
% 0.19/0.40 (![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[160, 153])).
% 0.19/0.40 tff(162,plain,
% 0.19/0.40 (((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_1(iV8467))) | (~cTOP(tptp_fun_Y_1(iV8467))))))) | (~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_1(iV8467))) | (~cTOP(tptp_fun_Y_1(iV8467))))))) | (~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(163,plain,
% 0.19/0.40 ((~((~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_1(iV8467))) | (~cTOP(tptp_fun_Y_1(iV8467))))))) | (~(cC14(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cTOP(Y))))))) <=> (~((~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_1(iV8467))) | (~cTOP(tptp_fun_Y_1(iV8467))))))) | (~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(164,plain,
% 0.19/0.40 (((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_1(iV8467))) | (~cTOP(tptp_fun_Y_1(iV8467))))))) | (~(cC14(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cTOP(Y)))))))) <=> ((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_1(iV8467))) | (~cTOP(tptp_fun_Y_1(iV8467))))))) | (~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[163])).
% 0.19/0.40 tff(165,plain,
% 0.19/0.40 (((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_1(iV8467))) | (~cTOP(tptp_fun_Y_1(iV8467))))))) | (~(cC14(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cTOP(Y)))))))) <=> ((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_1(iV8467))) | (~cTOP(tptp_fun_Y_1(iV8467))))))) | (~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[164, 162])).
% 0.19/0.40 tff(166,plain,
% 0.19/0.40 ((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_1(iV8467))) | (~cTOP(tptp_fun_Y_1(iV8467))))))) | (~(cC14(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cTOP(Y)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(167,plain,
% 0.19/0.40 ((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_1(iV8467))) | (~cTOP(tptp_fun_Y_1(iV8467))))))) | (~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.19/0.40 tff(168,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[167, 161, 148])).
% 0.19/0.40 tff(169,plain,(~((~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_1(iV8467))) | (~cTOP(tptp_fun_Y_1(iV8467))))))) | (~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(170,plain,
% 0.19/0.40 (((~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_1(iV8467))) | (~cTOP(tptp_fun_Y_1(iV8467))))))) | (~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))))) | (cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(171,plain,
% 0.19/0.40 (cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[170, 169])).
% 0.19/0.40 tff(172,assumption,(![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))), introduced(assumption)).
% 0.19/0.40 tff(173,plain,
% 0.19/0.40 (cTOP(iV8470) <=> cTOP(iV8470)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(174,axiom,(cTOP(iV8470)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_68')).
% 0.19/0.40 tff(175,plain,
% 0.19/0.40 (cTOP(iV8470)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.19/0.40 tff(176,plain,
% 0.19/0.40 (rR1(iV8467, iV8470) <=> rR1(iV8467, iV8470)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(177,axiom,(rR1(iV8467, iV8470)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_62')).
% 0.19/0.40 tff(178,plain,
% 0.19/0.40 (rR1(iV8467, iV8470)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.19/0.40 tff(179,plain,
% 0.19/0.40 (((~![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))) | ((~cTOP(iV8470)) | (~rR1(iV8467, iV8470)))) <=> ((~![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))) | (~cTOP(iV8470)) | (~rR1(iV8467, iV8470)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(180,plain,
% 0.19/0.40 ((~![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))) | ((~cTOP(iV8470)) | (~rR1(iV8467, iV8470)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(181,plain,
% 0.19/0.40 ((~![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))) | (~cTOP(iV8470)) | (~rR1(iV8467, iV8470))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.19/0.40 tff(182,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[181, 178, 175, 172])).
% 0.19/0.40 tff(183,plain,(~![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(184,plain,
% 0.19/0.40 ((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(185,plain,
% 0.19/0.40 ((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | cC14(iV8467)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.19/0.40 tff(186,plain,
% 0.19/0.40 (cC14(iV8467)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[185, 171])).
% 0.19/0.40 tff(187,assumption,((~((~cC8(iV8467)) | (~(cC6(tptp_fun_Y_16(iV8467)) | (~rR1(iV8467, tptp_fun_Y_16(iV8467))))))) | (~(cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y)))))), introduced(assumption)).
% 0.19/0.40 tff(188,plain,
% 0.19/0.40 (^[X: $i] : refl((~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y))))))) <=> (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(189,plain,
% 0.19/0.40 (![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[188])).
% 0.19/0.40 tff(190,plain,
% 0.19/0.40 (^[X: $i] : rewrite((~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y))))))) <=> (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(191,plain,
% 0.19/0.40 (![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[190])).
% 0.19/0.40 tff(192,plain,
% 0.19/0.40 (![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y)))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[191, 189])).
% 0.19/0.40 tff(193,plain,
% 0.19/0.40 (^[X: $i] : trans(monotonicity(rewrite(((~cC8(X)) | (rR1(X, tptp_fun_Y_16(X)) & (~cC6(tptp_fun_Y_16(X))))) <=> ((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))), rewrite((cC8(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC6(Y))))) <=> (cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y))))), ((((~cC8(X)) | (rR1(X, tptp_fun_Y_16(X)) & (~cC6(tptp_fun_Y_16(X))))) & (cC8(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC6(Y)))))) <=> (((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X)))))) & (cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y))))))), rewrite((((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X)))))) & (cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y))))) <=> (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y)))))))), ((((~cC8(X)) | (rR1(X, tptp_fun_Y_16(X)) & (~cC6(tptp_fun_Y_16(X))))) & (cC8(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC6(Y)))))) <=> (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(194,plain,
% 0.19/0.40 (![X: $i] : (((~cC8(X)) | (rR1(X, tptp_fun_Y_16(X)) & (~cC6(tptp_fun_Y_16(X))))) & (cC8(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC6(Y)))))) <=> ![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[193])).
% 0.19/0.40 tff(195,plain,
% 0.19/0.40 (![X: $i] : (cC8(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC6(Y)))) <=> ![X: $i] : (cC8(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC6(Y))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(196,axiom,(![X: $i] : (cC8(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC6(Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_39')).
% 0.19/0.40 tff(197,plain,
% 0.19/0.40 (![X: $i] : (cC8(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC6(Y))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.19/0.40 tff(198,plain,(
% 0.19/0.40 ![X: $i] : (((~cC8(X)) | (rR1(X, tptp_fun_Y_16(X)) & (~cC6(tptp_fun_Y_16(X))))) & (cC8(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC6(Y))))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[197])).
% 0.19/0.40 tff(199,plain,
% 0.19/0.40 (![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[198, 194])).
% 0.19/0.40 tff(200,plain,
% 0.19/0.40 (![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[199, 192])).
% 0.19/0.40 tff(201,plain,
% 0.19/0.40 ((~![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y)))))))) | (~((~((~cC8(iV8467)) | (~(cC6(tptp_fun_Y_16(iV8467)) | (~rR1(iV8467, tptp_fun_Y_16(iV8467))))))) | (~(cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(202,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[201, 200, 187])).
% 0.19/0.40 tff(203,plain,(~((~((~cC8(iV8467)) | (~(cC6(tptp_fun_Y_16(iV8467)) | (~rR1(iV8467, tptp_fun_Y_16(iV8467))))))) | (~(cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(204,plain,
% 0.19/0.40 (((~((~cC8(iV8467)) | (~(cC6(tptp_fun_Y_16(iV8467)) | (~rR1(iV8467, tptp_fun_Y_16(iV8467))))))) | (~(cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y)))))) | (cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(205,plain,
% 0.19/0.40 (cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[204, 203])).
% 0.19/0.40 tff(206,assumption,(![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y)))), introduced(assumption)).
% 0.19/0.40 tff(207,plain,
% 0.19/0.40 ((~cC6(iV8469)) <=> (~cC6(iV8469))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(208,axiom,(~cC6(iV8469)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_65')).
% 0.19/0.40 tff(209,plain,
% 0.19/0.40 (~cC6(iV8469)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.19/0.40 tff(210,plain,
% 0.19/0.40 (rR1(iV8467, iV8469) <=> rR1(iV8467, iV8469)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(211,axiom,(rR1(iV8467, iV8469)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_58')).
% 0.19/0.40 tff(212,plain,
% 0.19/0.40 (rR1(iV8467, iV8469)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.19/0.40 tff(213,plain,
% 0.19/0.40 (((~![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y)))) | (cC6(iV8469) | (~rR1(iV8467, iV8469)))) <=> ((~![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y)))) | cC6(iV8469) | (~rR1(iV8467, iV8469)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(214,plain,
% 0.19/0.40 ((~![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y)))) | (cC6(iV8469) | (~rR1(iV8467, iV8469)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(215,plain,
% 0.19/0.40 ((~![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y)))) | cC6(iV8469) | (~rR1(iV8467, iV8469))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.19/0.40 tff(216,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[215, 212, 209, 206])).
% 0.19/0.40 tff(217,plain,(~![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(218,plain,
% 0.19/0.40 ((~(cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y))))) | cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(219,plain,
% 0.19/0.40 ((~(cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y))))) | cC8(iV8467)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[218, 217])).
% 0.19/0.40 tff(220,plain,
% 0.19/0.40 (cC8(iV8467)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[219, 205])).
% 0.19/0.40 tff(221,assumption,((~((~cC48(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))) | (~(cC48(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))))), introduced(assumption)).
% 0.19/0.40 tff(222,plain,
% 0.19/0.40 (^[X: $i] : refl((~((~((~cC48(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC48(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))) <=> (~((~((~cC48(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC48(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(223,plain,
% 0.19/0.40 (![X: $i] : (~((~((~cC48(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC48(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC48(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC48(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[222])).
% 0.19/0.40 tff(224,plain,
% 0.19/0.40 (^[X: $i] : rewrite((~((~((~cC48(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC48(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))) <=> (~((~((~cC48(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC48(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(225,plain,
% 0.19/0.40 (![X: $i] : (~((~((~cC48(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC48(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC48(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC48(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[224])).
% 0.19/0.40 tff(226,plain,
% 0.19/0.40 (![X: $i] : (~((~((~cC48(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC48(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC48(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC48(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[225, 223])).
% 0.19/0.40 tff(227,plain,
% 0.19/0.40 (^[X: $i] : trans(monotonicity(rewrite(((~cC48(X)) | (rR1(X, tptp_fun_Y_3(X)) & (~cC2(tptp_fun_Y_3(X))))) <=> ((~cC48(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))), rewrite((cC48(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC2(Y))))) <=> (cC48(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))), ((((~cC48(X)) | (rR1(X, tptp_fun_Y_3(X)) & (~cC2(tptp_fun_Y_3(X))))) & (cC48(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC2(Y)))))) <=> (((~cC48(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X)))))) & (cC48(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))), rewrite((((~cC48(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X)))))) & (cC48(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))) <=> (~((~((~cC48(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC48(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))), ((((~cC48(X)) | (rR1(X, tptp_fun_Y_3(X)) & (~cC2(tptp_fun_Y_3(X))))) & (cC48(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC2(Y)))))) <=> (~((~((~cC48(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC48(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(228,plain,
% 0.19/0.40 (![X: $i] : (((~cC48(X)) | (rR1(X, tptp_fun_Y_3(X)) & (~cC2(tptp_fun_Y_3(X))))) & (cC48(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC2(Y)))))) <=> ![X: $i] : (~((~((~cC48(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC48(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[227])).
% 0.19/0.40 tff(229,plain,
% 0.19/0.40 (![X: $i] : (cC48(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC2(Y)))) <=> ![X: $i] : (cC48(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC2(Y))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(230,axiom,(![X: $i] : (cC48(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC2(Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_22')).
% 0.19/0.40 tff(231,plain,
% 0.19/0.40 (![X: $i] : (cC48(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC2(Y))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.19/0.40 tff(232,plain,(
% 0.19/0.40 ![X: $i] : (((~cC48(X)) | (rR1(X, tptp_fun_Y_3(X)) & (~cC2(tptp_fun_Y_3(X))))) & (cC48(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC2(Y))))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[231])).
% 0.19/0.40 tff(233,plain,
% 0.19/0.40 (![X: $i] : (~((~((~cC48(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC48(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[232, 228])).
% 0.19/0.40 tff(234,plain,
% 0.19/0.40 (![X: $i] : (~((~((~cC48(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC48(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[233, 226])).
% 0.19/0.40 tff(235,plain,
% 0.19/0.40 ((~![X: $i] : (~((~((~cC48(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC48(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))) | (~((~((~cC48(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))) | (~(cC48(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(236,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[235, 234, 221])).
% 0.19/0.40 tff(237,plain,(~((~((~cC48(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))) | (~(cC48(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(238,plain,
% 0.19/0.40 (((~((~cC48(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))) | (~(cC48(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))))) | (cC48(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(239,plain,
% 0.19/0.40 (cC48(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[238, 237])).
% 0.19/0.40 tff(240,assumption,(![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))), introduced(assumption)).
% 0.19/0.40 tff(241,plain,
% 0.19/0.40 ((~cC2(iV8468)) <=> (~cC2(iV8468))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(242,axiom,(~cC2(iV8468)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_63')).
% 0.19/0.40 tff(243,plain,
% 0.19/0.40 (~cC2(iV8468)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.19/0.40 tff(244,plain,
% 0.19/0.40 (rR1(iV8467, iV8468) <=> rR1(iV8467, iV8468)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(245,axiom,(rR1(iV8467, iV8468)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_57')).
% 0.19/0.40 tff(246,plain,
% 0.19/0.40 (rR1(iV8467, iV8468)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.19/0.40 tff(247,plain,
% 0.19/0.40 (((~![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))) | (cC2(iV8468) | (~rR1(iV8467, iV8468)))) <=> ((~![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))) | cC2(iV8468) | (~rR1(iV8467, iV8468)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(248,plain,
% 0.19/0.40 ((~![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))) | (cC2(iV8468) | (~rR1(iV8467, iV8468)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(249,plain,
% 0.19/0.40 ((~![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))) | cC2(iV8468) | (~rR1(iV8467, iV8468))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.19/0.40 tff(250,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[249, 246, 243, 240])).
% 0.19/0.40 tff(251,plain,(~![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(252,plain,
% 0.19/0.40 ((~(cC48(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | cC48(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(253,plain,
% 0.19/0.40 ((~(cC48(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | cC48(iV8467)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[252, 251])).
% 0.19/0.40 tff(254,plain,
% 0.19/0.40 (cC48(iV8467)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[253, 239])).
% 0.19/0.40 tff(255,assumption,(~(cC10(iV8467) <=> (~((~cC4(iV8467)) | (~cC8(iV8467)))))), introduced(assumption)).
% 0.19/0.40 tff(256,plain,
% 0.19/0.40 (^[X: $i] : refl((cC10(X) <=> (~((~cC4(X)) | (~cC8(X))))) <=> (cC10(X) <=> (~((~cC4(X)) | (~cC8(X))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(257,plain,
% 0.19/0.40 (![X: $i] : (cC10(X) <=> (~((~cC4(X)) | (~cC8(X))))) <=> ![X: $i] : (cC10(X) <=> (~((~cC4(X)) | (~cC8(X)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[256])).
% 0.19/0.40 tff(258,plain,
% 0.19/0.40 (^[X: $i] : rewrite((cC10(X) <=> (cC4(X) & cC8(X))) <=> (cC10(X) <=> (~((~cC4(X)) | (~cC8(X))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(259,plain,
% 0.19/0.40 (![X: $i] : (cC10(X) <=> (cC4(X) & cC8(X))) <=> ![X: $i] : (cC10(X) <=> (~((~cC4(X)) | (~cC8(X)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[258])).
% 0.19/0.40 tff(260,plain,
% 0.19/0.40 (![X: $i] : (cC10(X) <=> (cC4(X) & cC8(X))) <=> ![X: $i] : (cC10(X) <=> (cC4(X) & cC8(X)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(261,axiom,(![X: $i] : (cC10(X) <=> (cC4(X) & cC8(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_2')).
% 0.19/0.40 tff(262,plain,
% 0.19/0.40 (![X: $i] : (cC10(X) <=> (cC4(X) & cC8(X)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.19/0.40 tff(263,plain,(
% 0.19/0.40 ![X: $i] : (cC10(X) <=> (cC4(X) & cC8(X)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[262])).
% 0.19/0.40 tff(264,plain,
% 0.19/0.40 (![X: $i] : (cC10(X) <=> (~((~cC4(X)) | (~cC8(X)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[263, 259])).
% 0.19/0.40 tff(265,plain,
% 0.19/0.40 (![X: $i] : (cC10(X) <=> (~((~cC4(X)) | (~cC8(X)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[264, 257])).
% 0.19/0.40 tff(266,plain,
% 0.19/0.40 ((~![X: $i] : (cC10(X) <=> (~((~cC4(X)) | (~cC8(X)))))) | (cC10(iV8467) <=> (~((~cC4(iV8467)) | (~cC8(iV8467)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(267,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[266, 265, 255])).
% 0.19/0.40 tff(268,plain,(cC10(iV8467) <=> (~((~cC4(iV8467)) | (~cC8(iV8467))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(269,assumption,((~((~cC4(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))) | (~(cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))))), introduced(assumption)).
% 0.19/0.40 tff(270,plain,
% 0.19/0.40 (^[X: $i] : refl((~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))) <=> (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(271,plain,
% 0.19/0.40 (![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[270])).
% 0.19/0.40 tff(272,plain,
% 0.19/0.40 (^[X: $i] : rewrite((~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))) <=> (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(273,plain,
% 0.19/0.40 (![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[272])).
% 0.19/0.40 tff(274,plain,
% 0.19/0.40 (![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[273, 271])).
% 0.19/0.40 tff(275,plain,
% 0.19/0.40 (^[X: $i] : trans(monotonicity(rewrite(((~cC4(X)) | (rR1(X, tptp_fun_Y_3(X)) & (~cC2(tptp_fun_Y_3(X))))) <=> ((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))), rewrite((cC4(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC2(Y))))) <=> (cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))), ((((~cC4(X)) | (rR1(X, tptp_fun_Y_3(X)) & (~cC2(tptp_fun_Y_3(X))))) & (cC4(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC2(Y)))))) <=> (((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X)))))) & (cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))), rewrite((((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X)))))) & (cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))) <=> (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))), ((((~cC4(X)) | (rR1(X, tptp_fun_Y_3(X)) & (~cC2(tptp_fun_Y_3(X))))) & (cC4(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC2(Y)))))) <=> (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(276,plain,
% 0.19/0.40 (![X: $i] : (((~cC4(X)) | (rR1(X, tptp_fun_Y_3(X)) & (~cC2(tptp_fun_Y_3(X))))) & (cC4(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC2(Y)))))) <=> ![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[275])).
% 0.19/0.41 tff(277,plain,
% 0.19/0.41 (![X: $i] : (cC4(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC2(Y)))) <=> ![X: $i] : (cC4(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC2(Y))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(278,axiom,(![X: $i] : (cC4(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC2(Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_17')).
% 0.19/0.41 tff(279,plain,
% 0.19/0.41 (![X: $i] : (cC4(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC2(Y))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.19/0.41 tff(280,plain,(
% 0.19/0.41 ![X: $i] : (((~cC4(X)) | (rR1(X, tptp_fun_Y_3(X)) & (~cC2(tptp_fun_Y_3(X))))) & (cC4(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC2(Y))))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[279])).
% 0.19/0.41 tff(281,plain,
% 0.19/0.41 (![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[280, 276])).
% 0.19/0.41 tff(282,plain,
% 0.19/0.41 (![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[281, 274])).
% 0.19/0.41 tff(283,plain,
% 0.19/0.41 ((~![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))) | (~((~((~cC4(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))) | (~(cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(284,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[283, 282, 269])).
% 0.19/0.41 tff(285,plain,(~((~((~cC4(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))) | (~(cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(286,plain,
% 0.19/0.41 (((~((~cC4(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))) | (~(cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))))) | (cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(287,plain,
% 0.19/0.41 (cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[286, 285])).
% 0.19/0.41 tff(288,plain,
% 0.19/0.41 ((~(cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(289,plain,
% 0.19/0.41 ((~(cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | cC4(iV8467)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[288, 251])).
% 0.19/0.41 tff(290,plain,
% 0.19/0.41 (cC4(iV8467)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[289, 287])).
% 0.19/0.41 tff(291,plain,
% 0.19/0.41 ((~((~cC4(iV8467)) | (~cC8(iV8467)))) | (~cC4(iV8467)) | (~cC8(iV8467))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(292,plain,
% 0.19/0.41 (~((~cC4(iV8467)) | (~cC8(iV8467)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[291, 290, 220])).
% 0.19/0.41 tff(293,plain,
% 0.19/0.41 ((~(cC10(iV8467) <=> (~((~cC4(iV8467)) | (~cC8(iV8467)))))) | cC10(iV8467) | ((~cC4(iV8467)) | (~cC8(iV8467)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(294,plain,
% 0.19/0.41 ((~(cC10(iV8467) <=> (~((~cC4(iV8467)) | (~cC8(iV8467)))))) | cC10(iV8467)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[293, 292])).
% 0.19/0.41 tff(295,plain,
% 0.19/0.41 (cC10(iV8467)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[294, 268])).
% 0.19/0.41 tff(296,assumption,((~((~cC20(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))) | (~(cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))))), introduced(assumption)).
% 0.19/0.41 tff(297,plain,
% 0.19/0.41 (^[X: $i] : refl((~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))) <=> (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(298,plain,
% 0.19/0.41 (![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[297])).
% 0.19/0.41 tff(299,plain,
% 0.19/0.41 (^[X: $i] : rewrite((~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))) <=> (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(300,plain,
% 0.19/0.41 (![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[299])).
% 0.19/0.41 tff(301,plain,
% 0.19/0.41 (![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[300, 298])).
% 0.19/0.41 tff(302,plain,
% 0.19/0.41 (^[X: $i] : trans(monotonicity(rewrite(((~cC20(X)) | (rR1(X, tptp_fun_Y_3(X)) & (~cC2(tptp_fun_Y_3(X))))) <=> ((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))), rewrite((cC20(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC2(Y))))) <=> (cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))), ((((~cC20(X)) | (rR1(X, tptp_fun_Y_3(X)) & (~cC2(tptp_fun_Y_3(X))))) & (cC20(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC2(Y)))))) <=> (((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X)))))) & (cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))), rewrite((((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X)))))) & (cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))) <=> (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))), ((((~cC20(X)) | (rR1(X, tptp_fun_Y_3(X)) & (~cC2(tptp_fun_Y_3(X))))) & (cC20(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC2(Y)))))) <=> (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(303,plain,
% 0.19/0.41 (![X: $i] : (((~cC20(X)) | (rR1(X, tptp_fun_Y_3(X)) & (~cC2(tptp_fun_Y_3(X))))) & (cC20(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC2(Y)))))) <=> ![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[302])).
% 0.19/0.41 tff(304,plain,
% 0.19/0.41 (![X: $i] : (cC20(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC2(Y)))) <=> ![X: $i] : (cC20(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC2(Y))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(305,axiom,(![X: $i] : (cC20(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC2(Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_7')).
% 0.19/0.41 tff(306,plain,
% 0.19/0.41 (![X: $i] : (cC20(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC2(Y))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[305, 304])).
% 0.19/0.41 tff(307,plain,(
% 0.19/0.41 ![X: $i] : (((~cC20(X)) | (rR1(X, tptp_fun_Y_3(X)) & (~cC2(tptp_fun_Y_3(X))))) & (cC20(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC2(Y))))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[306])).
% 0.19/0.41 tff(308,plain,
% 0.19/0.41 (![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[307, 303])).
% 0.19/0.41 tff(309,plain,
% 0.19/0.41 (![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[308, 301])).
% 0.19/0.41 tff(310,plain,
% 0.19/0.41 ((~![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))) | (~((~((~cC20(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))) | (~(cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(311,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[310, 309, 296])).
% 0.19/0.41 tff(312,plain,(~((~((~cC20(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))) | (~(cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(313,plain,
% 0.19/0.41 (((~((~cC20(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))) | (~(cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))))) | (cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(314,plain,
% 0.19/0.41 (cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[313, 312])).
% 0.19/0.41 tff(315,plain,
% 0.19/0.41 ((~(cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(316,plain,
% 0.19/0.41 ((~(cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | cC20(iV8467)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[315, 251])).
% 0.19/0.41 tff(317,plain,
% 0.19/0.41 (cC20(iV8467)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[316, 314])).
% 0.19/0.41 tff(318,plain,
% 0.19/0.41 (^[X: $i] : refl((cC80(X) <=> (~(cC2(X) | cC78(X)))) <=> (cC80(X) <=> (~(cC2(X) | cC78(X)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(319,plain,
% 0.19/0.41 (![X: $i] : (cC80(X) <=> (~(cC2(X) | cC78(X)))) <=> ![X: $i] : (cC80(X) <=> (~(cC2(X) | cC78(X))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[318])).
% 0.19/0.41 tff(320,plain,
% 0.19/0.41 (^[X: $i] : rewrite((cC80(X) <=> ((~cC2(X)) & (~cC78(X)))) <=> (cC80(X) <=> (~(cC2(X) | cC78(X)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(321,plain,
% 0.19/0.41 (![X: $i] : (cC80(X) <=> ((~cC2(X)) & (~cC78(X)))) <=> ![X: $i] : (cC80(X) <=> (~(cC2(X) | cC78(X))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[320])).
% 0.19/0.41 tff(322,plain,
% 0.19/0.41 (![X: $i] : (cC80(X) <=> ((~cC2(X)) & (~cC78(X)))) <=> ![X: $i] : (cC80(X) <=> ((~cC2(X)) & (~cC78(X))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(323,axiom,(![X: $i] : (cC80(X) <=> ((~cC2(X)) & (~cC78(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_40')).
% 0.19/0.41 tff(324,plain,
% 0.19/0.41 (![X: $i] : (cC80(X) <=> ((~cC2(X)) & (~cC78(X))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.19/0.41 tff(325,plain,(
% 0.19/0.41 ![X: $i] : (cC80(X) <=> ((~cC2(X)) & (~cC78(X))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[324])).
% 0.19/0.41 tff(326,plain,
% 0.19/0.41 (![X: $i] : (cC80(X) <=> (~(cC2(X) | cC78(X))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[325, 321])).
% 0.19/0.41 tff(327,plain,
% 0.19/0.41 (![X: $i] : (cC80(X) <=> (~(cC2(X) | cC78(X))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[326, 319])).
% 0.19/0.41 tff(328,plain,
% 0.19/0.41 ((~![X: $i] : (cC80(X) <=> (~(cC2(X) | cC78(X))))) | (cC80(iV8471) <=> (~(cC2(iV8471) | cC78(iV8471))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(329,plain,
% 0.19/0.41 (cC80(iV8471) <=> (~(cC2(iV8471) | cC78(iV8471)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[328, 327])).
% 0.19/0.41 tff(330,plain,
% 0.19/0.41 ((~cC78(iV8471)) <=> (~cC78(iV8471))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(331,axiom,(~cC78(iV8471)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_71')).
% 0.19/0.41 tff(332,plain,
% 0.19/0.41 (~cC78(iV8471)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.19/0.41 tff(333,plain,
% 0.19/0.41 ((~cC2(iV8471)) <=> (~cC2(iV8471))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(334,axiom,(~cC2(iV8471)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_70')).
% 0.19/0.41 tff(335,plain,
% 0.19/0.41 (~cC2(iV8471)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[334, 333])).
% 0.19/0.41 tff(336,plain,
% 0.19/0.41 ((~(cC2(iV8471) | cC78(iV8471))) | cC2(iV8471) | cC78(iV8471)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(337,plain,
% 0.19/0.41 (~(cC2(iV8471) | cC78(iV8471))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[336, 335, 332])).
% 0.19/0.41 tff(338,plain,
% 0.19/0.41 ((~(cC80(iV8471) <=> (~(cC2(iV8471) | cC78(iV8471))))) | cC80(iV8471) | (cC2(iV8471) | cC78(iV8471))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(339,plain,
% 0.19/0.41 ((~(cC80(iV8471) <=> (~(cC2(iV8471) | cC78(iV8471))))) | cC80(iV8471)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[338, 337])).
% 0.19/0.41 tff(340,plain,
% 0.19/0.41 (cC80(iV8471)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[339, 329])).
% 0.19/0.41 tff(341,plain,
% 0.19/0.41 ((~(~((~cC10(iV8467)) | (~cC48(iV8467)) | (~cC4(iV8467)) | (~cC82(iV8467)) | (~cC14(iV8467)) | (~cC8(iV8467)) | (~cC20(iV8467)) | (~cC62(iV8467)) | (~cC34(iV8467)) | (~cC80(iV8471)) | (~cC60(iV8472)) | (~cC58(iV8472))))) <=> ((~cC10(iV8467)) | (~cC48(iV8467)) | (~cC4(iV8467)) | (~cC82(iV8467)) | (~cC14(iV8467)) | (~cC8(iV8467)) | (~cC20(iV8467)) | (~cC62(iV8467)) | (~cC34(iV8467)) | (~cC80(iV8471)) | (~cC60(iV8472)) | (~cC58(iV8472)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(342,plain,
% 0.19/0.41 ((cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cC62(iV8467) & cC34(iV8467) & cC80(iV8471) & cC60(iV8472) & cC58(iV8472)) <=> (~((~cC10(iV8467)) | (~cC48(iV8467)) | (~cC4(iV8467)) | (~cC82(iV8467)) | (~cC14(iV8467)) | (~cC8(iV8467)) | (~cC20(iV8467)) | (~cC62(iV8467)) | (~cC34(iV8467)) | (~cC80(iV8471)) | (~cC60(iV8472)) | (~cC58(iV8472))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(343,plain,
% 0.19/0.41 ((~(cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cC62(iV8467) & cC34(iV8467) & cC80(iV8471) & cC60(iV8472) & cC58(iV8472))) <=> (~(~((~cC10(iV8467)) | (~cC48(iV8467)) | (~cC4(iV8467)) | (~cC82(iV8467)) | (~cC14(iV8467)) | (~cC8(iV8467)) | (~cC20(iV8467)) | (~cC62(iV8467)) | (~cC34(iV8467)) | (~cC80(iV8471)) | (~cC60(iV8472)) | (~cC58(iV8472)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[342])).
% 0.19/0.41 tff(344,plain,
% 0.19/0.41 ((~(cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cC62(iV8467) & cC34(iV8467) & cC80(iV8471) & cC60(iV8472) & cC58(iV8472))) <=> ((~cC10(iV8467)) | (~cC48(iV8467)) | (~cC4(iV8467)) | (~cC82(iV8467)) | (~cC14(iV8467)) | (~cC8(iV8467)) | (~cC20(iV8467)) | (~cC62(iV8467)) | (~cC34(iV8467)) | (~cC80(iV8471)) | (~cC60(iV8472)) | (~cC58(iV8472)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[343, 341])).
% 0.19/0.41 tff(345,plain,
% 0.19/0.41 ((~(cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cC62(iV8467) & cC34(iV8467) & cC80(iV8471) & cC60(iV8472) & cC58(iV8472))) <=> (~(cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cC62(iV8467) & cC34(iV8467) & cC80(iV8471) & cC60(iV8472) & cC58(iV8472)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(346,plain,
% 0.19/0.41 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cowlThing(iV8467) & cC62(iV8467) & cC34(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC60(iV8472) & cowlThing(iV8472) & cC58(iV8472))) <=> (~(cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cC62(iV8467) & cC34(iV8467) & cC80(iV8471) & cC60(iV8472) & cC58(iV8472)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(347,plain,
% 0.19/0.41 ((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cowlThing(iV8467) & cC62(iV8467) & cC34(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC60(iV8472) & cowlThing(iV8472) & cC58(iV8472)) <=> (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cowlThing(iV8467) & cC62(iV8467) & cC34(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC60(iV8472) & cowlThing(iV8472) & cC58(iV8472))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(348,plain,
% 0.19/0.41 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cowlThing(iV8467) & cC62(iV8467) & cC34(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC60(iV8472) & cowlThing(iV8472) & cC58(iV8472))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cowlThing(iV8467) & cC62(iV8467) & cC34(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC60(iV8472) & cowlThing(iV8472) & cC58(iV8472)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[347])).
% 0.19/0.41 tff(349,plain,
% 0.19/0.41 ((~((((((((((((((((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & cC10(iV8467)) & cC48(iV8467)) & cC4(iV8467)) & cC82(iV8467)) & cC14(iV8467)) & cC8(iV8467)) & cC20(iV8467)) & cowlThing(iV8467)) & cC62(iV8467)) & cC34(iV8467)) & cowlThing(iV8471)) & cC80(iV8471)) & cC60(iV8472)) & cowlThing(iV8472)) & cC58(iV8472))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cowlThing(iV8467) & cC62(iV8467) & cC34(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC60(iV8472) & cowlThing(iV8472) & cC58(iV8472)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(350,axiom,(~((((((((((((((((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & cC10(iV8467)) & cC48(iV8467)) & cC4(iV8467)) & cC82(iV8467)) & cC14(iV8467)) & cC8(iV8467)) & cC20(iV8467)) & cowlThing(iV8467)) & cC62(iV8467)) & cC34(iV8467)) & cowlThing(iV8471)) & cC80(iV8471)) & cC60(iV8472)) & cowlThing(iV8472)) & cC58(iV8472))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','the_axiom')).
% 0.19/0.41 tff(351,plain,
% 0.19/0.41 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cowlThing(iV8467) & cC62(iV8467) & cC34(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC60(iV8472) & cowlThing(iV8472) & cC58(iV8472))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.19/0.41 tff(352,plain,
% 0.19/0.41 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cowlThing(iV8467) & cC62(iV8467) & cC34(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC60(iV8472) & cowlThing(iV8472) & cC58(iV8472))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[351, 348])).
% 0.19/0.41 tff(353,plain,
% 0.19/0.41 (~(cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cC62(iV8467) & cC34(iV8467) & cC80(iV8471) & cC60(iV8472) & cC58(iV8472))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[352, 346])).
% 0.19/0.41 tff(354,plain,
% 0.19/0.41 (~(cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cC62(iV8467) & cC34(iV8467) & cC80(iV8471) & cC60(iV8472) & cC58(iV8472))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[353, 345])).
% 0.19/0.41 tff(355,plain,
% 0.19/0.41 ((~cC10(iV8467)) | (~cC48(iV8467)) | (~cC4(iV8467)) | (~cC82(iV8467)) | (~cC14(iV8467)) | (~cC8(iV8467)) | (~cC20(iV8467)) | (~cC62(iV8467)) | (~cC34(iV8467)) | (~cC80(iV8471)) | (~cC60(iV8472)) | (~cC58(iV8472))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[354, 344])).
% 0.19/0.41 tff(356,plain,
% 0.19/0.41 ((~cC10(iV8467)) | (~cC48(iV8467)) | (~cC4(iV8467)) | (~cC82(iV8467)) | (~cC14(iV8467)) | (~cC8(iV8467)) | (~cC20(iV8467)) | (~cC62(iV8467)) | (~cC34(iV8467)) | (~cC60(iV8472)) | (~cC58(iV8472))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[355, 340])).
% 0.19/0.41 tff(357,plain,
% 0.19/0.41 (~cC82(iV8467)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[356, 317, 290, 295, 254, 220, 186, 147, 111, 77, 56])).
% 0.19/0.41 tff(358,plain,
% 0.19/0.41 ((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(359,plain,
% 0.19/0.41 ((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[358, 357])).
% 0.19/0.42 tff(360,plain,
% 0.19/0.42 (![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[359, 22])).
% 0.19/0.42 tff(361,plain,
% 0.19/0.42 (rR1(iV8467, iV8471) <=> rR1(iV8467, iV8471)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(362,axiom,(rR1(iV8467, iV8471)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_55')).
% 0.19/0.42 tff(363,plain,
% 0.19/0.42 (rR1(iV8467, iV8471)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.19/0.42 tff(364,plain,
% 0.19/0.42 (((~![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))) | ((~cC80(iV8471)) | (~rR1(iV8467, iV8471)))) <=> ((~![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))) | (~cC80(iV8471)) | (~rR1(iV8467, iV8471)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(365,plain,
% 0.19/0.42 ((~![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))) | ((~cC80(iV8471)) | (~rR1(iV8467, iV8471)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(366,plain,
% 0.19/0.42 ((~![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))) | (~cC80(iV8471)) | (~rR1(iV8467, iV8471))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[365, 364])).
% 0.19/0.42 tff(367,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[366, 363, 340, 360])).
% 0.19/0.42 % SZS output end Proof
%------------------------------------------------------------------------------