TSTP Solution File: KRS131+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS131+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 17:44:54 EDT 2022
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS131+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Sep 1 09:38:15 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(rp_type, type, (
% 0.21/0.39 rp: ( $i * $i ) > $o)).
% 0.21/0.39 tff(tptp_fun_Y0_1_type, type, (
% 0.21/0.39 tptp_fun_Y0_1: $i > $i)).
% 0.21/0.39 tff(tptp_fun_Y_0_type, type, (
% 0.21/0.39 tptp_fun_Y_0: $i > $i)).
% 0.21/0.39 tff(tptp_fun_X_3_type, type, (
% 0.21/0.39 tptp_fun_X_3: $i)).
% 0.21/0.39 tff(cNothing_type, type, (
% 0.21/0.39 cNothing: $i > $o)).
% 0.21/0.39 tff(rq_type, type, (
% 0.21/0.39 rq: ( $i * $i ) > $o)).
% 0.21/0.39 tff(cnotA_type, type, (
% 0.21/0.39 cnotA: $i > $o)).
% 0.21/0.39 tff(cA_type, type, (
% 0.21/0.39 cA: $i > $o)).
% 0.21/0.39 tff(cowlThing_type, type, (
% 0.21/0.39 cowlThing: $i > $o)).
% 0.21/0.39 tff(tptp_fun_Y_2_type, type, (
% 0.21/0.39 tptp_fun_Y_2: $i > $i)).
% 0.21/0.39 tff(cowlNothing_type, type, (
% 0.21/0.39 cowlNothing: $i > $o)).
% 0.21/0.39 tff(xsd_integer_type, type, (
% 0.21/0.39 xsd_integer: $i > $o)).
% 0.21/0.39 tff(xsd_string_type, type, (
% 0.21/0.39 xsd_string: $i > $o)).
% 0.21/0.39 tff(1,assumption,(cowlNothing(tptp_fun_Y_2(X!3)) | (~cowlThing(tptp_fun_Y_2(X!3)))), introduced(assumption)).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 (^[X: $i] : refl((~(cowlNothing(X) | (~cowlThing(X)))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X)))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (^[X: $i] : rewrite((cowlThing(X) & (~cowlNothing(X))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(7,axiom,(![X: $i] : (cowlThing(X) & (~cowlNothing(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_0')).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 (![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.21/0.39 tff(9,plain,(
% 0.21/0.39 ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[8])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 ((~![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))) | (~(cowlNothing(tptp_fun_Y_2(X!3)) | (~cowlThing(tptp_fun_Y_2(X!3)))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[12, 11, 1])).
% 0.21/0.39 tff(14,plain,(~(cowlNothing(tptp_fun_Y_2(X!3)) | (~cowlThing(tptp_fun_Y_2(X!3))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 ((cowlNothing(tptp_fun_Y_2(X!3)) | (~cowlThing(tptp_fun_Y_2(X!3)))) | cowlThing(tptp_fun_Y_2(X!3))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 (cowlThing(tptp_fun_Y_2(X!3))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.21/0.39 tff(17,assumption,(~cA(X!3)), introduced(assumption)).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 ((~(cnotA(X!3) <=> (~cA(X!3)))) <=> (cnotA(X!3) <=> cA(X!3))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 ((~![X: $i] : (cnotA(X) <=> (~cA(X)))) <=> (~![X: $i] : (cnotA(X) <=> (~cA(X))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i] : (cnotA(X) <=> (~cA(X))))) <=> (~![X: $i] : (cnotA(X) <=> (~cA(X))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 ((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i] : (cnotA(X) <=> (~cA(X)))) <=> (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i] : (cnotA(X) <=> (~cA(X))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i] : (cnotA(X) <=> (~cA(X))))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i] : (cnotA(X) <=> (~cA(X)))))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[21])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 ((~((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![X: $i] : (cnotA(X) <=> (~cA(X))))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i] : (cnotA(X) <=> (~cA(X)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(24,axiom,(~((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![X: $i] : (cnotA(X) <=> (~cA(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','the_axiom')).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i] : (cnotA(X) <=> (~cA(X))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i] : (cnotA(X) <=> (~cA(X))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.21/0.39 tff(27,plain,
% 0.21/0.39 (~![X: $i] : (cnotA(X) <=> (~cA(X)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[26, 20])).
% 0.21/0.39 tff(28,plain,
% 0.21/0.39 (~![X: $i] : (cnotA(X) <=> (~cA(X)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[27, 19])).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 (~![X: $i] : (cnotA(X) <=> (~cA(X)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[28, 19])).
% 0.21/0.39 tff(30,plain,
% 0.21/0.39 (~![X: $i] : (cnotA(X) <=> (~cA(X)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[29, 19])).
% 0.21/0.39 tff(31,plain,
% 0.21/0.39 (~![X: $i] : (cnotA(X) <=> (~cA(X)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[30, 19])).
% 0.21/0.39 tff(32,plain,
% 0.21/0.39 (~![X: $i] : (cnotA(X) <=> (~cA(X)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[31, 19])).
% 0.21/0.39 tff(33,plain,(
% 0.21/0.39 ~(cnotA(X!3) <=> (~cA(X!3)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[32])).
% 0.21/0.39 tff(34,plain,
% 0.21/0.39 (cnotA(X!3) <=> cA(X!3)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[33, 18])).
% 0.21/0.39 tff(35,plain,
% 0.21/0.39 ((~cnotA(X!3)) | cA(X!3) | (~(cnotA(X!3) <=> cA(X!3)))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(36,plain,
% 0.21/0.39 ((~cnotA(X!3)) | cA(X!3)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.21/0.39 tff(37,plain,
% 0.21/0.39 (~cnotA(X!3)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[36, 17])).
% 0.21/0.39 tff(38,plain,
% 0.21/0.39 (^[X: $i] : refl((~((~((~cnotA(X)) | ![Y: $i] : (cNothing(Y) | (~rq(X, Y))))) | (~(cnotA(X) | (~(cNothing(tptp_fun_Y_2(X)) | (~rq(X, tptp_fun_Y_2(X))))))))) <=> (~((~((~cnotA(X)) | ![Y: $i] : (cNothing(Y) | (~rq(X, Y))))) | (~(cnotA(X) | (~(cNothing(tptp_fun_Y_2(X)) | (~rq(X, tptp_fun_Y_2(X))))))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(39,plain,
% 0.21/0.39 (![X: $i] : (~((~((~cnotA(X)) | ![Y: $i] : (cNothing(Y) | (~rq(X, Y))))) | (~(cnotA(X) | (~(cNothing(tptp_fun_Y_2(X)) | (~rq(X, tptp_fun_Y_2(X))))))))) <=> ![X: $i] : (~((~((~cnotA(X)) | ![Y: $i] : (cNothing(Y) | (~rq(X, Y))))) | (~(cnotA(X) | (~(cNothing(tptp_fun_Y_2(X)) | (~rq(X, tptp_fun_Y_2(X)))))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[38])).
% 0.21/0.39 tff(40,plain,
% 0.21/0.39 (^[X: $i] : rewrite((~((~((~cnotA(X)) | ![Y: $i] : (cNothing(Y) | (~rq(X, Y))))) | (~(cnotA(X) | (~(cNothing(tptp_fun_Y_2(X)) | (~rq(X, tptp_fun_Y_2(X))))))))) <=> (~((~((~cnotA(X)) | ![Y: $i] : (cNothing(Y) | (~rq(X, Y))))) | (~(cnotA(X) | (~(cNothing(tptp_fun_Y_2(X)) | (~rq(X, tptp_fun_Y_2(X))))))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(41,plain,
% 0.21/0.39 (![X: $i] : (~((~((~cnotA(X)) | ![Y: $i] : (cNothing(Y) | (~rq(X, Y))))) | (~(cnotA(X) | (~(cNothing(tptp_fun_Y_2(X)) | (~rq(X, tptp_fun_Y_2(X))))))))) <=> ![X: $i] : (~((~((~cnotA(X)) | ![Y: $i] : (cNothing(Y) | (~rq(X, Y))))) | (~(cnotA(X) | (~(cNothing(tptp_fun_Y_2(X)) | (~rq(X, tptp_fun_Y_2(X)))))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[40])).
% 0.21/0.39 tff(42,plain,
% 0.21/0.39 (![X: $i] : (~((~((~cnotA(X)) | ![Y: $i] : (cNothing(Y) | (~rq(X, Y))))) | (~(cnotA(X) | (~(cNothing(tptp_fun_Y_2(X)) | (~rq(X, tptp_fun_Y_2(X))))))))) <=> ![X: $i] : (~((~((~cnotA(X)) | ![Y: $i] : (cNothing(Y) | (~rq(X, Y))))) | (~(cnotA(X) | (~(cNothing(tptp_fun_Y_2(X)) | (~rq(X, tptp_fun_Y_2(X)))))))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[41, 39])).
% 0.21/0.39 tff(43,plain,
% 0.21/0.39 (^[X: $i] : trans(monotonicity(rewrite(((~cnotA(X)) | ![Y: $i] : (cNothing(Y) | (~rq(X, Y)))) <=> ((~cnotA(X)) | ![Y: $i] : (cNothing(Y) | (~rq(X, Y))))), ((((~cnotA(X)) | ![Y: $i] : (cNothing(Y) | (~rq(X, Y)))) & (cnotA(X) | (~(cNothing(tptp_fun_Y_2(X)) | (~rq(X, tptp_fun_Y_2(X))))))) <=> (((~cnotA(X)) | ![Y: $i] : (cNothing(Y) | (~rq(X, Y)))) & (cnotA(X) | (~(cNothing(tptp_fun_Y_2(X)) | (~rq(X, tptp_fun_Y_2(X))))))))), rewrite((((~cnotA(X)) | ![Y: $i] : (cNothing(Y) | (~rq(X, Y)))) & (cnotA(X) | (~(cNothing(tptp_fun_Y_2(X)) | (~rq(X, tptp_fun_Y_2(X))))))) <=> (~((~((~cnotA(X)) | ![Y: $i] : (cNothing(Y) | (~rq(X, Y))))) | (~(cnotA(X) | (~(cNothing(tptp_fun_Y_2(X)) | (~rq(X, tptp_fun_Y_2(X)))))))))), ((((~cnotA(X)) | ![Y: $i] : (cNothing(Y) | (~rq(X, Y)))) & (cnotA(X) | (~(cNothing(tptp_fun_Y_2(X)) | (~rq(X, tptp_fun_Y_2(X))))))) <=> (~((~((~cnotA(X)) | ![Y: $i] : (cNothing(Y) | (~rq(X, Y))))) | (~(cnotA(X) | (~(cNothing(tptp_fun_Y_2(X)) | (~rq(X, tptp_fun_Y_2(X)))))))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(44,plain,
% 0.21/0.39 (![X: $i] : (((~cnotA(X)) | ![Y: $i] : (cNothing(Y) | (~rq(X, Y)))) & (cnotA(X) | (~(cNothing(tptp_fun_Y_2(X)) | (~rq(X, tptp_fun_Y_2(X))))))) <=> ![X: $i] : (~((~((~cnotA(X)) | ![Y: $i] : (cNothing(Y) | (~rq(X, Y))))) | (~(cnotA(X) | (~(cNothing(tptp_fun_Y_2(X)) | (~rq(X, tptp_fun_Y_2(X)))))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[43])).
% 0.21/0.39 tff(45,plain,
% 0.21/0.39 (![X: $i] : (cnotA(X) <=> ![Y: $i] : (cNothing(Y) | (~rq(X, Y)))) <=> ![X: $i] : (cnotA(X) <=> ![Y: $i] : (cNothing(Y) | (~rq(X, Y))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(46,plain,
% 0.21/0.39 (^[X: $i] : rewrite((cnotA(X) <=> ![Y: $i] : (rq(X, Y) => cNothing(Y))) <=> (cnotA(X) <=> ![Y: $i] : (cNothing(Y) | (~rq(X, Y)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(47,plain,
% 0.21/0.39 (![X: $i] : (cnotA(X) <=> ![Y: $i] : (rq(X, Y) => cNothing(Y))) <=> ![X: $i] : (cnotA(X) <=> ![Y: $i] : (cNothing(Y) | (~rq(X, Y))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[46])).
% 0.21/0.39 tff(48,axiom,(![X: $i] : (cnotA(X) <=> ![Y: $i] : (rq(X, Y) => cNothing(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_5')).
% 0.21/0.39 tff(49,plain,
% 0.21/0.39 (![X: $i] : (cnotA(X) <=> ![Y: $i] : (cNothing(Y) | (~rq(X, Y))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.21/0.39 tff(50,plain,
% 0.21/0.39 (![X: $i] : (cnotA(X) <=> ![Y: $i] : (cNothing(Y) | (~rq(X, Y))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.21/0.39 tff(51,plain,(
% 0.21/0.39 ![X: $i] : (((~cnotA(X)) | ![Y: $i] : (cNothing(Y) | (~rq(X, Y)))) & (cnotA(X) | (~(cNothing(tptp_fun_Y_2(X)) | (~rq(X, tptp_fun_Y_2(X)))))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[50])).
% 0.21/0.39 tff(52,plain,
% 0.21/0.39 (![X: $i] : (~((~((~cnotA(X)) | ![Y: $i] : (cNothing(Y) | (~rq(X, Y))))) | (~(cnotA(X) | (~(cNothing(tptp_fun_Y_2(X)) | (~rq(X, tptp_fun_Y_2(X)))))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.21/0.39 tff(53,plain,
% 0.21/0.39 (![X: $i] : (~((~((~cnotA(X)) | ![Y: $i] : (cNothing(Y) | (~rq(X, Y))))) | (~(cnotA(X) | (~(cNothing(tptp_fun_Y_2(X)) | (~rq(X, tptp_fun_Y_2(X)))))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[52, 42])).
% 0.21/0.39 tff(54,plain,
% 0.21/0.39 ((~![X: $i] : (~((~((~cnotA(X)) | ![Y: $i] : (cNothing(Y) | (~rq(X, Y))))) | (~(cnotA(X) | (~(cNothing(tptp_fun_Y_2(X)) | (~rq(X, tptp_fun_Y_2(X)))))))))) | (~((~((~cnotA(X!3)) | ![Y: $i] : (cNothing(Y) | (~rq(X!3, Y))))) | (~(cnotA(X!3) | (~(cNothing(tptp_fun_Y_2(X!3)) | (~rq(X!3, tptp_fun_Y_2(X!3)))))))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(55,plain,
% 0.21/0.39 (~((~((~cnotA(X!3)) | ![Y: $i] : (cNothing(Y) | (~rq(X!3, Y))))) | (~(cnotA(X!3) | (~(cNothing(tptp_fun_Y_2(X!3)) | (~rq(X!3, tptp_fun_Y_2(X!3))))))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.21/0.39 tff(56,plain,
% 0.21/0.39 (((~((~cnotA(X!3)) | ![Y: $i] : (cNothing(Y) | (~rq(X!3, Y))))) | (~(cnotA(X!3) | (~(cNothing(tptp_fun_Y_2(X!3)) | (~rq(X!3, tptp_fun_Y_2(X!3)))))))) | (cnotA(X!3) | (~(cNothing(tptp_fun_Y_2(X!3)) | (~rq(X!3, tptp_fun_Y_2(X!3))))))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(57,plain,
% 0.21/0.39 (cnotA(X!3) | (~(cNothing(tptp_fun_Y_2(X!3)) | (~rq(X!3, tptp_fun_Y_2(X!3)))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.21/0.40 tff(58,plain,
% 0.21/0.40 ((~(cnotA(X!3) | (~(cNothing(tptp_fun_Y_2(X!3)) | (~rq(X!3, tptp_fun_Y_2(X!3))))))) | cnotA(X!3) | (~(cNothing(tptp_fun_Y_2(X!3)) | (~rq(X!3, tptp_fun_Y_2(X!3)))))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(59,plain,
% 0.21/0.40 (cnotA(X!3) | (~(cNothing(tptp_fun_Y_2(X!3)) | (~rq(X!3, tptp_fun_Y_2(X!3)))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.21/0.40 tff(60,plain,
% 0.21/0.40 (~(cNothing(tptp_fun_Y_2(X!3)) | (~rq(X!3, tptp_fun_Y_2(X!3))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[59, 37])).
% 0.21/0.40 tff(61,plain,
% 0.21/0.40 ((cNothing(tptp_fun_Y_2(X!3)) | (~rq(X!3, tptp_fun_Y_2(X!3)))) | rq(X!3, tptp_fun_Y_2(X!3))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(62,plain,
% 0.21/0.40 (rq(X!3, tptp_fun_Y_2(X!3))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.21/0.40 tff(63,plain,
% 0.21/0.40 (^[X: $i] : refl((~((~((~cA(X)) | (~((~rq(X, tptp_fun_Y_0(X))) | (~cowlThing(tptp_fun_Y_0(X))))))) | (~(cA(X) | ![Y: $i] : ((~rq(X, Y)) | (~cowlThing(Y))))))) <=> (~((~((~cA(X)) | (~((~rq(X, tptp_fun_Y_0(X))) | (~cowlThing(tptp_fun_Y_0(X))))))) | (~(cA(X) | ![Y: $i] : ((~rq(X, Y)) | (~cowlThing(Y))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(64,plain,
% 0.21/0.40 (![X: $i] : (~((~((~cA(X)) | (~((~rq(X, tptp_fun_Y_0(X))) | (~cowlThing(tptp_fun_Y_0(X))))))) | (~(cA(X) | ![Y: $i] : ((~rq(X, Y)) | (~cowlThing(Y))))))) <=> ![X: $i] : (~((~((~cA(X)) | (~((~rq(X, tptp_fun_Y_0(X))) | (~cowlThing(tptp_fun_Y_0(X))))))) | (~(cA(X) | ![Y: $i] : ((~rq(X, Y)) | (~cowlThing(Y)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[63])).
% 0.21/0.40 tff(65,plain,
% 0.21/0.40 (^[X: $i] : rewrite((~((~((~cA(X)) | (~((~rq(X, tptp_fun_Y_0(X))) | (~cowlThing(tptp_fun_Y_0(X))))))) | (~(cA(X) | ![Y: $i] : ((~rq(X, Y)) | (~cowlThing(Y))))))) <=> (~((~((~cA(X)) | (~((~rq(X, tptp_fun_Y_0(X))) | (~cowlThing(tptp_fun_Y_0(X))))))) | (~(cA(X) | ![Y: $i] : ((~rq(X, Y)) | (~cowlThing(Y))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(66,plain,
% 0.21/0.40 (![X: $i] : (~((~((~cA(X)) | (~((~rq(X, tptp_fun_Y_0(X))) | (~cowlThing(tptp_fun_Y_0(X))))))) | (~(cA(X) | ![Y: $i] : ((~rq(X, Y)) | (~cowlThing(Y))))))) <=> ![X: $i] : (~((~((~cA(X)) | (~((~rq(X, tptp_fun_Y_0(X))) | (~cowlThing(tptp_fun_Y_0(X))))))) | (~(cA(X) | ![Y: $i] : ((~rq(X, Y)) | (~cowlThing(Y)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[65])).
% 0.21/0.40 tff(67,plain,
% 0.21/0.40 (![X: $i] : (~((~((~cA(X)) | (~((~rq(X, tptp_fun_Y_0(X))) | (~cowlThing(tptp_fun_Y_0(X))))))) | (~(cA(X) | ![Y: $i] : ((~rq(X, Y)) | (~cowlThing(Y))))))) <=> ![X: $i] : (~((~((~cA(X)) | (~((~rq(X, tptp_fun_Y_0(X))) | (~cowlThing(tptp_fun_Y_0(X))))))) | (~(cA(X) | ![Y: $i] : ((~rq(X, Y)) | (~cowlThing(Y)))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[66, 64])).
% 0.21/0.40 tff(68,plain,
% 0.21/0.40 (^[X: $i] : trans(monotonicity(rewrite(((~cA(X)) | (rq(X, tptp_fun_Y_0(X)) & cowlThing(tptp_fun_Y_0(X)))) <=> ((~cA(X)) | (~((~rq(X, tptp_fun_Y_0(X))) | (~cowlThing(tptp_fun_Y_0(X))))))), rewrite((cA(X) | ![Y: $i] : (~(rq(X, Y) & cowlThing(Y)))) <=> (cA(X) | ![Y: $i] : ((~rq(X, Y)) | (~cowlThing(Y))))), ((((~cA(X)) | (rq(X, tptp_fun_Y_0(X)) & cowlThing(tptp_fun_Y_0(X)))) & (cA(X) | ![Y: $i] : (~(rq(X, Y) & cowlThing(Y))))) <=> (((~cA(X)) | (~((~rq(X, tptp_fun_Y_0(X))) | (~cowlThing(tptp_fun_Y_0(X)))))) & (cA(X) | ![Y: $i] : ((~rq(X, Y)) | (~cowlThing(Y))))))), rewrite((((~cA(X)) | (~((~rq(X, tptp_fun_Y_0(X))) | (~cowlThing(tptp_fun_Y_0(X)))))) & (cA(X) | ![Y: $i] : ((~rq(X, Y)) | (~cowlThing(Y))))) <=> (~((~((~cA(X)) | (~((~rq(X, tptp_fun_Y_0(X))) | (~cowlThing(tptp_fun_Y_0(X))))))) | (~(cA(X) | ![Y: $i] : ((~rq(X, Y)) | (~cowlThing(Y)))))))), ((((~cA(X)) | (rq(X, tptp_fun_Y_0(X)) & cowlThing(tptp_fun_Y_0(X)))) & (cA(X) | ![Y: $i] : (~(rq(X, Y) & cowlThing(Y))))) <=> (~((~((~cA(X)) | (~((~rq(X, tptp_fun_Y_0(X))) | (~cowlThing(tptp_fun_Y_0(X))))))) | (~(cA(X) | ![Y: $i] : ((~rq(X, Y)) | (~cowlThing(Y)))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(69,plain,
% 0.21/0.40 (![X: $i] : (((~cA(X)) | (rq(X, tptp_fun_Y_0(X)) & cowlThing(tptp_fun_Y_0(X)))) & (cA(X) | ![Y: $i] : (~(rq(X, Y) & cowlThing(Y))))) <=> ![X: $i] : (~((~((~cA(X)) | (~((~rq(X, tptp_fun_Y_0(X))) | (~cowlThing(tptp_fun_Y_0(X))))))) | (~(cA(X) | ![Y: $i] : ((~rq(X, Y)) | (~cowlThing(Y)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[68])).
% 0.21/0.40 tff(70,plain,
% 0.21/0.40 (![X: $i] : (cA(X) <=> ?[Y: $i] : (rq(X, Y) & cowlThing(Y))) <=> ![X: $i] : (cA(X) <=> ?[Y: $i] : (rq(X, Y) & cowlThing(Y)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(71,axiom,(![X: $i] : (cA(X) <=> ?[Y: $i] : (rq(X, Y) & cowlThing(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_2')).
% 0.21/0.40 tff(72,plain,
% 0.21/0.40 (![X: $i] : (cA(X) <=> ?[Y: $i] : (rq(X, Y) & cowlThing(Y)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.21/0.40 tff(73,plain,(
% 0.21/0.40 ![X: $i] : (((~cA(X)) | (rq(X, tptp_fun_Y_0(X)) & cowlThing(tptp_fun_Y_0(X)))) & (cA(X) | ![Y: $i] : (~(rq(X, Y) & cowlThing(Y)))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[72])).
% 0.21/0.40 tff(74,plain,
% 0.21/0.40 (![X: $i] : (~((~((~cA(X)) | (~((~rq(X, tptp_fun_Y_0(X))) | (~cowlThing(tptp_fun_Y_0(X))))))) | (~(cA(X) | ![Y: $i] : ((~rq(X, Y)) | (~cowlThing(Y)))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.21/0.40 tff(75,plain,
% 0.21/0.40 (![X: $i] : (~((~((~cA(X)) | (~((~rq(X, tptp_fun_Y_0(X))) | (~cowlThing(tptp_fun_Y_0(X))))))) | (~(cA(X) | ![Y: $i] : ((~rq(X, Y)) | (~cowlThing(Y)))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.21/0.40 tff(76,plain,
% 0.21/0.40 (((~![X: $i] : (~((~((~cA(X)) | (~((~rq(X, tptp_fun_Y_0(X))) | (~cowlThing(tptp_fun_Y_0(X))))))) | (~(cA(X) | ![Y: $i] : ((~rq(X, Y)) | (~cowlThing(Y)))))))) | (~((~((~cA(X!3)) | (~((~rq(X!3, tptp_fun_Y_0(X!3))) | (~cowlThing(tptp_fun_Y_0(X!3))))))) | (~(cA(X!3) | ![Y: $i] : ((~cowlThing(Y)) | (~rq(X!3, Y)))))))) <=> ((~![X: $i] : (~((~((~cA(X)) | (~((~rq(X, tptp_fun_Y_0(X))) | (~cowlThing(tptp_fun_Y_0(X))))))) | (~(cA(X) | ![Y: $i] : ((~rq(X, Y)) | (~cowlThing(Y)))))))) | (~((~((~cA(X!3)) | (~((~rq(X!3, tptp_fun_Y_0(X!3))) | (~cowlThing(tptp_fun_Y_0(X!3))))))) | (~(cA(X!3) | ![Y: $i] : ((~cowlThing(Y)) | (~rq(X!3, Y))))))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(77,plain,
% 0.21/0.40 ((~((~((~cA(X!3)) | (~((~rq(X!3, tptp_fun_Y_0(X!3))) | (~cowlThing(tptp_fun_Y_0(X!3))))))) | (~(cA(X!3) | ![Y: $i] : ((~rq(X!3, Y)) | (~cowlThing(Y))))))) <=> (~((~((~cA(X!3)) | (~((~rq(X!3, tptp_fun_Y_0(X!3))) | (~cowlThing(tptp_fun_Y_0(X!3))))))) | (~(cA(X!3) | ![Y: $i] : ((~cowlThing(Y)) | (~rq(X!3, Y)))))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(78,plain,
% 0.21/0.40 (((~![X: $i] : (~((~((~cA(X)) | (~((~rq(X, tptp_fun_Y_0(X))) | (~cowlThing(tptp_fun_Y_0(X))))))) | (~(cA(X) | ![Y: $i] : ((~rq(X, Y)) | (~cowlThing(Y)))))))) | (~((~((~cA(X!3)) | (~((~rq(X!3, tptp_fun_Y_0(X!3))) | (~cowlThing(tptp_fun_Y_0(X!3))))))) | (~(cA(X!3) | ![Y: $i] : ((~rq(X!3, Y)) | (~cowlThing(Y)))))))) <=> ((~![X: $i] : (~((~((~cA(X)) | (~((~rq(X, tptp_fun_Y_0(X))) | (~cowlThing(tptp_fun_Y_0(X))))))) | (~(cA(X) | ![Y: $i] : ((~rq(X, Y)) | (~cowlThing(Y)))))))) | (~((~((~cA(X!3)) | (~((~rq(X!3, tptp_fun_Y_0(X!3))) | (~cowlThing(tptp_fun_Y_0(X!3))))))) | (~(cA(X!3) | ![Y: $i] : ((~cowlThing(Y)) | (~rq(X!3, Y))))))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[77])).
% 0.21/0.40 tff(79,plain,
% 0.21/0.40 (((~![X: $i] : (~((~((~cA(X)) | (~((~rq(X, tptp_fun_Y_0(X))) | (~cowlThing(tptp_fun_Y_0(X))))))) | (~(cA(X) | ![Y: $i] : ((~rq(X, Y)) | (~cowlThing(Y)))))))) | (~((~((~cA(X!3)) | (~((~rq(X!3, tptp_fun_Y_0(X!3))) | (~cowlThing(tptp_fun_Y_0(X!3))))))) | (~(cA(X!3) | ![Y: $i] : ((~rq(X!3, Y)) | (~cowlThing(Y)))))))) <=> ((~![X: $i] : (~((~((~cA(X)) | (~((~rq(X, tptp_fun_Y_0(X))) | (~cowlThing(tptp_fun_Y_0(X))))))) | (~(cA(X) | ![Y: $i] : ((~rq(X, Y)) | (~cowlThing(Y)))))))) | (~((~((~cA(X!3)) | (~((~rq(X!3, tptp_fun_Y_0(X!3))) | (~cowlThing(tptp_fun_Y_0(X!3))))))) | (~(cA(X!3) | ![Y: $i] : ((~cowlThing(Y)) | (~rq(X!3, Y))))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[78, 76])).
% 0.21/0.40 tff(80,plain,
% 0.21/0.40 ((~![X: $i] : (~((~((~cA(X)) | (~((~rq(X, tptp_fun_Y_0(X))) | (~cowlThing(tptp_fun_Y_0(X))))))) | (~(cA(X) | ![Y: $i] : ((~rq(X, Y)) | (~cowlThing(Y)))))))) | (~((~((~cA(X!3)) | (~((~rq(X!3, tptp_fun_Y_0(X!3))) | (~cowlThing(tptp_fun_Y_0(X!3))))))) | (~(cA(X!3) | ![Y: $i] : ((~rq(X!3, Y)) | (~cowlThing(Y)))))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(81,plain,
% 0.21/0.40 ((~![X: $i] : (~((~((~cA(X)) | (~((~rq(X, tptp_fun_Y_0(X))) | (~cowlThing(tptp_fun_Y_0(X))))))) | (~(cA(X) | ![Y: $i] : ((~rq(X, Y)) | (~cowlThing(Y)))))))) | (~((~((~cA(X!3)) | (~((~rq(X!3, tptp_fun_Y_0(X!3))) | (~cowlThing(tptp_fun_Y_0(X!3))))))) | (~(cA(X!3) | ![Y: $i] : ((~cowlThing(Y)) | (~rq(X!3, Y)))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.21/0.40 tff(82,plain,
% 0.21/0.40 (~((~((~cA(X!3)) | (~((~rq(X!3, tptp_fun_Y_0(X!3))) | (~cowlThing(tptp_fun_Y_0(X!3))))))) | (~(cA(X!3) | ![Y: $i] : ((~cowlThing(Y)) | (~rq(X!3, Y))))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[81, 75])).
% 0.21/0.40 tff(83,plain,
% 0.21/0.40 (((~((~cA(X!3)) | (~((~rq(X!3, tptp_fun_Y_0(X!3))) | (~cowlThing(tptp_fun_Y_0(X!3))))))) | (~(cA(X!3) | ![Y: $i] : ((~cowlThing(Y)) | (~rq(X!3, Y)))))) | (cA(X!3) | ![Y: $i] : ((~cowlThing(Y)) | (~rq(X!3, Y))))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(84,plain,
% 0.21/0.40 (cA(X!3) | ![Y: $i] : ((~cowlThing(Y)) | (~rq(X!3, Y)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.21/0.40 tff(85,plain,
% 0.21/0.40 ((~(cA(X!3) | ![Y: $i] : ((~cowlThing(Y)) | (~rq(X!3, Y))))) | cA(X!3) | ![Y: $i] : ((~cowlThing(Y)) | (~rq(X!3, Y)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(86,plain,
% 0.21/0.40 (cA(X!3) | ![Y: $i] : ((~cowlThing(Y)) | (~rq(X!3, Y)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.21/0.40 tff(87,plain,
% 0.21/0.40 (![Y: $i] : ((~cowlThing(Y)) | (~rq(X!3, Y)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[86, 17])).
% 0.21/0.40 tff(88,plain,
% 0.21/0.40 (((~![Y: $i] : ((~cowlThing(Y)) | (~rq(X!3, Y)))) | ((~cowlThing(tptp_fun_Y_2(X!3))) | (~rq(X!3, tptp_fun_Y_2(X!3))))) <=> ((~![Y: $i] : ((~cowlThing(Y)) | (~rq(X!3, Y)))) | (~cowlThing(tptp_fun_Y_2(X!3))) | (~rq(X!3, tptp_fun_Y_2(X!3))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(89,plain,
% 0.21/0.40 ((~![Y: $i] : ((~cowlThing(Y)) | (~rq(X!3, Y)))) | ((~cowlThing(tptp_fun_Y_2(X!3))) | (~rq(X!3, tptp_fun_Y_2(X!3))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(90,plain,
% 0.21/0.40 ((~![Y: $i] : ((~cowlThing(Y)) | (~rq(X!3, Y)))) | (~cowlThing(tptp_fun_Y_2(X!3))) | (~rq(X!3, tptp_fun_Y_2(X!3)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.21/0.40 tff(91,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[90, 87, 62, 16])).
% 0.21/0.40 tff(92,plain,(cA(X!3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(93,plain,
% 0.21/0.40 (cnotA(X!3) | (~cA(X!3)) | (~(cnotA(X!3) <=> cA(X!3)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(94,plain,
% 0.21/0.40 (cnotA(X!3) | (~cA(X!3))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[93, 34])).
% 0.21/0.40 tff(95,plain,
% 0.21/0.40 (cnotA(X!3)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[94, 92])).
% 0.21/0.40 tff(96,plain,
% 0.21/0.40 (((~((~cnotA(X!3)) | ![Y: $i] : (cNothing(Y) | (~rq(X!3, Y))))) | (~(cnotA(X!3) | (~(cNothing(tptp_fun_Y_2(X!3)) | (~rq(X!3, tptp_fun_Y_2(X!3)))))))) | ((~cnotA(X!3)) | ![Y: $i] : (cNothing(Y) | (~rq(X!3, Y))))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(97,plain,
% 0.21/0.40 ((~cnotA(X!3)) | ![Y: $i] : (cNothing(Y) | (~rq(X!3, Y)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[96, 55])).
% 0.21/0.40 tff(98,plain,
% 0.21/0.40 ((~((~cnotA(X!3)) | ![Y: $i] : (cNothing(Y) | (~rq(X!3, Y))))) | (~cnotA(X!3)) | ![Y: $i] : (cNothing(Y) | (~rq(X!3, Y)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(99,plain,
% 0.21/0.40 ((~cnotA(X!3)) | ![Y: $i] : (cNothing(Y) | (~rq(X!3, Y)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.21/0.40 tff(100,plain,
% 0.21/0.40 (![Y: $i] : (cNothing(Y) | (~rq(X!3, Y)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[99, 95])).
% 0.21/0.40 tff(101,plain,
% 0.21/0.40 (((~((~cA(X!3)) | (~((~rq(X!3, tptp_fun_Y_0(X!3))) | (~cowlThing(tptp_fun_Y_0(X!3))))))) | (~(cA(X!3) | ![Y: $i] : ((~cowlThing(Y)) | (~rq(X!3, Y)))))) | ((~cA(X!3)) | (~((~rq(X!3, tptp_fun_Y_0(X!3))) | (~cowlThing(tptp_fun_Y_0(X!3))))))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(102,plain,
% 0.21/0.40 ((~cA(X!3)) | (~((~rq(X!3, tptp_fun_Y_0(X!3))) | (~cowlThing(tptp_fun_Y_0(X!3)))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[101, 82])).
% 0.21/0.40 tff(103,plain,
% 0.21/0.40 ((~((~cA(X!3)) | (~((~rq(X!3, tptp_fun_Y_0(X!3))) | (~cowlThing(tptp_fun_Y_0(X!3))))))) | (~cA(X!3)) | (~((~rq(X!3, tptp_fun_Y_0(X!3))) | (~cowlThing(tptp_fun_Y_0(X!3)))))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(104,plain,
% 0.21/0.40 ((~cA(X!3)) | (~((~rq(X!3, tptp_fun_Y_0(X!3))) | (~cowlThing(tptp_fun_Y_0(X!3)))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.21/0.40 tff(105,plain,
% 0.21/0.40 (~((~rq(X!3, tptp_fun_Y_0(X!3))) | (~cowlThing(tptp_fun_Y_0(X!3))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[104, 92])).
% 0.21/0.40 tff(106,plain,
% 0.21/0.40 (((~rq(X!3, tptp_fun_Y_0(X!3))) | (~cowlThing(tptp_fun_Y_0(X!3)))) | rq(X!3, tptp_fun_Y_0(X!3))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(107,plain,
% 0.21/0.40 (rq(X!3, tptp_fun_Y_0(X!3))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.21/0.40 tff(108,plain,
% 0.21/0.40 (((~![Y: $i] : (cNothing(Y) | (~rq(X!3, Y)))) | (cNothing(tptp_fun_Y_0(X!3)) | (~rq(X!3, tptp_fun_Y_0(X!3))))) <=> ((~![Y: $i] : (cNothing(Y) | (~rq(X!3, Y)))) | cNothing(tptp_fun_Y_0(X!3)) | (~rq(X!3, tptp_fun_Y_0(X!3))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(109,plain,
% 0.21/0.40 ((~![Y: $i] : (cNothing(Y) | (~rq(X!3, Y)))) | (cNothing(tptp_fun_Y_0(X!3)) | (~rq(X!3, tptp_fun_Y_0(X!3))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(110,plain,
% 0.21/0.40 ((~![Y: $i] : (cNothing(Y) | (~rq(X!3, Y)))) | cNothing(tptp_fun_Y_0(X!3)) | (~rq(X!3, tptp_fun_Y_0(X!3)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.21/0.40 tff(111,plain,
% 0.21/0.40 (cNothing(tptp_fun_Y_0(X!3))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[110, 107, 100])).
% 0.21/0.40 tff(112,plain,
% 0.21/0.40 (^[X: $i] : refl(((~cNothing(X)) | rp(X, tptp_fun_Y0_1(X))) <=> ((~cNothing(X)) | rp(X, tptp_fun_Y0_1(X))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(113,plain,
% 0.21/0.40 (![X: $i] : ((~cNothing(X)) | rp(X, tptp_fun_Y0_1(X))) <=> ![X: $i] : ((~cNothing(X)) | rp(X, tptp_fun_Y0_1(X)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[112])).
% 0.21/0.40 tff(114,plain,
% 0.21/0.40 (![X: $i] : ((~cNothing(X)) | ?[Y0: $i] : rp(X, Y0)) <=> ![X: $i] : ((~cNothing(X)) | ?[Y0: $i] : rp(X, Y0))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(115,plain,
% 0.21/0.40 (^[X: $i] : rewrite((cNothing(X) => ?[Y0: $i] : rp(X, Y0)) <=> ((~cNothing(X)) | ?[Y0: $i] : rp(X, Y0)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(116,plain,
% 0.21/0.40 (![X: $i] : (cNothing(X) => ?[Y0: $i] : rp(X, Y0)) <=> ![X: $i] : ((~cNothing(X)) | ?[Y0: $i] : rp(X, Y0))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[115])).
% 0.21/0.40 tff(117,axiom,(![X: $i] : (cNothing(X) => ?[Y0: $i] : rp(X, Y0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_4')).
% 0.21/0.40 tff(118,plain,
% 0.21/0.40 (![X: $i] : ((~cNothing(X)) | ?[Y0: $i] : rp(X, Y0))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.21/0.40 tff(119,plain,
% 0.21/0.40 (![X: $i] : ((~cNothing(X)) | ?[Y0: $i] : rp(X, Y0))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.21/0.40 tff(120,plain,(
% 0.21/0.40 ![X: $i] : ((~cNothing(X)) | rp(X, tptp_fun_Y0_1(X)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[119])).
% 0.21/0.40 tff(121,plain,
% 0.21/0.40 (![X: $i] : ((~cNothing(X)) | rp(X, tptp_fun_Y0_1(X)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.21/0.40 tff(122,plain,
% 0.21/0.40 (((~![X: $i] : ((~cNothing(X)) | rp(X, tptp_fun_Y0_1(X)))) | ((~cNothing(tptp_fun_Y_0(X!3))) | rp(tptp_fun_Y_0(X!3), tptp_fun_Y0_1(tptp_fun_Y_0(X!3))))) <=> ((~![X: $i] : ((~cNothing(X)) | rp(X, tptp_fun_Y0_1(X)))) | (~cNothing(tptp_fun_Y_0(X!3))) | rp(tptp_fun_Y_0(X!3), tptp_fun_Y0_1(tptp_fun_Y_0(X!3))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(123,plain,
% 0.21/0.40 ((~![X: $i] : ((~cNothing(X)) | rp(X, tptp_fun_Y0_1(X)))) | ((~cNothing(tptp_fun_Y_0(X!3))) | rp(tptp_fun_Y_0(X!3), tptp_fun_Y0_1(tptp_fun_Y_0(X!3))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(124,plain,
% 0.21/0.40 ((~![X: $i] : ((~cNothing(X)) | rp(X, tptp_fun_Y0_1(X)))) | (~cNothing(tptp_fun_Y_0(X!3))) | rp(tptp_fun_Y_0(X!3), tptp_fun_Y0_1(tptp_fun_Y_0(X!3)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.21/0.40 tff(125,plain,
% 0.21/0.40 (rp(tptp_fun_Y_0(X!3), tptp_fun_Y0_1(tptp_fun_Y_0(X!3)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[124, 121, 111])).
% 0.21/0.40 tff(126,plain,
% 0.21/0.40 (^[X: $i] : refl(((~cNothing(X)) | ![Y: $i] : (~rp(X, Y))) <=> ((~cNothing(X)) | ![Y: $i] : (~rp(X, Y))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(127,plain,
% 0.21/0.40 (![X: $i] : ((~cNothing(X)) | ![Y: $i] : (~rp(X, Y))) <=> ![X: $i] : ((~cNothing(X)) | ![Y: $i] : (~rp(X, Y)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[126])).
% 0.21/0.41 tff(128,plain,
% 0.21/0.41 (^[X: $i] : rewrite(((~cNothing(X)) | ![Y: $i] : (~rp(X, Y))) <=> ((~cNothing(X)) | ![Y: $i] : (~rp(X, Y))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(129,plain,
% 0.21/0.41 (![X: $i] : ((~cNothing(X)) | ![Y: $i] : (~rp(X, Y))) <=> ![X: $i] : ((~cNothing(X)) | ![Y: $i] : (~rp(X, Y)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[128])).
% 0.21/0.41 tff(130,plain,
% 0.21/0.41 (![X: $i] : ((~cNothing(X)) | ![Y: $i] : (~rp(X, Y))) <=> ![X: $i] : ((~cNothing(X)) | ![Y: $i] : (~rp(X, Y)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[129, 127])).
% 0.21/0.41 tff(131,plain,
% 0.21/0.41 (![X: $i] : ((~cNothing(X)) | (~?[Y: $i] : rp(X, Y))) <=> ![X: $i] : ((~cNothing(X)) | (~?[Y: $i] : rp(X, Y)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(132,plain,
% 0.21/0.41 (^[X: $i] : trans(monotonicity(rewrite((~?[Y: $i] : rp(X, Y)) <=> (~?[Y: $i] : rp(X, Y))), ((cNothing(X) => (~?[Y: $i] : rp(X, Y))) <=> (cNothing(X) => (~?[Y: $i] : rp(X, Y))))), rewrite((cNothing(X) => (~?[Y: $i] : rp(X, Y))) <=> ((~cNothing(X)) | (~?[Y: $i] : rp(X, Y)))), ((cNothing(X) => (~?[Y: $i] : rp(X, Y))) <=> ((~cNothing(X)) | (~?[Y: $i] : rp(X, Y)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(133,plain,
% 0.21/0.41 (![X: $i] : (cNothing(X) => (~?[Y: $i] : rp(X, Y))) <=> ![X: $i] : ((~cNothing(X)) | (~?[Y: $i] : rp(X, Y)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[132])).
% 0.21/0.41 tff(134,axiom,(![X: $i] : (cNothing(X) => (~?[Y: $i] : rp(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_3')).
% 0.21/0.41 tff(135,plain,
% 0.21/0.41 (![X: $i] : ((~cNothing(X)) | (~?[Y: $i] : rp(X, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.21/0.41 tff(136,plain,
% 0.21/0.41 (![X: $i] : ((~cNothing(X)) | (~?[Y: $i] : rp(X, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[135, 131])).
% 0.21/0.41 tff(137,plain,(
% 0.21/0.41 ![X: $i] : ((~cNothing(X)) | ![Y: $i] : (~rp(X, Y)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[136])).
% 0.21/0.41 tff(138,plain,
% 0.21/0.41 (![X: $i] : ((~cNothing(X)) | ![Y: $i] : (~rp(X, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[137, 130])).
% 0.21/0.41 tff(139,plain,
% 0.21/0.41 (((~![X: $i] : ((~cNothing(X)) | ![Y: $i] : (~rp(X, Y)))) | ((~cNothing(tptp_fun_Y_0(X!3))) | ![Y: $i] : (~rp(tptp_fun_Y_0(X!3), Y)))) <=> ((~![X: $i] : ((~cNothing(X)) | ![Y: $i] : (~rp(X, Y)))) | (~cNothing(tptp_fun_Y_0(X!3))) | ![Y: $i] : (~rp(tptp_fun_Y_0(X!3), Y)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(140,plain,
% 0.21/0.41 ((~![X: $i] : ((~cNothing(X)) | ![Y: $i] : (~rp(X, Y)))) | ((~cNothing(tptp_fun_Y_0(X!3))) | ![Y: $i] : (~rp(tptp_fun_Y_0(X!3), Y)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(141,plain,
% 0.21/0.41 ((~![X: $i] : ((~cNothing(X)) | ![Y: $i] : (~rp(X, Y)))) | (~cNothing(tptp_fun_Y_0(X!3))) | ![Y: $i] : (~rp(tptp_fun_Y_0(X!3), Y))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.21/0.41 tff(142,plain,
% 0.21/0.41 (![Y: $i] : (~rp(tptp_fun_Y_0(X!3), Y))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[141, 138, 111])).
% 0.21/0.41 tff(143,plain,
% 0.21/0.41 ((~![Y: $i] : (~rp(tptp_fun_Y_0(X!3), Y))) | (~rp(tptp_fun_Y_0(X!3), tptp_fun_Y0_1(tptp_fun_Y_0(X!3))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(144,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[143, 142, 125])).
% 0.21/0.41 % SZS output end Proof
%------------------------------------------------------------------------------