TSTP Solution File: SWC135+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC135+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 : Tue Sep 20 11:55:31 EDT 2022
% Result : Theorem 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC135+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 21:59:03 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 % SZS output start Proof
% 0.20/0.48 tff(cyclefreeP_type, type, (
% 0.20/0.48 cyclefreeP: $i > $o)).
% 0.20/0.48 tff(nil_type, type, (
% 0.20/0.48 nil: $i)).
% 0.20/0.48 tff(tptp_fun_V_48_type, type, (
% 0.20/0.48 tptp_fun_V_48: $i)).
% 0.20/0.48 tff(tptp_fun_X_50_type, type, (
% 0.20/0.48 tptp_fun_X_50: $i)).
% 0.20/0.48 tff(ssList_type, type, (
% 0.20/0.48 ssList: $i > $o)).
% 0.20/0.48 tff(neq_type, type, (
% 0.20/0.48 neq: ( $i * $i ) > $o)).
% 0.20/0.48 tff(tptp_fun_W_49_type, type, (
% 0.20/0.48 tptp_fun_W_49: $i)).
% 0.20/0.48 tff(tptp_fun_U_47_type, type, (
% 0.20/0.48 tptp_fun_U_47: $i)).
% 0.20/0.48 tff(1,plain,
% 0.20/0.48 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~(cyclefreeP(V!48) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | neq(X!50, nil) | (~ssList(X!50)))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(cyclefreeP(V!48) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | neq(X!50, nil) | (~ssList(X!50)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(2,plain,
% 0.20/0.48 ((ssList(V!48) & (ssList(W!49) & (~(cyclefreeP(V!48) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | neq(X!50, nil) | (~ssList(X!50)))))) <=> (ssList(V!48) & ssList(W!49) & (~(cyclefreeP(V!48) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | neq(X!50, nil) | (~ssList(X!50)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(3,plain,
% 0.20/0.48 (((~(~ssList(W!49))) & (~(cyclefreeP(V!48) | (~(V!48 = X!50)) | neq(X!50, nil) | (~(U!47 = W!49)) | (~ssList(X!50))))) <=> (ssList(W!49) & (~(cyclefreeP(V!48) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | neq(X!50, nil) | (~ssList(X!50)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(4,plain,
% 0.20/0.48 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(5,plain,
% 0.20/0.48 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~(cyclefreeP(V!48) | (~(V!48 = X!50)) | neq(X!50, nil) | (~(U!47 = W!49)) | (~ssList(X!50)))))) <=> (ssList(V!48) & (ssList(W!49) & (~(cyclefreeP(V!48) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | neq(X!50, nil) | (~ssList(X!50))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[4, 3])).
% 0.20/0.48 tff(6,plain,
% 0.20/0.48 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~(cyclefreeP(V!48) | (~(V!48 = X!50)) | neq(X!50, nil) | (~(U!47 = W!49)) | (~ssList(X!50)))))) <=> (ssList(V!48) & ssList(W!49) & (~(cyclefreeP(V!48) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | neq(X!50, nil) | (~ssList(X!50)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[5, 2])).
% 0.20/0.48 tff(7,plain,
% 0.20/0.48 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(8,plain,
% 0.20/0.48 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~(cyclefreeP(V!48) | (~(V!48 = X!50)) | neq(X!50, nil) | (~(U!47 = W!49)) | (~ssList(X!50))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~(cyclefreeP(V!48) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | neq(X!50, nil) | (~ssList(X!50))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[7, 6])).
% 0.20/0.48 tff(9,plain,
% 0.20/0.48 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~(cyclefreeP(V!48) | (~(V!48 = X!50)) | neq(X!50, nil) | (~(U!47 = W!49)) | (~ssList(X!50))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(cyclefreeP(V!48) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | neq(X!50, nil) | (~ssList(X!50)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[8, 1])).
% 0.20/0.48 tff(10,plain,
% 0.20/0.48 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (cyclefreeP(V) | (~(V = X)) | neq(X, nil) | (~(U = W)) | (~ssList(X))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (cyclefreeP(V) | (~(V = X)) | neq(X, nil) | (~(U = W)) | (~ssList(X)))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(11,plain,
% 0.20/0.48 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(V = X)) | (~(U = W))) | neq(X, nil)) | cyclefreeP(V))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (cyclefreeP(V) | (~(V = X)) | neq(X, nil) | (~(U = W)) | (~ssList(X)))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(12,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(V = X)) | (~(U = W))) | neq(X, nil)) | cyclefreeP(V))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.20/0.48 tff(13,plain,
% 0.20/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (cyclefreeP(V) | (~(V = X)) | neq(X, nil) | (~(U = W)) | (~ssList(X))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.20/0.48 tff(14,plain,
% 0.20/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (cyclefreeP(V) | (~(V = X)) | neq(X, nil) | (~(U = W)) | (~ssList(X))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.20/0.48 tff(15,plain,
% 0.20/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (cyclefreeP(V) | (~(V = X)) | neq(X, nil) | (~(U = W)) | (~ssList(X))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.20/0.48 tff(16,plain,
% 0.20/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (cyclefreeP(V) | (~(V = X)) | neq(X, nil) | (~(U = W)) | (~ssList(X))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.20/0.48 tff(17,plain,
% 0.20/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (cyclefreeP(V) | (~(V = X)) | neq(X, nil) | (~(U = W)) | (~ssList(X))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.20/0.48 tff(18,plain,
% 0.20/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (cyclefreeP(V) | (~(V = X)) | neq(X, nil) | (~(U = W)) | (~ssList(X))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.20/0.48 tff(19,plain,
% 0.20/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (cyclefreeP(V) | (~(V = X)) | neq(X, nil) | (~(U = W)) | (~ssList(X))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.20/0.48 tff(20,plain,
% 0.20/0.48 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(cyclefreeP(V!48) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | neq(X!50, nil) | (~ssList(X!50))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[19, 9])).
% 0.20/0.48 tff(21,plain,
% 0.20/0.48 (~(cyclefreeP(V!48) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | neq(X!50, nil) | (~ssList(X!50)))),
% 0.20/0.48 inference(and_elim,[status(thm)],[20])).
% 0.20/0.48 tff(22,plain,
% 0.20/0.48 (V!48 = X!50),
% 0.20/0.48 inference(or_elim,[status(thm)],[21])).
% 0.20/0.48 tff(23,plain,
% 0.20/0.48 (X!50 = V!48),
% 0.20/0.48 inference(symmetry,[status(thm)],[22])).
% 0.20/0.48 tff(24,plain,
% 0.20/0.48 (ssList(X!50)),
% 0.20/0.48 inference(or_elim,[status(thm)],[21])).
% 0.20/0.48 tff(25,plain,
% 0.20/0.48 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(26,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.48 tff(27,plain,
% 0.20/0.48 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(28,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.48 tff(29,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[28, 26])).
% 0.20/0.48 tff(30,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(31,plain,
% 0.20/0.48 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))), (![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(32,plain,
% 0.20/0.48 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.48 tff(33,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax15')).
% 0.20/0.48 tff(34,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.48 tff(35,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.20/0.48 tff(36,plain,(
% 0.20/0.48 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[35])).
% 0.20/0.48 tff(37,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(39,plain,
% 0.20/0.48 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(40,plain,
% 0.20/0.48 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.48 tff(41,plain,
% 0.20/0.48 (![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[40, 37, 24])).
% 0.20/0.48 tff(42,plain,
% 0.20/0.48 (ssList(nil) <=> ssList(nil)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(43,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.20/0.48 tff(44,plain,
% 0.20/0.48 (ssList(nil)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.48 tff(45,plain,
% 0.20/0.48 (((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | ((~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | (~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(46,plain,
% 0.20/0.48 ((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | ((~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(47,plain,
% 0.20/0.48 ((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | (~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.48 tff(48,plain,
% 0.20/0.48 (neq(X!50, nil) <=> (~(X!50 = nil))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[47, 44, 41])).
% 0.20/0.48 tff(49,plain,
% 0.20/0.48 (~neq(X!50, nil)),
% 0.20/0.48 inference(or_elim,[status(thm)],[21])).
% 0.20/0.48 tff(50,plain,
% 0.20/0.48 ((~(neq(X!50, nil) <=> (~(X!50 = nil)))) | neq(X!50, nil) | (X!50 = nil)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(51,plain,
% 0.20/0.48 ((~(neq(X!50, nil) <=> (~(X!50 = nil)))) | (X!50 = nil)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.20/0.48 tff(52,plain,
% 0.20/0.48 (X!50 = nil),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[51, 48])).
% 0.20/0.48 tff(53,plain,
% 0.20/0.48 (nil = X!50),
% 0.20/0.48 inference(symmetry,[status(thm)],[52])).
% 0.20/0.48 tff(54,plain,
% 0.20/0.48 (nil = V!48),
% 0.20/0.48 inference(transitivity,[status(thm)],[53, 23])).
% 0.20/0.48 tff(55,plain,
% 0.20/0.48 (cyclefreeP(nil) <=> cyclefreeP(V!48)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[54])).
% 0.20/0.48 tff(56,plain,
% 0.20/0.48 (cyclefreeP(V!48) <=> cyclefreeP(nil)),
% 0.20/0.48 inference(symmetry,[status(thm)],[55])).
% 0.20/0.48 tff(57,plain,
% 0.20/0.48 ((~cyclefreeP(V!48)) <=> (~cyclefreeP(nil))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[56])).
% 0.20/0.48 tff(58,plain,
% 0.20/0.48 (~cyclefreeP(V!48)),
% 0.20/0.48 inference(or_elim,[status(thm)],[21])).
% 0.20/0.48 tff(59,plain,
% 0.20/0.48 (~cyclefreeP(nil)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.48 tff(60,plain,
% 0.20/0.48 (cyclefreeP(nil) <=> cyclefreeP(nil)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(61,axiom,(cyclefreeP(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax60')).
% 0.20/0.48 tff(62,plain,
% 0.20/0.48 (cyclefreeP(nil)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.48 tff(63,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[62, 59])).
% 0.20/0.48 % SZS output end Proof
%------------------------------------------------------------------------------