TSTP Solution File: SWC369+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC369+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 11:57:28 EDT 2022
% Result : Theorem 0.63s 0.63s
% Output : Proof 0.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC369+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Sep 4 00:22:17 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.
% 0.63/0.63 % SZS status Theorem
% 0.63/0.63 % SZS output start Proof
% 0.63/0.63 tff(tptp_fun_W_49_type, type, (
% 0.63/0.63 tptp_fun_W_49: $i)).
% 0.63/0.63 tff(nil_type, type, (
% 0.63/0.63 nil: $i)).
% 0.63/0.63 tff(segmentP_type, type, (
% 0.63/0.63 segmentP: ( $i * $i ) > $o)).
% 0.63/0.63 tff(ssList_type, type, (
% 0.63/0.63 ssList: $i > $o)).
% 0.63/0.63 tff(tptp_fun_X_50_type, type, (
% 0.63/0.63 tptp_fun_X_50: $i)).
% 0.63/0.63 tff(neq_type, type, (
% 0.63/0.63 neq: ( $i * $i ) > $o)).
% 0.63/0.63 tff(tptp_fun_V_48_type, type, (
% 0.63/0.63 tptp_fun_V_48: $i)).
% 0.63/0.63 tff(tptp_fun_U_47_type, type, (
% 0.63/0.63 tptp_fun_U_47: $i)).
% 0.63/0.63 tff(1,plain,
% 0.63/0.63 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~(segmentP(V!48, U!47) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49)))) | ((~(nil = W!49)) & (nil = X!50)) | (~ssList(X!50)))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(segmentP(V!48, U!47) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49)))) | ((~(nil = W!49)) & (nil = X!50)) | (~ssList(X!50)))))),
% 0.63/0.63 inference(rewrite,[status(thm)],[])).
% 0.63/0.63 tff(2,plain,
% 0.63/0.63 ((ssList(V!48) & (ssList(W!49) & (~(segmentP(V!48, U!47) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49)))) | ((~(nil = W!49)) & (nil = X!50)) | (~ssList(X!50)))))) <=> (ssList(V!48) & ssList(W!49) & (~(segmentP(V!48, U!47) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49)))) | ((~(nil = W!49)) & (nil = X!50)) | (~ssList(X!50)))))),
% 0.63/0.63 inference(rewrite,[status(thm)],[])).
% 0.63/0.63 tff(3,plain,
% 0.63/0.63 (((~(~ssList(W!49))) & (~(segmentP(V!48, U!47) | (~(V!48 = X!50)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49)))) | ((~(nil = W!49)) & (nil = X!50)) | (~(U!47 = W!49)) | (~ssList(X!50))))) <=> (ssList(W!49) & (~(segmentP(V!48, U!47) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49)))) | ((~(nil = W!49)) & (nil = X!50)) | (~ssList(X!50)))))),
% 0.63/0.63 inference(rewrite,[status(thm)],[])).
% 0.63/0.63 tff(4,plain,
% 0.63/0.63 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 0.63/0.63 inference(rewrite,[status(thm)],[])).
% 0.63/0.63 tff(5,plain,
% 0.63/0.63 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~(segmentP(V!48, U!47) | (~(V!48 = X!50)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49)))) | ((~(nil = W!49)) & (nil = X!50)) | (~(U!47 = W!49)) | (~ssList(X!50)))))) <=> (ssList(V!48) & (ssList(W!49) & (~(segmentP(V!48, U!47) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49)))) | ((~(nil = W!49)) & (nil = X!50)) | (~ssList(X!50))))))),
% 0.63/0.63 inference(monotonicity,[status(thm)],[4, 3])).
% 0.63/0.63 tff(6,plain,
% 0.63/0.63 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~(segmentP(V!48, U!47) | (~(V!48 = X!50)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49)))) | ((~(nil = W!49)) & (nil = X!50)) | (~(U!47 = W!49)) | (~ssList(X!50)))))) <=> (ssList(V!48) & ssList(W!49) & (~(segmentP(V!48, U!47) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49)))) | ((~(nil = W!49)) & (nil = X!50)) | (~ssList(X!50)))))),
% 0.63/0.63 inference(transitivity,[status(thm)],[5, 2])).
% 0.63/0.63 tff(7,plain,
% 0.63/0.63 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 0.63/0.63 inference(rewrite,[status(thm)],[])).
% 0.63/0.63 tff(8,plain,
% 0.63/0.63 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~(segmentP(V!48, U!47) | (~(V!48 = X!50)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49)))) | ((~(nil = W!49)) & (nil = X!50)) | (~(U!47 = W!49)) | (~ssList(X!50))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~(segmentP(V!48, U!47) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49)))) | ((~(nil = W!49)) & (nil = X!50)) | (~ssList(X!50))))))),
% 0.63/0.63 inference(monotonicity,[status(thm)],[7, 6])).
% 0.63/0.63 tff(9,plain,
% 0.63/0.63 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~(segmentP(V!48, U!47) | (~(V!48 = X!50)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49)))) | ((~(nil = W!49)) & (nil = X!50)) | (~(U!47 = W!49)) | (~ssList(X!50))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(segmentP(V!48, U!47) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49)))) | ((~(nil = W!49)) & (nil = X!50)) | (~ssList(X!50)))))),
% 0.63/0.63 inference(transitivity,[status(thm)],[8, 1])).
% 0.63/0.63 tff(10,plain,
% 0.63/0.63 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~(V = X)) | (neq(X, nil) & ((~neq(W, nil)) | (~segmentP(X, W)))) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~ssList(X))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~(V = X)) | (neq(X, nil) & ((~neq(W, nil)) | (~segmentP(X, W)))) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~ssList(X)))))))),
% 0.63/0.63 inference(rewrite,[status(thm)],[])).
% 0.63/0.63 tff(11,plain,
% 0.63/0.63 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | segmentP(V, U)) | ((~(nil = W)) & (nil = X))) | (neq(X, nil) & ((~neq(W, nil)) | (~segmentP(X, W)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~(V = X)) | (neq(X, nil) & ((~neq(W, nil)) | (~segmentP(X, W)))) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~ssList(X)))))))),
% 0.63/0.63 inference(rewrite,[status(thm)],[])).
% 0.63/0.63 tff(12,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | segmentP(V, U)) | ((~(nil = W)) & (nil = X))) | (neq(X, nil) & ((~neq(W, nil)) | (~segmentP(X, W)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.63/0.63 tff(13,plain,
% 0.63/0.63 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~(V = X)) | (neq(X, nil) & ((~neq(W, nil)) | (~segmentP(X, W)))) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~ssList(X))))))),
% 0.63/0.63 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.63/0.63 tff(14,plain,
% 0.63/0.63 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~(V = X)) | (neq(X, nil) & ((~neq(W, nil)) | (~segmentP(X, W)))) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~ssList(X))))))),
% 0.63/0.63 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.63/0.63 tff(15,plain,
% 0.63/0.63 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~(V = X)) | (neq(X, nil) & ((~neq(W, nil)) | (~segmentP(X, W)))) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~ssList(X))))))),
% 0.63/0.63 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.63/0.63 tff(16,plain,
% 0.63/0.63 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~(V = X)) | (neq(X, nil) & ((~neq(W, nil)) | (~segmentP(X, W)))) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~ssList(X))))))),
% 0.63/0.63 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.63/0.63 tff(17,plain,
% 0.63/0.63 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~(V = X)) | (neq(X, nil) & ((~neq(W, nil)) | (~segmentP(X, W)))) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~ssList(X))))))),
% 0.63/0.63 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.63/0.63 tff(18,plain,
% 0.63/0.63 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~(V = X)) | (neq(X, nil) & ((~neq(W, nil)) | (~segmentP(X, W)))) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~ssList(X))))))),
% 0.63/0.63 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.63/0.63 tff(19,plain,
% 0.63/0.63 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~(V = X)) | (neq(X, nil) & ((~neq(W, nil)) | (~segmentP(X, W)))) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~ssList(X))))))),
% 0.63/0.63 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.63/0.63 tff(20,plain,
% 0.63/0.63 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(segmentP(V!48, U!47) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49)))) | ((~(nil = W!49)) & (nil = X!50)) | (~ssList(X!50))))),
% 0.63/0.63 inference(modus_ponens,[status(thm)],[19, 9])).
% 0.63/0.64 tff(21,plain,
% 0.63/0.64 (ssList(W!49)),
% 0.63/0.64 inference(and_elim,[status(thm)],[20])).
% 0.63/0.64 tff(22,plain,
% 0.63/0.64 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(23,plain,
% 0.63/0.64 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[22])).
% 0.63/0.64 tff(24,plain,
% 0.63/0.64 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(25,plain,
% 0.63/0.64 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(26,plain,
% 0.63/0.64 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[25])).
% 0.63/0.64 tff(27,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax58')).
% 0.63/0.64 tff(28,plain,
% 0.63/0.64 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.63/0.64 tff(29,plain,
% 0.63/0.64 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.63/0.64 tff(30,plain,(
% 0.63/0.64 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.63/0.64 inference(skolemize,[status(sab)],[29])).
% 0.63/0.64 tff(31,plain,
% 0.63/0.64 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.63/0.64 tff(32,plain,
% 0.63/0.64 (((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(W!49)) | (segmentP(nil, W!49) <=> (nil = W!49)))) <=> ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(W!49)) | (segmentP(nil, W!49) <=> (nil = W!49)))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(33,plain,
% 0.63/0.64 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(W!49)) | (segmentP(nil, W!49) <=> (nil = W!49)))),
% 0.63/0.64 inference(quant_inst,[status(thm)],[])).
% 0.63/0.64 tff(34,plain,
% 0.63/0.64 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(W!49)) | (segmentP(nil, W!49) <=> (nil = W!49))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.63/0.64 tff(35,plain,
% 0.63/0.64 (segmentP(nil, W!49) <=> (nil = W!49)),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[34, 31, 21])).
% 0.63/0.64 tff(36,plain,
% 0.63/0.64 (~(segmentP(V!48, U!47) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49)))) | ((~(nil = W!49)) & (nil = X!50)) | (~ssList(X!50)))),
% 0.63/0.64 inference(and_elim,[status(thm)],[20])).
% 0.63/0.64 tff(37,plain,
% 0.63/0.64 (ssList(X!50)),
% 0.63/0.64 inference(or_elim,[status(thm)],[36])).
% 0.63/0.64 tff(38,plain,
% 0.63/0.64 (^[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))))))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(39,plain,
% 0.63/0.64 (![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)))))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[38])).
% 0.63/0.64 tff(40,plain,
% 0.63/0.64 (^[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))))))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(41,plain,
% 0.63/0.64 (![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)))))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[40])).
% 0.63/0.64 tff(42,plain,
% 0.63/0.64 (![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)))))),
% 0.63/0.64 inference(transitivity,[status(thm)],[41, 39])).
% 0.63/0.64 tff(43,plain,
% 0.63/0.64 (![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)))))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(44,plain,
% 0.63/0.64 (^[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)))))))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(45,plain,
% 0.63/0.64 (![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)))))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[44])).
% 0.63/0.64 tff(46,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax15')).
% 0.63/0.64 tff(47,plain,
% 0.63/0.64 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.63/0.64 tff(48,plain,
% 0.63/0.64 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.63/0.64 tff(49,plain,(
% 0.63/0.64 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.63/0.64 inference(skolemize,[status(sab)],[48])).
% 0.63/0.64 tff(50,plain,
% 0.63/0.64 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.63/0.64 tff(51,plain,
% 0.63/0.64 (((~![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)))))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(52,plain,
% 0.63/0.64 ((~![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)))))),
% 0.63/0.64 inference(quant_inst,[status(thm)],[])).
% 0.63/0.64 tff(53,plain,
% 0.63/0.64 ((~![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))))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.63/0.64 tff(54,plain,
% 0.63/0.64 (![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[53, 50, 37])).
% 0.63/0.64 tff(55,plain,
% 0.63/0.64 (ssList(nil) <=> ssList(nil)),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(56,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.63/0.64 tff(57,plain,
% 0.63/0.64 (ssList(nil)),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.63/0.64 tff(58,plain,
% 0.63/0.64 (((~![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))))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(59,plain,
% 0.63/0.64 ((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | ((~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil))))),
% 0.63/0.64 inference(quant_inst,[status(thm)],[])).
% 0.63/0.64 tff(60,plain,
% 0.63/0.64 ((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | (~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil)))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.63/0.64 tff(61,plain,
% 0.63/0.64 (neq(X!50, nil) <=> (~(X!50 = nil))),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[60, 57, 54])).
% 0.63/0.64 tff(62,plain,
% 0.63/0.64 (U!47 = W!49),
% 0.63/0.64 inference(or_elim,[status(thm)],[36])).
% 0.63/0.64 tff(63,plain,
% 0.63/0.64 (V!48 = X!50),
% 0.63/0.64 inference(or_elim,[status(thm)],[36])).
% 0.63/0.64 tff(64,plain,
% 0.63/0.64 (segmentP(V!48, U!47) <=> segmentP(X!50, W!49)),
% 0.63/0.64 inference(monotonicity,[status(thm)],[63, 62])).
% 0.63/0.64 tff(65,plain,
% 0.63/0.64 ((~segmentP(V!48, U!47)) <=> (~segmentP(X!50, W!49))),
% 0.63/0.64 inference(monotonicity,[status(thm)],[64])).
% 0.63/0.64 tff(66,plain,
% 0.63/0.64 (~segmentP(V!48, U!47)),
% 0.63/0.64 inference(or_elim,[status(thm)],[36])).
% 0.63/0.64 tff(67,plain,
% 0.63/0.64 (~segmentP(X!50, W!49)),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.63/0.64 tff(68,plain,
% 0.63/0.64 (((~neq(W!49, nil)) | (~segmentP(X!50, W!49))) | segmentP(X!50, W!49)),
% 0.63/0.64 inference(tautology,[status(thm)],[])).
% 0.63/0.64 tff(69,plain,
% 0.63/0.64 ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.63/0.64 tff(70,plain,
% 0.63/0.64 ((~(~((~neq(X!50, nil)) | (~((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))))) <=> ((~neq(X!50, nil)) | (~((~neq(W!49, nil)) | (~segmentP(X!50, W!49)))))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(71,plain,
% 0.63/0.64 ((neq(X!50, nil) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49)))) <=> (~((~neq(X!50, nil)) | (~((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(72,plain,
% 0.63/0.64 ((~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))) <=> (~(~((~neq(X!50, nil)) | (~((~neq(W!49, nil)) | (~segmentP(X!50, W!49)))))))),
% 0.63/0.64 inference(monotonicity,[status(thm)],[71])).
% 0.63/0.64 tff(73,plain,
% 0.63/0.64 ((~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))) <=> ((~neq(X!50, nil)) | (~((~neq(W!49, nil)) | (~segmentP(X!50, W!49)))))),
% 0.63/0.64 inference(transitivity,[status(thm)],[72, 70])).
% 0.63/0.64 tff(74,plain,
% 0.63/0.64 (~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))),
% 0.63/0.64 inference(or_elim,[status(thm)],[36])).
% 0.63/0.64 tff(75,plain,
% 0.63/0.64 ((~neq(X!50, nil)) | (~((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.63/0.64 tff(76,plain,
% 0.63/0.64 (~neq(X!50, nil)),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[75, 69])).
% 0.63/0.64 tff(77,plain,
% 0.63/0.64 ((~(neq(X!50, nil) <=> (~(X!50 = nil)))) | neq(X!50, nil) | (X!50 = nil)),
% 0.63/0.64 inference(tautology,[status(thm)],[])).
% 0.63/0.64 tff(78,plain,
% 0.63/0.64 ((~(neq(X!50, nil) <=> (~(X!50 = nil)))) | (X!50 = nil)),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.63/0.64 tff(79,plain,
% 0.63/0.64 (X!50 = nil),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[78, 61])).
% 0.63/0.64 tff(80,plain,
% 0.63/0.64 (nil = X!50),
% 0.63/0.64 inference(symmetry,[status(thm)],[79])).
% 0.63/0.64 tff(81,plain,
% 0.63/0.64 (segmentP(nil, W!49) <=> segmentP(X!50, W!49)),
% 0.63/0.64 inference(monotonicity,[status(thm)],[80])).
% 0.63/0.64 tff(82,plain,
% 0.63/0.64 (segmentP(X!50, W!49) <=> segmentP(nil, W!49)),
% 0.63/0.64 inference(symmetry,[status(thm)],[81])).
% 0.63/0.64 tff(83,plain,
% 0.63/0.64 ((~segmentP(X!50, W!49)) <=> (~segmentP(nil, W!49))),
% 0.63/0.64 inference(monotonicity,[status(thm)],[82])).
% 0.63/0.64 tff(84,plain,
% 0.63/0.64 (~segmentP(nil, W!49)),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[67, 83])).
% 0.63/0.64 tff(85,plain,
% 0.63/0.64 ((~(~((nil = W!49) | (~(nil = X!50))))) <=> ((nil = W!49) | (~(nil = X!50)))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(86,plain,
% 0.63/0.65 (((~(nil = W!49)) & (nil = X!50)) <=> (~((nil = W!49) | (~(nil = X!50))))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(87,plain,
% 0.63/0.65 ((~((~(nil = W!49)) & (nil = X!50))) <=> (~(~((nil = W!49) | (~(nil = X!50)))))),
% 0.63/0.65 inference(monotonicity,[status(thm)],[86])).
% 0.63/0.65 tff(88,plain,
% 0.63/0.65 ((~((~(nil = W!49)) & (nil = X!50))) <=> ((nil = W!49) | (~(nil = X!50)))),
% 0.63/0.65 inference(transitivity,[status(thm)],[87, 85])).
% 0.63/0.65 tff(89,plain,
% 0.63/0.65 (~((~(nil = W!49)) & (nil = X!50))),
% 0.63/0.65 inference(or_elim,[status(thm)],[36])).
% 0.63/0.65 tff(90,plain,
% 0.63/0.65 ((nil = W!49) | (~(nil = X!50))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.63/0.65 tff(91,plain,
% 0.63/0.65 (nil = W!49),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[90, 80])).
% 0.63/0.65 tff(92,plain,
% 0.63/0.65 ((~(segmentP(nil, W!49) <=> (nil = W!49))) | segmentP(nil, W!49) | (~(nil = W!49))),
% 0.63/0.65 inference(tautology,[status(thm)],[])).
% 0.63/0.65 tff(93,plain,
% 0.63/0.65 ($false),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[92, 91, 84, 35])).
% 0.63/0.65 % SZS output end Proof
%------------------------------------------------------------------------------