TSTP Solution File: SWC019+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC019+1 : TPTP v8.1.0. Released v2.4.0.
% 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 : Tue Sep 20 11:54:41 EDT 2022
% Result : Theorem 0.20s 0.51s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWC019+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 20:45:29 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33 Usage: tptp [options] [-file:]file
% 0.13/0.33 -h, -? prints this message.
% 0.13/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.33 -m, -model generate model.
% 0.13/0.33 -p, -proof generate proof.
% 0.13/0.33 -c, -core generate unsat core of named formulas.
% 0.13/0.33 -st, -statistics display statistics.
% 0.13/0.33 -t:timeout set timeout (in second).
% 0.13/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33 -<param>:<value> configuration parameter and value.
% 0.13/0.33 -o:<output-file> file to place output in.
% 0.20/0.51 % SZS status Theorem
% 0.20/0.51 % SZS output start Proof
% 0.20/0.51 tff(tptp_fun_U_47_type, type, (
% 0.20/0.51 tptp_fun_U_47: $i)).
% 0.20/0.51 tff(nil_type, type, (
% 0.20/0.51 nil: $i)).
% 0.20/0.51 tff(tptp_fun_W_49_type, type, (
% 0.20/0.51 tptp_fun_W_49: $i)).
% 0.20/0.51 tff(frontsegP_type, type, (
% 0.20/0.51 frontsegP: ( $i * $i ) > $o)).
% 0.20/0.51 tff(tptp_fun_V_48_type, type, (
% 0.20/0.51 tptp_fun_V_48: $i)).
% 0.20/0.51 tff(neq_type, type, (
% 0.20/0.51 neq: ( $i * $i ) > $o)).
% 0.20/0.51 tff(ssList_type, type, (
% 0.20/0.51 ssList: $i > $o)).
% 0.20/0.51 tff(tptp_fun_X_50_type, type, (
% 0.20/0.51 tptp_fun_X_50: $i)).
% 0.20/0.51 tff(1,plain,
% 0.20/0.51 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (X!50 = W!49) & (U!47 = W!49) & (~((nil = V!48) & (nil = U!47))) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (X!50 = W!49) & (U!47 = W!49) & (~((nil = V!48) & (nil = U!47))) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(2,plain,
% 0.20/0.51 ((ssList(V!48) & (ssList(W!49) & (X!50 = W!49) & (U!47 = W!49) & (~((nil = V!48) & (nil = U!47))) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))))) <=> (ssList(V!48) & ssList(W!49) & (X!50 = W!49) & (U!47 = W!49) & (~((nil = V!48) & (nil = U!47))) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(3,plain,
% 0.20/0.51 ((ssList(W!49) & ((X!50 = W!49) & (U!47 = W!49) & (~((nil = V!48) & (nil = U!47))) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))))) <=> (ssList(W!49) & (X!50 = W!49) & (U!47 = W!49) & (~((nil = V!48) & (nil = U!47))) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(4,plain,
% 0.20/0.51 (((~(~(X!50 = W!49))) & (~(~(U!47 = W!49))) & (~((nil = V!48) & (nil = U!47))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y)))) <=> ((X!50 = W!49) & (U!47 = W!49) & (~((nil = V!48) & (nil = U!47))) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(5,plain,
% 0.20/0.51 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(6,plain,
% 0.20/0.51 (((~(~ssList(W!49))) & ((~(~(X!50 = W!49))) & (~(~(U!47 = W!49))) & (~((nil = V!48) & (nil = U!47))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))))) <=> (ssList(W!49) & ((X!50 = W!49) & (U!47 = W!49) & (~((nil = V!48) & (nil = U!47))) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y)))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[5, 4])).
% 0.20/0.51 tff(7,plain,
% 0.20/0.51 (((~(~ssList(W!49))) & ((~(~(X!50 = W!49))) & (~(~(U!47 = W!49))) & (~((nil = V!48) & (nil = U!47))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))))) <=> (ssList(W!49) & (X!50 = W!49) & (U!47 = W!49) & (~((nil = V!48) & (nil = U!47))) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[6, 3])).
% 0.20/0.51 tff(8,plain,
% 0.20/0.51 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(9,plain,
% 0.20/0.51 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(X!50 = W!49))) & (~(~(U!47 = W!49))) & (~((nil = V!48) & (nil = U!47))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y)))))) <=> (ssList(V!48) & (ssList(W!49) & (X!50 = W!49) & (U!47 = W!49) & (~((nil = V!48) & (nil = U!47))) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y)))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[8, 7])).
% 0.20/0.52 tff(10,plain,
% 0.20/0.52 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(X!50 = W!49))) & (~(~(U!47 = W!49))) & (~((nil = V!48) & (nil = U!47))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y)))))) <=> (ssList(V!48) & ssList(W!49) & (X!50 = W!49) & (U!47 = W!49) & (~((nil = V!48) & (nil = U!47))) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[9, 2])).
% 0.20/0.52 tff(11,plain,
% 0.20/0.52 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(12,plain,
% 0.20/0.52 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(X!50 = W!49))) & (~(~(U!47 = W!49))) & (~((nil = V!48) & (nil = U!47))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (X!50 = W!49) & (U!47 = W!49) & (~((nil = V!48) & (nil = U!47))) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[11, 10])).
% 0.20/0.52 tff(13,plain,
% 0.20/0.52 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(X!50 = W!49))) & (~(~(U!47 = W!49))) & (~((nil = V!48) & (nil = U!47))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (X!50 = W!49) & (U!47 = W!49) & (~((nil = V!48) & (nil = U!47))) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[12, 1])).
% 0.20/0.52 tff(14,plain,
% 0.20/0.52 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(X = W)) | (~(U = W)) | ((nil = V) & (nil = U)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(X = W)) | (~(U = W)) | ((nil = V) & (nil = U)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y)))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(15,plain,
% 0.20/0.52 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | (~(X = W))) | ?[Y: $i] : (((ssList(Y) & neq(Y, nil)) & frontsegP(V, Y)) & frontsegP(U, Y))) | ((nil = V) & (nil = U)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(X = W)) | (~(U = W)) | ((nil = V) & (nil = U)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y)))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(16,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | (~(X = W))) | ?[Y: $i] : (((ssList(Y) & neq(Y, nil)) & frontsegP(V, Y)) & frontsegP(U, Y))) | ((nil = V) & (nil = U)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.20/0.52 tff(17,plain,
% 0.20/0.52 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(X = W)) | (~(U = W)) | ((nil = V) & (nil = U)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.52 tff(18,plain,
% 0.20/0.52 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(X = W)) | (~(U = W)) | ((nil = V) & (nil = U)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.20/0.52 tff(19,plain,
% 0.20/0.52 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(X = W)) | (~(U = W)) | ((nil = V) & (nil = U)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.52 tff(20,plain,
% 0.20/0.52 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(X = W)) | (~(U = W)) | ((nil = V) & (nil = U)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.20/0.52 tff(21,plain,
% 0.20/0.52 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(X = W)) | (~(U = W)) | ((nil = V) & (nil = U)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.20/0.52 tff(22,plain,
% 0.20/0.52 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(X = W)) | (~(U = W)) | ((nil = V) & (nil = U)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.20/0.52 tff(23,plain,
% 0.20/0.52 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(X = W)) | (~(U = W)) | ((nil = V) & (nil = U)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[22, 14])).
% 0.20/0.52 tff(24,plain,
% 0.20/0.52 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (X!50 = W!49) & (U!47 = W!49) & (~((nil = V!48) & (nil = U!47))) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.20/0.52 tff(25,plain,
% 0.20/0.52 (U!47 = W!49),
% 0.20/0.52 inference(and_elim,[status(thm)],[24])).
% 0.20/0.52 tff(26,plain,
% 0.20/0.52 (W!49 = U!47),
% 0.20/0.52 inference(symmetry,[status(thm)],[25])).
% 0.20/0.52 tff(27,plain,
% 0.20/0.52 (ssList(W!49)),
% 0.20/0.52 inference(and_elim,[status(thm)],[24])).
% 0.20/0.52 tff(28,plain,
% 0.20/0.52 (^[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))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(29,plain,
% 0.20/0.52 (![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)))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.52 tff(30,plain,
% 0.20/0.52 (^[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))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(31,plain,
% 0.20/0.52 (![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)))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.52 tff(32,plain,
% 0.20/0.52 (![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)))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[31, 29])).
% 0.20/0.52 tff(33,plain,
% 0.20/0.52 (![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)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(34,plain,
% 0.20/0.52 (^[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)))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(35,plain,
% 0.20/0.52 (![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)))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.52 tff(36,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax15')).
% 0.20/0.52 tff(37,plain,
% 0.20/0.52 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.52 tff(38,plain,
% 0.20/0.52 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.20/0.52 tff(39,plain,(
% 0.20/0.52 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.20/0.52 inference(skolemize,[status(sab)],[38])).
% 0.20/0.52 tff(40,plain,
% 0.20/0.52 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.20/0.52 tff(41,plain,
% 0.20/0.52 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(42,plain,
% 0.20/0.52 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V)))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(43,plain,
% 0.20/0.52 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.52 tff(44,plain,
% 0.20/0.52 (![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[43, 40, 27])).
% 0.20/0.52 tff(45,plain,
% 0.20/0.52 (ssList(nil) <=> ssList(nil)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(46,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.20/0.52 tff(47,plain,
% 0.20/0.52 (ssList(nil)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.52 tff(48,plain,
% 0.20/0.52 (((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | ((~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | (~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(49,plain,
% 0.20/0.52 ((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | ((~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(50,plain,
% 0.20/0.52 ((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | (~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.52 tff(51,plain,
% 0.20/0.52 (neq(W!49, nil) <=> (~(W!49 = nil))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[50, 47, 44])).
% 0.20/0.52 tff(52,plain,
% 0.20/0.52 (V!48 = X!50),
% 0.20/0.52 inference(and_elim,[status(thm)],[24])).
% 0.20/0.52 tff(53,plain,
% 0.20/0.52 (X!50 = V!48),
% 0.20/0.52 inference(symmetry,[status(thm)],[52])).
% 0.20/0.52 tff(54,plain,
% 0.20/0.52 (X!50 = W!49),
% 0.20/0.52 inference(and_elim,[status(thm)],[24])).
% 0.20/0.52 tff(55,plain,
% 0.20/0.52 (W!49 = X!50),
% 0.20/0.52 inference(symmetry,[status(thm)],[54])).
% 0.20/0.52 tff(56,plain,
% 0.20/0.52 (U!47 = V!48),
% 0.20/0.52 inference(transitivity,[status(thm)],[25, 55, 53])).
% 0.20/0.52 tff(57,plain,
% 0.20/0.52 (frontsegP(U!47, W!49) <=> frontsegP(V!48, W!49)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[56])).
% 0.20/0.52 tff(58,plain,
% 0.20/0.52 (frontsegP(V!48, W!49) <=> frontsegP(U!47, W!49)),
% 0.20/0.52 inference(symmetry,[status(thm)],[57])).
% 0.20/0.52 tff(59,plain,
% 0.20/0.52 (W!49 = V!48),
% 0.20/0.52 inference(transitivity,[status(thm)],[55, 53])).
% 0.20/0.52 tff(60,plain,
% 0.20/0.52 (frontsegP(W!49, W!49) <=> frontsegP(V!48, W!49)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[59])).
% 0.20/0.52 tff(61,plain,
% 0.20/0.52 (frontsegP(W!49, W!49) <=> frontsegP(U!47, W!49)),
% 0.20/0.52 inference(transitivity,[status(thm)],[60, 58])).
% 0.20/0.52 tff(62,plain,
% 0.20/0.52 (^[U: $i] : refl(((~ssList(U)) | frontsegP(U, U)) <=> ((~ssList(U)) | frontsegP(U, U)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(63,plain,
% 0.20/0.52 (![U: $i] : ((~ssList(U)) | frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[62])).
% 0.20/0.52 tff(64,plain,
% 0.20/0.52 (![U: $i] : ((~ssList(U)) | frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(65,plain,
% 0.20/0.52 (^[U: $i] : rewrite((ssList(U) => frontsegP(U, U)) <=> ((~ssList(U)) | frontsegP(U, U)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(66,plain,
% 0.20/0.52 (![U: $i] : (ssList(U) => frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[65])).
% 0.20/0.52 tff(67,axiom,(![U: $i] : (ssList(U) => frontsegP(U, U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax42')).
% 0.20/0.52 tff(68,plain,
% 0.20/0.52 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.52 tff(69,plain,
% 0.20/0.52 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.20/0.52 tff(70,plain,(
% 0.20/0.52 ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.20/0.52 inference(skolemize,[status(sab)],[69])).
% 0.20/0.52 tff(71,plain,
% 0.20/0.52 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.20/0.52 tff(72,plain,
% 0.20/0.52 (((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | ((~ssList(W!49)) | frontsegP(W!49, W!49))) <=> ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | (~ssList(W!49)) | frontsegP(W!49, W!49))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(73,plain,
% 0.20/0.52 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | ((~ssList(W!49)) | frontsegP(W!49, W!49))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(74,plain,
% 0.20/0.52 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | (~ssList(W!49)) | frontsegP(W!49, W!49)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.52 tff(75,plain,
% 0.20/0.52 (frontsegP(W!49, W!49)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[74, 71, 27])).
% 0.20/0.52 tff(76,plain,
% 0.20/0.52 (frontsegP(U!47, W!49)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[75, 61])).
% 0.20/0.52 tff(77,plain,
% 0.20/0.52 (frontsegP(V!48, W!49)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[75, 60])).
% 0.20/0.52 tff(78,plain,
% 0.20/0.52 (^[Y: $i] : refl(((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(79,plain,
% 0.20/0.52 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y))) <=> ![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[78])).
% 0.20/0.52 tff(80,plain,
% 0.20/0.52 (^[Y: $i] : trans(monotonicity(rewrite((ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y)) <=> (~((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y))))), ((~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) <=> (~(~((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y))))))), rewrite((~(~((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y))))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))), ((~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(81,plain,
% 0.20/0.52 (![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) <=> ![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.52 tff(82,plain,
% 0.20/0.52 (![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y)))),
% 0.20/0.52 inference(and_elim,[status(thm)],[24])).
% 0.20/0.52 tff(83,plain,
% 0.20/0.52 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.52 tff(84,plain,
% 0.20/0.52 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.20/0.52 tff(85,plain,
% 0.20/0.52 (((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))) | ((~ssList(W!49)) | (~frontsegP(V!48, W!49)) | (~neq(W!49, nil)) | (~frontsegP(U!47, W!49)))) <=> ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))) | (~ssList(W!49)) | (~frontsegP(V!48, W!49)) | (~neq(W!49, nil)) | (~frontsegP(U!47, W!49)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(86,plain,
% 0.20/0.52 (((~ssList(W!49)) | (~neq(W!49, nil)) | (~frontsegP(V!48, W!49)) | (~frontsegP(U!47, W!49))) <=> ((~ssList(W!49)) | (~frontsegP(V!48, W!49)) | (~neq(W!49, nil)) | (~frontsegP(U!47, W!49)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(87,plain,
% 0.20/0.52 (((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))) | ((~ssList(W!49)) | (~neq(W!49, nil)) | (~frontsegP(V!48, W!49)) | (~frontsegP(U!47, W!49)))) <=> ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))) | ((~ssList(W!49)) | (~frontsegP(V!48, W!49)) | (~neq(W!49, nil)) | (~frontsegP(U!47, W!49))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[86])).
% 0.20/0.52 tff(88,plain,
% 0.20/0.52 (((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))) | ((~ssList(W!49)) | (~neq(W!49, nil)) | (~frontsegP(V!48, W!49)) | (~frontsegP(U!47, W!49)))) <=> ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))) | (~ssList(W!49)) | (~frontsegP(V!48, W!49)) | (~neq(W!49, nil)) | (~frontsegP(U!47, W!49)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[87, 85])).
% 0.20/0.52 tff(89,plain,
% 0.20/0.52 ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))) | ((~ssList(W!49)) | (~neq(W!49, nil)) | (~frontsegP(V!48, W!49)) | (~frontsegP(U!47, W!49)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(90,plain,
% 0.20/0.52 ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))) | (~ssList(W!49)) | (~frontsegP(V!48, W!49)) | (~neq(W!49, nil)) | (~frontsegP(U!47, W!49))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.52 tff(91,plain,
% 0.20/0.52 ((~frontsegP(V!48, W!49)) | (~neq(W!49, nil)) | (~frontsegP(U!47, W!49))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[90, 27, 84])).
% 0.20/0.52 tff(92,plain,
% 0.20/0.52 (~neq(W!49, nil)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[91, 77, 76])).
% 0.20/0.52 tff(93,plain,
% 0.20/0.52 ((~(neq(W!49, nil) <=> (~(W!49 = nil)))) | neq(W!49, nil) | (W!49 = nil)),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(94,plain,
% 0.20/0.52 (W!49 = nil),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[93, 92, 51])).
% 0.20/0.52 tff(95,plain,
% 0.20/0.52 (nil = W!49),
% 0.20/0.52 inference(symmetry,[status(thm)],[94])).
% 0.20/0.52 tff(96,plain,
% 0.20/0.52 (nil = U!47),
% 0.20/0.52 inference(transitivity,[status(thm)],[95, 26])).
% 0.20/0.52 tff(97,plain,
% 0.20/0.52 (V!48 = U!47),
% 0.20/0.52 inference(transitivity,[status(thm)],[52, 54, 26])).
% 0.20/0.52 tff(98,plain,
% 0.20/0.52 ((nil = V!48) <=> (nil = U!47)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[97])).
% 0.20/0.52 tff(99,plain,
% 0.20/0.52 ((nil = U!47) <=> (nil = V!48)),
% 0.20/0.52 inference(symmetry,[status(thm)],[98])).
% 0.20/0.52 tff(100,plain,
% 0.20/0.52 (nil = V!48),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[96, 99])).
% 0.20/0.52 tff(101,plain,
% 0.20/0.52 ((~(~((~(nil = V!48)) | (~(nil = U!47))))) <=> ((~(nil = V!48)) | (~(nil = U!47)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(102,plain,
% 0.20/0.52 (((nil = V!48) & (nil = U!47)) <=> (~((~(nil = V!48)) | (~(nil = U!47))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(103,plain,
% 0.20/0.52 ((~((nil = V!48) & (nil = U!47))) <=> (~(~((~(nil = V!48)) | (~(nil = U!47)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[102])).
% 0.20/0.52 tff(104,plain,
% 0.20/0.52 ((~((nil = V!48) & (nil = U!47))) <=> ((~(nil = V!48)) | (~(nil = U!47)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[103, 101])).
% 0.20/0.52 tff(105,plain,
% 0.20/0.52 (~((nil = V!48) & (nil = U!47))),
% 0.20/0.52 inference(and_elim,[status(thm)],[24])).
% 0.20/0.52 tff(106,plain,
% 0.20/0.52 ((~(nil = V!48)) | (~(nil = U!47))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.53 tff(107,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[106, 100, 96])).
% 0.20/0.53 % SZS output end Proof
%------------------------------------------------------------------------------