TSTP Solution File: SWC051+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC051+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 11:54:55 EDT 2022
% Result : Theorem 0.20s 0.52s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC051+1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n016.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
% 0.19/0.34 % CPULimit : 300
% 0.19/0.34 % WCLimit : 300
% 0.19/0.34 % DateTime : Sat Sep 3 21:20:53 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.19/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.35 Usage: tptp [options] [-file:]file
% 0.19/0.35 -h, -? prints this message.
% 0.19/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.35 -m, -model generate model.
% 0.19/0.35 -p, -proof generate proof.
% 0.19/0.35 -c, -core generate unsat core of named formulas.
% 0.19/0.35 -st, -statistics display statistics.
% 0.19/0.35 -t:timeout set timeout (in second).
% 0.19/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.35 -<param>:<value> configuration parameter and value.
% 0.19/0.35 -o:<output-file> file to place output in.
% 0.20/0.52 % SZS status Theorem
% 0.20/0.52 % SZS output start Proof
% 0.20/0.52 tff(neq_type, type, (
% 0.20/0.52 neq: ( $i * $i ) > $o)).
% 0.20/0.52 tff(nil_type, type, (
% 0.20/0.52 nil: $i)).
% 0.20/0.52 tff(tptp_fun_W_49_type, type, (
% 0.20/0.52 tptp_fun_W_49: $i)).
% 0.20/0.52 tff(rearsegP_type, type, (
% 0.20/0.52 rearsegP: ( $i * $i ) > $o)).
% 0.20/0.52 tff(tptp_fun_X_50_type, type, (
% 0.20/0.52 tptp_fun_X_50: $i)).
% 0.20/0.52 tff(tptp_fun_V_48_type, type, (
% 0.20/0.52 tptp_fun_V_48: $i)).
% 0.20/0.52 tff(tptp_fun_U_47_type, type, (
% 0.20/0.52 tptp_fun_U_47: $i)).
% 0.20/0.52 tff(ssList_type, type, (
% 0.20/0.52 ssList: $i > $o)).
% 0.20/0.52 tff(1,plain,
% 0.20/0.52 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))) & (~((~(nil = W!49)) & (nil = X!50))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(V!48, Y) & rearsegP(U!47, Y))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))) & (~((~(nil = W!49)) & (nil = X!50))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(V!48, Y) & rearsegP(U!47, Y))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(2,plain,
% 0.20/0.52 ((ssList(V!48) & (ssList(W!49) & (U!47 = W!49) & (~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))) & (~((~(nil = W!49)) & (nil = X!50))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(V!48, Y) & rearsegP(U!47, Y))))) <=> (ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))) & (~((~(nil = W!49)) & (nil = X!50))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(V!48, Y) & rearsegP(U!47, Y))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(3,plain,
% 0.20/0.52 ((ssList(W!49) & ((U!47 = W!49) & (~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))) & (~((~(nil = W!49)) & (nil = X!50))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(V!48, Y) & rearsegP(U!47, Y))))) <=> (ssList(W!49) & (U!47 = W!49) & (~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))) & (~((~(nil = W!49)) & (nil = X!50))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(V!48, Y) & rearsegP(U!47, Y))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(4,plain,
% 0.20/0.52 (((~(~(U!47 = W!49))) & (~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(V!48, Y) & rearsegP(U!47, Y)))) <=> ((U!47 = W!49) & (~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))) & (~((~(nil = W!49)) & (nil = X!50))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(V!48, Y) & rearsegP(U!47, Y))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(5,plain,
% 0.20/0.52 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(6,plain,
% 0.20/0.52 (((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(V!48, Y) & rearsegP(U!47, Y))))) <=> (ssList(W!49) & ((U!47 = W!49) & (~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))) & (~((~(nil = W!49)) & (nil = X!50))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(V!48, Y) & rearsegP(U!47, Y)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[5, 4])).
% 0.20/0.52 tff(7,plain,
% 0.20/0.52 (((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(V!48, Y) & rearsegP(U!47, Y))))) <=> (ssList(W!49) & (U!47 = W!49) & (~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))) & (~((~(nil = W!49)) & (nil = X!50))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(V!48, Y) & rearsegP(U!47, Y))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[6, 3])).
% 0.20/0.52 tff(8,plain,
% 0.20/0.52 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(9,plain,
% 0.20/0.52 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(V!48, Y) & rearsegP(U!47, Y)))))) <=> (ssList(V!48) & (ssList(W!49) & (U!47 = W!49) & (~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))) & (~((~(nil = W!49)) & (nil = X!50))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(V!48, Y) & rearsegP(U!47, Y)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[8, 7])).
% 0.20/0.52 tff(10,plain,
% 0.20/0.52 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(V!48, Y) & rearsegP(U!47, Y)))))) <=> (ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))) & (~((~(nil = W!49)) & (nil = X!50))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(V!48, Y) & rearsegP(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))) & ((~(~(U!47 = W!49))) & (~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(V!48, Y) & rearsegP(U!47, Y))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))) & (~((~(nil = W!49)) & (nil = X!50))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(V!48, Y) & rearsegP(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))) & ((~(~(U!47 = W!49))) & (~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(V!48, Y) & rearsegP(U!47, Y))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))) & (~((~(nil = W!49)) & (nil = X!50))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(V!48, Y) & rearsegP(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] : ((~(U = W)) | (neq(X, nil) & ((~neq(W, nil)) | (~rearsegP(X, W)))) | ((~(nil = W)) & (nil = X)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & rearsegP(V, Y) & rearsegP(U, Y))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (neq(X, nil) & ((~neq(W, nil)) | (~rearsegP(X, W)))) | ((~(nil = W)) & (nil = X)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & rearsegP(V, Y) & rearsegP(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))) | (~neq(V, nil))) | ?[Y: $i] : (((ssList(Y) & neq(Y, nil)) & rearsegP(V, Y)) & rearsegP(U, Y))) | ((~(nil = W)) & (nil = X))) | (neq(X, nil) & ((~neq(W, nil)) | (~rearsegP(X, W)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (neq(X, nil) & ((~neq(W, nil)) | (~rearsegP(X, W)))) | ((~(nil = W)) & (nil = X)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & rearsegP(V, Y) & rearsegP(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))) | (~neq(V, nil))) | ?[Y: $i] : (((ssList(Y) & neq(Y, nil)) & rearsegP(V, Y)) & rearsegP(U, Y))) | ((~(nil = W)) & (nil = X))) | (neq(X, nil) & ((~neq(W, nil)) | (~rearsegP(X, W)))))))))), 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] : ((~(U = W)) | (neq(X, nil) & ((~neq(W, nil)) | (~rearsegP(X, W)))) | ((~(nil = W)) & (nil = X)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & rearsegP(V, Y) & rearsegP(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] : ((~(U = W)) | (neq(X, nil) & ((~neq(W, nil)) | (~rearsegP(X, W)))) | ((~(nil = W)) & (nil = X)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & rearsegP(V, Y) & rearsegP(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] : ((~(U = W)) | (neq(X, nil) & ((~neq(W, nil)) | (~rearsegP(X, W)))) | ((~(nil = W)) & (nil = X)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & rearsegP(V, Y) & rearsegP(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] : ((~(U = W)) | (neq(X, nil) & ((~neq(W, nil)) | (~rearsegP(X, W)))) | ((~(nil = W)) & (nil = X)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & rearsegP(V, Y) & rearsegP(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] : ((~(U = W)) | (neq(X, nil) & ((~neq(W, nil)) | (~rearsegP(X, W)))) | ((~(nil = W)) & (nil = X)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & rearsegP(V, Y) & rearsegP(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] : ((~(U = W)) | (neq(X, nil) & ((~neq(W, nil)) | (~rearsegP(X, W)))) | ((~(nil = W)) & (nil = X)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & rearsegP(V, Y) & rearsegP(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] : ((~(U = W)) | (neq(X, nil) & ((~neq(W, nil)) | (~rearsegP(X, W)))) | ((~(nil = W)) & (nil = X)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & rearsegP(V, Y) & rearsegP(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) & (U!47 = W!49) & (~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))) & (~((~(nil = W!49)) & (nil = X!50))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(V!48, Y) & rearsegP(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 (V!48 = X!50),
% 0.20/0.52 inference(and_elim,[status(thm)],[24])).
% 0.20/0.53 tff(26,plain,
% 0.20/0.53 (neq(V!48, nil) <=> neq(X!50, nil)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[25])).
% 0.20/0.53 tff(27,plain,
% 0.20/0.53 (neq(V!48, nil)),
% 0.20/0.53 inference(and_elim,[status(thm)],[24])).
% 0.20/0.53 tff(28,plain,
% 0.20/0.53 (neq(X!50, nil)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.53 tff(29,plain,
% 0.20/0.53 ((~(~((~neq(X!50, nil)) | (~((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))))) <=> ((~neq(X!50, nil)) | (~((~neq(W!49, nil)) | (~rearsegP(X!50, W!49)))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(30,plain,
% 0.20/0.53 ((neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49)))) <=> (~((~neq(X!50, nil)) | (~((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(31,plain,
% 0.20/0.53 ((~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))) <=> (~(~((~neq(X!50, nil)) | (~((~neq(W!49, nil)) | (~rearsegP(X!50, W!49)))))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[30])).
% 0.20/0.53 tff(32,plain,
% 0.20/0.53 ((~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))) <=> ((~neq(X!50, nil)) | (~((~neq(W!49, nil)) | (~rearsegP(X!50, W!49)))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[31, 29])).
% 0.20/0.53 tff(33,plain,
% 0.20/0.53 (~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))),
% 0.20/0.53 inference(and_elim,[status(thm)],[24])).
% 0.20/0.53 tff(34,plain,
% 0.20/0.53 ((~neq(X!50, nil)) | (~((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.53 tff(35,plain,
% 0.20/0.53 (~((~neq(W!49, nil)) | (~rearsegP(X!50, W!49)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[34, 28])).
% 0.20/0.53 tff(36,plain,
% 0.20/0.53 (((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))) | neq(W!49, nil)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(37,plain,
% 0.20/0.53 (neq(W!49, nil)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.20/0.53 tff(38,plain,
% 0.20/0.53 (rearsegP(V!48, W!49) <=> rearsegP(X!50, W!49)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[25])).
% 0.20/0.53 tff(39,plain,
% 0.20/0.53 (rearsegP(X!50, W!49) <=> rearsegP(V!48, W!49)),
% 0.20/0.53 inference(symmetry,[status(thm)],[38])).
% 0.20/0.53 tff(40,plain,
% 0.20/0.53 (((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))) | rearsegP(X!50, W!49)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(41,plain,
% 0.20/0.53 (rearsegP(X!50, W!49)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[40, 35])).
% 0.20/0.53 tff(42,plain,
% 0.20/0.53 (rearsegP(V!48, W!49)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[41, 39])).
% 0.20/0.53 tff(43,plain,
% 0.20/0.53 (U!47 = W!49),
% 0.20/0.53 inference(and_elim,[status(thm)],[24])).
% 0.20/0.53 tff(44,plain,
% 0.20/0.53 (W!49 = U!47),
% 0.20/0.53 inference(symmetry,[status(thm)],[43])).
% 0.20/0.53 tff(45,plain,
% 0.20/0.53 (rearsegP(W!49, W!49) <=> rearsegP(U!47, W!49)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[44])).
% 0.20/0.53 tff(46,plain,
% 0.20/0.53 (ssList(W!49)),
% 0.20/0.53 inference(and_elim,[status(thm)],[24])).
% 0.20/0.53 tff(47,plain,
% 0.20/0.53 (^[U: $i] : refl(((~ssList(U)) | rearsegP(U, U)) <=> ((~ssList(U)) | rearsegP(U, U)))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(48,plain,
% 0.20/0.53 (![U: $i] : ((~ssList(U)) | rearsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.53 tff(49,plain,
% 0.20/0.53 (![U: $i] : ((~ssList(U)) | rearsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(50,plain,
% 0.20/0.53 (^[U: $i] : rewrite((ssList(U) => rearsegP(U, U)) <=> ((~ssList(U)) | rearsegP(U, U)))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(51,plain,
% 0.20/0.53 (![U: $i] : (ssList(U) => rearsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.53 tff(52,axiom,(![U: $i] : (ssList(U) => rearsegP(U, U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax49')).
% 0.20/0.53 tff(53,plain,
% 0.20/0.53 (![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.53 tff(54,plain,
% 0.20/0.53 (![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.20/0.53 tff(55,plain,(
% 0.20/0.53 ![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 0.20/0.53 inference(skolemize,[status(sab)],[54])).
% 0.20/0.53 tff(56,plain,
% 0.20/0.53 (![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.20/0.53 tff(57,plain,
% 0.20/0.53 (((~![U: $i] : ((~ssList(U)) | rearsegP(U, U))) | ((~ssList(W!49)) | rearsegP(W!49, W!49))) <=> ((~![U: $i] : ((~ssList(U)) | rearsegP(U, U))) | (~ssList(W!49)) | rearsegP(W!49, W!49))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(58,plain,
% 0.20/0.53 ((~![U: $i] : ((~ssList(U)) | rearsegP(U, U))) | ((~ssList(W!49)) | rearsegP(W!49, W!49))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(59,plain,
% 0.20/0.53 ((~![U: $i] : ((~ssList(U)) | rearsegP(U, U))) | (~ssList(W!49)) | rearsegP(W!49, W!49)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.53 tff(60,plain,
% 0.20/0.53 (rearsegP(W!49, W!49)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[59, 56, 46])).
% 0.20/0.53 tff(61,plain,
% 0.20/0.53 (rearsegP(U!47, W!49)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[60, 45])).
% 0.20/0.53 tff(62,plain,
% 0.20/0.53 (^[Y: $i] : refl(((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(V!48, Y)) | (~rearsegP(U!47, Y))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(V!48, Y)) | (~rearsegP(U!47, Y))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(63,plain,
% 0.20/0.53 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(V!48, Y)) | (~rearsegP(U!47, Y))) <=> ![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(V!48, Y)) | (~rearsegP(U!47, Y)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[62])).
% 0.20/0.53 tff(64,plain,
% 0.20/0.53 (^[Y: $i] : trans(monotonicity(rewrite((ssList(Y) & neq(Y, nil) & rearsegP(V!48, Y) & rearsegP(U!47, Y)) <=> (~((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(V!48, Y)) | (~rearsegP(U!47, Y))))), ((~(ssList(Y) & neq(Y, nil) & rearsegP(V!48, Y) & rearsegP(U!47, Y))) <=> (~(~((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(V!48, Y)) | (~rearsegP(U!47, Y))))))), rewrite((~(~((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(V!48, Y)) | (~rearsegP(U!47, Y))))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(V!48, Y)) | (~rearsegP(U!47, Y)))), ((~(ssList(Y) & neq(Y, nil) & rearsegP(V!48, Y) & rearsegP(U!47, Y))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(V!48, Y)) | (~rearsegP(U!47, Y)))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(65,plain,
% 0.20/0.53 (![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(V!48, Y) & rearsegP(U!47, Y))) <=> ![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(V!48, Y)) | (~rearsegP(U!47, Y)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.53 tff(66,plain,
% 0.20/0.53 (![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(V!48, Y) & rearsegP(U!47, Y)))),
% 0.20/0.53 inference(and_elim,[status(thm)],[24])).
% 0.20/0.53 tff(67,plain,
% 0.20/0.53 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(V!48, Y)) | (~rearsegP(U!47, Y)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.53 tff(68,plain,
% 0.20/0.53 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(V!48, Y)) | (~rearsegP(U!47, Y)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.20/0.53 tff(69,plain,
% 0.20/0.53 (((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(V!48, Y)) | (~rearsegP(U!47, Y)))) | ((~ssList(W!49)) | (~neq(W!49, nil)) | (~rearsegP(U!47, W!49)) | (~rearsegP(V!48, W!49)))) <=> ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(V!48, Y)) | (~rearsegP(U!47, Y)))) | (~ssList(W!49)) | (~neq(W!49, nil)) | (~rearsegP(U!47, W!49)) | (~rearsegP(V!48, W!49)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(70,plain,
% 0.20/0.53 (((~ssList(W!49)) | (~neq(W!49, nil)) | (~rearsegP(V!48, W!49)) | (~rearsegP(U!47, W!49))) <=> ((~ssList(W!49)) | (~neq(W!49, nil)) | (~rearsegP(U!47, W!49)) | (~rearsegP(V!48, W!49)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(71,plain,
% 0.20/0.53 (((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(V!48, Y)) | (~rearsegP(U!47, Y)))) | ((~ssList(W!49)) | (~neq(W!49, nil)) | (~rearsegP(V!48, W!49)) | (~rearsegP(U!47, W!49)))) <=> ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(V!48, Y)) | (~rearsegP(U!47, Y)))) | ((~ssList(W!49)) | (~neq(W!49, nil)) | (~rearsegP(U!47, W!49)) | (~rearsegP(V!48, W!49))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[70])).
% 0.20/0.53 tff(72,plain,
% 0.20/0.53 (((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(V!48, Y)) | (~rearsegP(U!47, Y)))) | ((~ssList(W!49)) | (~neq(W!49, nil)) | (~rearsegP(V!48, W!49)) | (~rearsegP(U!47, W!49)))) <=> ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(V!48, Y)) | (~rearsegP(U!47, Y)))) | (~ssList(W!49)) | (~neq(W!49, nil)) | (~rearsegP(U!47, W!49)) | (~rearsegP(V!48, W!49)))),
% 0.20/0.54 inference(transitivity,[status(thm)],[71, 69])).
% 0.20/0.54 tff(73,plain,
% 0.20/0.54 ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(V!48, Y)) | (~rearsegP(U!47, Y)))) | ((~ssList(W!49)) | (~neq(W!49, nil)) | (~rearsegP(V!48, W!49)) | (~rearsegP(U!47, W!49)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(74,plain,
% 0.20/0.54 ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(V!48, Y)) | (~rearsegP(U!47, Y)))) | (~ssList(W!49)) | (~neq(W!49, nil)) | (~rearsegP(U!47, W!49)) | (~rearsegP(V!48, W!49))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.54 tff(75,plain,
% 0.20/0.54 ((~neq(W!49, nil)) | (~rearsegP(U!47, W!49)) | (~rearsegP(V!48, W!49))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[74, 46, 68])).
% 0.20/0.54 tff(76,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[75, 61, 42, 37])).
% 0.20/0.54 % SZS output end Proof
%------------------------------------------------------------------------------