TSTP Solution File: SWC082+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC082+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 11:55:07 EDT 2022
% Result : Theorem 1.02s 0.90s
% Output : Proof 1.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SWC082+1 : TPTP v8.1.0. Released v2.4.0.
% 0.13/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.35 % Computer : n016.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat Sep 3 21:43:22 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.36 Usage: tptp [options] [-file:]file
% 0.15/0.36 -h, -? prints this message.
% 0.15/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.36 -m, -model generate model.
% 0.15/0.36 -p, -proof generate proof.
% 0.15/0.36 -c, -core generate unsat core of named formulas.
% 0.15/0.36 -st, -statistics display statistics.
% 0.15/0.36 -t:timeout set timeout (in second).
% 0.15/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.36 -<param>:<value> configuration parameter and value.
% 0.15/0.36 -o:<output-file> file to place output in.
% 1.02/0.90 % SZS status Theorem
% 1.02/0.90 % SZS output start Proof
% 1.02/0.90 tff(segmentP_type, type, (
% 1.02/0.90 segmentP: ( $i * $i ) > $o)).
% 1.02/0.90 tff(tptp_fun_Z_51_type, type, (
% 1.02/0.90 tptp_fun_Z_51: $i)).
% 1.02/0.90 tff(tptp_fun_V_48_type, type, (
% 1.02/0.90 tptp_fun_V_48: $i)).
% 1.02/0.90 tff(tptp_fun_X_50_type, type, (
% 1.02/0.90 tptp_fun_X_50: $i)).
% 1.02/0.90 tff(neq_type, type, (
% 1.02/0.90 neq: ( $i * $i ) > $o)).
% 1.02/0.90 tff(nil_type, type, (
% 1.02/0.90 nil: $i)).
% 1.02/0.90 tff(ssList_type, type, (
% 1.02/0.90 ssList: $i > $o)).
% 1.02/0.90 tff(tptp_fun_W_49_type, type, (
% 1.02/0.90 tptp_fun_W_49: $i)).
% 1.02/0.90 tff(tptp_fun_U_47_type, type, (
% 1.02/0.90 tptp_fun_U_47: $i)).
% 1.02/0.90 tff(1,plain,
% 1.02/0.90 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (U!47 = 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) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~neq(X!50, nil))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (U!47 = 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) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~neq(X!50, nil))))),
% 1.02/0.90 inference(rewrite,[status(thm)],[])).
% 1.02/0.90 tff(2,plain,
% 1.02/0.90 ((ssList(V!48) & (ssList(W!49) & (U!47 = 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) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~neq(X!50, nil))))) <=> (ssList(V!48) & ssList(W!49) & (U!47 = 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) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~neq(X!50, nil))))),
% 1.02/0.90 inference(rewrite,[status(thm)],[])).
% 1.02/0.90 tff(3,plain,
% 1.02/0.90 ((ssList(W!49) & ((U!47 = 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) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~neq(X!50, nil))))) <=> (ssList(W!49) & (U!47 = 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) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~neq(X!50, nil))))),
% 1.02/0.90 inference(rewrite,[status(thm)],[])).
% 1.02/0.90 tff(4,plain,
% 1.02/0.90 (((~(~(U!47 = 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) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~neq(X!50, nil)))) <=> ((U!47 = 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) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~neq(X!50, nil))))),
% 1.02/0.90 inference(rewrite,[status(thm)],[])).
% 1.02/0.90 tff(5,plain,
% 1.02/0.90 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 1.02/0.90 inference(rewrite,[status(thm)],[])).
% 1.02/0.90 tff(6,plain,
% 1.02/0.90 (((~(~ssList(W!49))) & ((~(~(U!47 = 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) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~neq(X!50, nil))))) <=> (ssList(W!49) & ((U!47 = 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) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~neq(X!50, nil)))))),
% 1.02/0.90 inference(monotonicity,[status(thm)],[5, 4])).
% 1.02/0.90 tff(7,plain,
% 1.02/0.90 (((~(~ssList(W!49))) & ((~(~(U!47 = 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) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~neq(X!50, nil))))) <=> (ssList(W!49) & (U!47 = 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) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~neq(X!50, nil))))),
% 1.02/0.90 inference(transitivity,[status(thm)],[6, 3])).
% 1.02/0.90 tff(8,plain,
% 1.02/0.90 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 1.02/0.90 inference(rewrite,[status(thm)],[])).
% 1.02/0.90 tff(9,plain,
% 1.02/0.90 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(U!47 = 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) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~neq(X!50, nil)))))) <=> (ssList(V!48) & (ssList(W!49) & (U!47 = 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) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~neq(X!50, nil)))))),
% 1.02/0.90 inference(monotonicity,[status(thm)],[8, 7])).
% 1.02/0.90 tff(10,plain,
% 1.02/0.90 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(U!47 = 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) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~neq(X!50, nil)))))) <=> (ssList(V!48) & ssList(W!49) & (U!47 = 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) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~neq(X!50, nil))))),
% 1.02/0.90 inference(transitivity,[status(thm)],[9, 2])).
% 1.02/0.90 tff(11,plain,
% 1.02/0.90 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 1.02/0.90 inference(rewrite,[status(thm)],[])).
% 1.02/0.90 tff(12,plain,
% 1.02/0.90 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(U!47 = 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) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~neq(X!50, nil))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (U!47 = 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) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~neq(X!50, nil)))))),
% 1.02/0.90 inference(monotonicity,[status(thm)],[11, 10])).
% 1.02/0.90 tff(13,plain,
% 1.02/0.90 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(U!47 = 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) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~neq(X!50, nil))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (U!47 = 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) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~neq(X!50, nil))))),
% 1.02/0.90 inference(transitivity,[status(thm)],[12, 1])).
% 1.02/0.90 tff(14,plain,
% 1.02/0.90 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | ((~(nil = W)) & (nil = X)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y)) | (![Z: $i] : ((~segmentP(W, Z)) | (~segmentP(X, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & neq(X, nil))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | ((~(nil = W)) & (nil = X)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y)) | (![Z: $i] : ((~segmentP(W, Z)) | (~segmentP(X, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & neq(X, nil)))))))),
% 1.02/0.90 inference(rewrite,[status(thm)],[])).
% 1.02/0.90 tff(15,plain,
% 1.02/0.90 ((~![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)) & segmentP(V, Y)) & segmentP(U, Y))) | ((~(nil = W)) & (nil = X))) | (![Z: $i] : (ssList(Z) => (((~neq(Z, nil)) | (~segmentP(X, Z))) | (~segmentP(W, Z)))) & neq(X, nil)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | ((~(nil = W)) & (nil = X)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y)) | (![Z: $i] : ((~segmentP(W, Z)) | (~segmentP(X, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & neq(X, nil)))))))),
% 1.02/0.90 inference(rewrite,[status(thm)],[])).
% 1.02/0.90 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)) & segmentP(V, Y)) & segmentP(U, Y))) | ((~(nil = W)) & (nil = X))) | (![Z: $i] : (ssList(Z) => (((~neq(Z, nil)) | (~segmentP(X, Z))) | (~segmentP(W, Z)))) & neq(X, nil)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 1.02/0.90 tff(17,plain,
% 1.02/0.90 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | ((~(nil = W)) & (nil = X)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y)) | (![Z: $i] : ((~segmentP(W, Z)) | (~segmentP(X, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & neq(X, nil))))))),
% 1.02/0.90 inference(modus_ponens,[status(thm)],[16, 15])).
% 1.02/0.90 tff(18,plain,
% 1.02/0.90 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | ((~(nil = W)) & (nil = X)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y)) | (![Z: $i] : ((~segmentP(W, Z)) | (~segmentP(X, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & neq(X, nil))))))),
% 1.02/0.90 inference(modus_ponens,[status(thm)],[17, 14])).
% 1.02/0.90 tff(19,plain,
% 1.02/0.90 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | ((~(nil = W)) & (nil = X)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y)) | (![Z: $i] : ((~segmentP(W, Z)) | (~segmentP(X, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & neq(X, nil))))))),
% 1.02/0.90 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.02/0.90 tff(20,plain,
% 1.02/0.90 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | ((~(nil = W)) & (nil = X)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y)) | (![Z: $i] : ((~segmentP(W, Z)) | (~segmentP(X, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & neq(X, nil))))))),
% 1.02/0.90 inference(modus_ponens,[status(thm)],[19, 14])).
% 1.02/0.90 tff(21,plain,
% 1.02/0.90 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | ((~(nil = W)) & (nil = X)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y)) | (![Z: $i] : ((~segmentP(W, Z)) | (~segmentP(X, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & neq(X, nil))))))),
% 1.02/0.90 inference(modus_ponens,[status(thm)],[20, 14])).
% 1.02/0.90 tff(22,plain,
% 1.02/0.90 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | ((~(nil = W)) & (nil = X)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y)) | (![Z: $i] : ((~segmentP(W, Z)) | (~segmentP(X, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & neq(X, nil))))))),
% 1.02/0.90 inference(modus_ponens,[status(thm)],[21, 14])).
% 1.02/0.90 tff(23,plain,
% 1.02/0.90 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | ((~(nil = W)) & (nil = X)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y)) | (![Z: $i] : ((~segmentP(W, Z)) | (~segmentP(X, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & neq(X, nil))))))),
% 1.02/0.90 inference(modus_ponens,[status(thm)],[22, 14])).
% 1.02/0.90 tff(24,plain,
% 1.02/0.90 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (U!47 = 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) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~neq(X!50, nil)))),
% 1.02/0.90 inference(modus_ponens,[status(thm)],[23, 13])).
% 1.02/0.90 tff(25,plain,
% 1.02/0.90 (V!48 = X!50),
% 1.02/0.90 inference(and_elim,[status(thm)],[24])).
% 1.02/0.90 tff(26,plain,
% 1.02/0.90 (segmentP(V!48, Z!51) <=> segmentP(X!50, Z!51)),
% 1.02/0.90 inference(monotonicity,[status(thm)],[25])).
% 1.02/0.90 tff(27,plain,
% 1.02/0.90 (segmentP(X!50, Z!51) <=> segmentP(V!48, Z!51)),
% 1.02/0.90 inference(symmetry,[status(thm)],[26])).
% 1.02/0.90 tff(28,plain,
% 1.02/0.90 (neq(V!48, nil) <=> neq(X!50, nil)),
% 1.02/0.90 inference(monotonicity,[status(thm)],[25])).
% 1.02/0.90 tff(29,plain,
% 1.02/0.90 (neq(V!48, nil)),
% 1.02/0.90 inference(and_elim,[status(thm)],[24])).
% 1.02/0.90 tff(30,plain,
% 1.02/0.90 (neq(X!50, nil)),
% 1.02/0.90 inference(modus_ponens,[status(thm)],[29, 28])).
% 1.02/0.90 tff(31,plain,
% 1.02/0.90 ((~((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~neq(X!50, nil))),
% 1.02/0.90 inference(and_elim,[status(thm)],[24])).
% 1.02/0.90 tff(32,plain,
% 1.02/0.90 (~((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))),
% 1.02/0.90 inference(unit_resolution,[status(thm)],[31, 30])).
% 1.02/0.90 tff(33,plain,
% 1.02/0.90 (((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51))) | segmentP(X!50, Z!51)),
% 1.02/0.90 inference(tautology,[status(thm)],[])).
% 1.02/0.90 tff(34,plain,
% 1.02/0.90 (segmentP(X!50, Z!51)),
% 1.02/0.90 inference(unit_resolution,[status(thm)],[33, 32])).
% 1.02/0.90 tff(35,plain,
% 1.02/0.90 (segmentP(V!48, Z!51)),
% 1.02/0.90 inference(modus_ponens,[status(thm)],[34, 27])).
% 1.02/0.90 tff(36,plain,
% 1.02/0.90 (U!47 = W!49),
% 1.02/0.90 inference(and_elim,[status(thm)],[24])).
% 1.02/0.90 tff(37,plain,
% 1.02/0.90 (segmentP(U!47, Z!51) <=> segmentP(W!49, Z!51)),
% 1.02/0.90 inference(monotonicity,[status(thm)],[36])).
% 1.02/0.90 tff(38,plain,
% 1.02/0.90 (segmentP(W!49, Z!51) <=> segmentP(U!47, Z!51)),
% 1.02/0.90 inference(symmetry,[status(thm)],[37])).
% 1.02/0.90 tff(39,plain,
% 1.02/0.90 (((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51))) | segmentP(W!49, Z!51)),
% 1.02/0.90 inference(tautology,[status(thm)],[])).
% 1.02/0.90 tff(40,plain,
% 1.02/0.90 (segmentP(W!49, Z!51)),
% 1.02/0.90 inference(unit_resolution,[status(thm)],[39, 32])).
% 1.02/0.90 tff(41,plain,
% 1.02/0.90 (segmentP(U!47, Z!51)),
% 1.02/0.90 inference(modus_ponens,[status(thm)],[40, 38])).
% 1.02/0.90 tff(42,plain,
% 1.02/0.90 (((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51))) | ssList(Z!51)),
% 1.02/0.90 inference(tautology,[status(thm)],[])).
% 1.02/0.90 tff(43,plain,
% 1.02/0.90 (ssList(Z!51)),
% 1.02/0.90 inference(unit_resolution,[status(thm)],[42, 32])).
% 1.02/0.90 tff(44,plain,
% 1.02/0.90 (((~segmentP(W!49, Z!51)) | (~segmentP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51))) | neq(Z!51, nil)),
% 1.02/0.90 inference(tautology,[status(thm)],[])).
% 1.02/0.90 tff(45,plain,
% 1.02/0.90 (neq(Z!51, nil)),
% 1.02/0.90 inference(unit_resolution,[status(thm)],[44, 32])).
% 1.02/0.90 tff(46,plain,
% 1.02/0.90 (^[Y: $i] : refl(((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y))) <=> ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y))))),
% 1.02/0.91 inference(bind,[status(th)],[])).
% 1.02/0.91 tff(47,plain,
% 1.02/0.91 (![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y))) <=> ![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))),
% 1.02/0.91 inference(quant_intro,[status(thm)],[46])).
% 1.02/0.91 tff(48,plain,
% 1.02/0.91 (^[Y: $i] : trans(monotonicity(rewrite((ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y)) <=> (~((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y))))), ((~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) <=> (~(~((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y))))))), rewrite((~(~((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y))))) <=> ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))), ((~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) <=> ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))))),
% 1.02/0.91 inference(bind,[status(th)],[])).
% 1.02/0.91 tff(49,plain,
% 1.02/0.91 (![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) <=> ![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))),
% 1.02/0.91 inference(quant_intro,[status(thm)],[48])).
% 1.02/0.91 tff(50,plain,
% 1.02/0.91 (![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y)))),
% 1.02/0.91 inference(and_elim,[status(thm)],[24])).
% 1.02/0.91 tff(51,plain,
% 1.02/0.91 (![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))),
% 1.02/0.91 inference(modus_ponens,[status(thm)],[50, 49])).
% 1.02/0.91 tff(52,plain,
% 1.02/0.91 (![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))),
% 1.02/0.91 inference(modus_ponens,[status(thm)],[51, 47])).
% 1.02/0.91 tff(53,plain,
% 1.02/0.91 (((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))) | ((~neq(Z!51, nil)) | (~ssList(Z!51)) | (~segmentP(V!48, Z!51)) | (~segmentP(U!47, Z!51)))) <=> ((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))) | (~neq(Z!51, nil)) | (~ssList(Z!51)) | (~segmentP(V!48, Z!51)) | (~segmentP(U!47, Z!51)))),
% 1.02/0.91 inference(rewrite,[status(thm)],[])).
% 1.02/0.91 tff(54,plain,
% 1.02/0.91 ((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))) | ((~neq(Z!51, nil)) | (~ssList(Z!51)) | (~segmentP(V!48, Z!51)) | (~segmentP(U!47, Z!51)))),
% 1.02/0.91 inference(quant_inst,[status(thm)],[])).
% 1.02/0.91 tff(55,plain,
% 1.02/0.91 ((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))) | (~neq(Z!51, nil)) | (~ssList(Z!51)) | (~segmentP(V!48, Z!51)) | (~segmentP(U!47, Z!51))),
% 1.02/0.91 inference(modus_ponens,[status(thm)],[54, 53])).
% 1.02/0.91 tff(56,plain,
% 1.02/0.91 ((~segmentP(V!48, Z!51)) | (~segmentP(U!47, Z!51))),
% 1.02/0.91 inference(unit_resolution,[status(thm)],[55, 52, 45, 43])).
% 1.02/0.91 tff(57,plain,
% 1.02/0.91 ($false),
% 1.02/0.91 inference(unit_resolution,[status(thm)],[56, 41, 35])).
% 1.02/0.91 % SZS output end Proof
%------------------------------------------------------------------------------