TSTP Solution File: SWC023+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC023+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 11:54:42 EDT 2022
% Result : Theorem 3.78s 2.71s
% Output : Proof 3.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC023+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 21:00:21 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 3.78/2.71 % SZS status Theorem
% 3.78/2.71 % SZS output start Proof
% 3.78/2.71 tff(frontsegP_type, type, (
% 3.78/2.71 frontsegP: ( $i * $i ) > $o)).
% 3.78/2.71 tff(tptp_fun_Z_51_type, type, (
% 3.78/2.71 tptp_fun_Z_51: $i)).
% 3.78/2.71 tff(tptp_fun_U_47_type, type, (
% 3.78/2.71 tptp_fun_U_47: $i)).
% 3.78/2.71 tff(tptp_fun_W_49_type, type, (
% 3.78/2.71 tptp_fun_W_49: $i)).
% 3.78/2.71 tff(tptp_fun_X_50_type, type, (
% 3.78/2.71 tptp_fun_X_50: $i)).
% 3.78/2.71 tff(nil_type, type, (
% 3.78/2.71 nil: $i)).
% 3.78/2.71 tff(ssList_type, type, (
% 3.78/2.71 ssList: $i > $o)).
% 3.78/2.71 tff(neq_type, type, (
% 3.78/2.71 neq: ( $i * $i ) > $o)).
% 3.78/2.71 tff(tptp_fun_V_48_type, type, (
% 3.78/2.71 tptp_fun_V_48: $i)).
% 3.78/2.71 tff(segmentP_type, type, (
% 3.78/2.71 segmentP: ( $i * $i ) > $o)).
% 3.78/2.71 tff(1,plain,
% 3.78/2.71 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) & ((~((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) & ((~((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 3.78/2.71 inference(rewrite,[status(thm)],[])).
% 3.78/2.71 tff(2,plain,
% 3.78/2.71 ((ssList(V!48) & (ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) & ((~((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))) <=> (ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) & ((~((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 3.78/2.71 inference(rewrite,[status(thm)],[])).
% 3.78/2.71 tff(3,plain,
% 3.78/2.71 ((ssList(W!49) & ((U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) & ((~((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))) <=> (ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) & ((~((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 3.78/2.71 inference(rewrite,[status(thm)],[])).
% 3.78/2.71 tff(4,plain,
% 3.78/2.71 (((~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) & ((~((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~((~(nil = X!50)) | (~(nil = W!49)))))) <=> ((U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) & ((~((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 3.78/2.71 inference(rewrite,[status(thm)],[])).
% 3.78/2.71 tff(5,plain,
% 3.78/2.71 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 3.78/2.71 inference(rewrite,[status(thm)],[])).
% 3.78/2.71 tff(6,plain,
% 3.78/2.71 (((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) & ((~((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~((~(nil = X!50)) | (~(nil = W!49))))))) <=> (ssList(W!49) & ((U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) & ((~((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~((~(nil = W!49)) | (~(nil = X!50)))))))),
% 3.78/2.71 inference(monotonicity,[status(thm)],[5, 4])).
% 3.78/2.71 tff(7,plain,
% 3.78/2.71 (((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) & ((~((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~((~(nil = X!50)) | (~(nil = W!49))))))) <=> (ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) & ((~((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 3.78/2.71 inference(transitivity,[status(thm)],[6, 3])).
% 3.78/2.71 tff(8,plain,
% 3.78/2.71 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 3.78/2.71 inference(rewrite,[status(thm)],[])).
% 3.78/2.71 tff(9,plain,
% 3.78/2.71 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) & ((~((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~((~(nil = X!50)) | (~(nil = W!49)))))))) <=> (ssList(V!48) & (ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) & ((~((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~((~(nil = W!49)) | (~(nil = X!50)))))))),
% 3.78/2.71 inference(monotonicity,[status(thm)],[8, 7])).
% 3.78/2.71 tff(10,plain,
% 3.78/2.71 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) & ((~((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~((~(nil = X!50)) | (~(nil = W!49)))))))) <=> (ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) & ((~((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 3.78/2.71 inference(transitivity,[status(thm)],[9, 2])).
% 3.78/2.71 tff(11,plain,
% 3.78/2.71 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 3.78/2.71 inference(rewrite,[status(thm)],[])).
% 3.78/2.71 tff(12,plain,
% 3.78/2.71 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) & ((~((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~((~(nil = X!50)) | (~(nil = W!49))))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) & ((~((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~((~(nil = W!49)) | (~(nil = X!50)))))))),
% 3.78/2.71 inference(monotonicity,[status(thm)],[11, 10])).
% 3.78/2.71 tff(13,plain,
% 3.78/2.71 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) & ((~((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~((~(nil = X!50)) | (~(nil = W!49))))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) & ((~((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 3.78/2.71 inference(transitivity,[status(thm)],[12, 1])).
% 3.78/2.71 tff(14,plain,
% 3.78/2.71 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y)) | (![Z: $i] : ((~frontsegP(W, Z)) | (~frontsegP(X, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & ((~(nil = X)) | (~(nil = W))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y)) | (![Z: $i] : ((~frontsegP(W, Z)) | (~frontsegP(X, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & ((~(nil = X)) | (~(nil = W)))))))))),
% 3.78/2.71 inference(rewrite,[status(thm)],[])).
% 3.78/2.71 tff(15,plain,
% 3.78/2.71 ((~![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)) & frontsegP(V, Y)) & frontsegP(U, Y))) | (![Z: $i] : (ssList(Z) => (((~neq(Z, nil)) | (~frontsegP(X, Z))) | (~frontsegP(W, Z)))) & ((~(nil = X)) | (~(nil = W)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y)) | (![Z: $i] : ((~frontsegP(W, Z)) | (~frontsegP(X, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & ((~(nil = X)) | (~(nil = W)))))))))),
% 3.78/2.71 inference(rewrite,[status(thm)],[])).
% 3.78/2.71 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)) & frontsegP(V, Y)) & frontsegP(U, Y))) | (![Z: $i] : (ssList(Z) => (((~neq(Z, nil)) | (~frontsegP(X, Z))) | (~frontsegP(W, Z)))) & ((~(nil = X)) | (~(nil = W)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 3.78/2.71 tff(17,plain,
% 3.78/2.71 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y)) | (![Z: $i] : ((~frontsegP(W, Z)) | (~frontsegP(X, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & ((~(nil = X)) | (~(nil = W))))))))),
% 3.78/2.71 inference(modus_ponens,[status(thm)],[16, 15])).
% 3.78/2.71 tff(18,plain,
% 3.78/2.71 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y)) | (![Z: $i] : ((~frontsegP(W, Z)) | (~frontsegP(X, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & ((~(nil = X)) | (~(nil = W))))))))),
% 3.78/2.71 inference(modus_ponens,[status(thm)],[17, 14])).
% 3.78/2.71 tff(19,plain,
% 3.78/2.71 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y)) | (![Z: $i] : ((~frontsegP(W, Z)) | (~frontsegP(X, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & ((~(nil = X)) | (~(nil = W))))))))),
% 3.78/2.71 inference(modus_ponens,[status(thm)],[18, 14])).
% 3.78/2.71 tff(20,plain,
% 3.78/2.71 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y)) | (![Z: $i] : ((~frontsegP(W, Z)) | (~frontsegP(X, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & ((~(nil = X)) | (~(nil = W))))))))),
% 3.78/2.71 inference(modus_ponens,[status(thm)],[19, 14])).
% 3.78/2.71 tff(21,plain,
% 3.78/2.71 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y)) | (![Z: $i] : ((~frontsegP(W, Z)) | (~frontsegP(X, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & ((~(nil = X)) | (~(nil = W))))))))),
% 3.78/2.71 inference(modus_ponens,[status(thm)],[20, 14])).
% 3.78/2.71 tff(22,plain,
% 3.78/2.71 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y)) | (![Z: $i] : ((~frontsegP(W, Z)) | (~frontsegP(X, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & ((~(nil = X)) | (~(nil = W))))))))),
% 3.78/2.71 inference(modus_ponens,[status(thm)],[21, 14])).
% 3.78/2.71 tff(23,plain,
% 3.78/2.71 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y)) | (![Z: $i] : ((~frontsegP(W, Z)) | (~frontsegP(X, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & ((~(nil = X)) | (~(nil = W))))))))),
% 3.78/2.71 inference(modus_ponens,[status(thm)],[22, 14])).
% 3.78/2.71 tff(24,plain,
% 3.78/2.71 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) & ((~((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~((~(nil = W!49)) | (~(nil = X!50)))))),
% 3.78/2.71 inference(modus_ponens,[status(thm)],[23, 13])).
% 3.78/2.71 tff(25,plain,
% 3.78/2.71 (U!47 = W!49),
% 3.78/2.71 inference(and_elim,[status(thm)],[24])).
% 3.78/2.71 tff(26,plain,
% 3.78/2.71 (frontsegP(U!47, Z!51) <=> frontsegP(W!49, Z!51)),
% 3.78/2.71 inference(monotonicity,[status(thm)],[25])).
% 3.78/2.71 tff(27,plain,
% 3.78/2.71 (frontsegP(W!49, Z!51) <=> frontsegP(U!47, Z!51)),
% 3.78/2.71 inference(symmetry,[status(thm)],[26])).
% 3.78/2.71 tff(28,plain,
% 3.78/2.71 (ssList(X!50)),
% 3.78/2.71 inference(and_elim,[status(thm)],[24])).
% 3.78/2.71 tff(29,plain,
% 3.78/2.71 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 3.78/2.71 inference(bind,[status(th)],[])).
% 3.78/2.71 tff(30,plain,
% 3.78/2.71 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 3.78/2.71 inference(quant_intro,[status(thm)],[29])).
% 3.78/2.71 tff(31,plain,
% 3.78/2.71 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 3.78/2.71 inference(rewrite,[status(thm)],[])).
% 3.78/2.71 tff(32,plain,
% 3.78/2.71 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 3.78/2.71 inference(bind,[status(th)],[])).
% 3.78/2.71 tff(33,plain,
% 3.78/2.71 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 3.78/2.71 inference(quant_intro,[status(thm)],[32])).
% 3.78/2.71 tff(34,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax58')).
% 3.78/2.71 tff(35,plain,
% 3.78/2.71 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 3.78/2.71 inference(modus_ponens,[status(thm)],[34, 33])).
% 3.78/2.71 tff(36,plain,
% 3.78/2.71 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 3.78/2.71 inference(modus_ponens,[status(thm)],[35, 31])).
% 3.78/2.71 tff(37,plain,(
% 3.78/2.71 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 3.78/2.71 inference(skolemize,[status(sab)],[36])).
% 3.78/2.71 tff(38,plain,
% 3.78/2.71 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 3.78/2.71 inference(modus_ponens,[status(thm)],[37, 30])).
% 3.78/2.71 tff(39,plain,
% 3.78/2.71 (((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(X!50)) | (segmentP(nil, X!50) <=> (nil = X!50)))) <=> ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(X!50)) | (segmentP(nil, X!50) <=> (nil = X!50)))),
% 3.78/2.71 inference(rewrite,[status(thm)],[])).
% 3.78/2.71 tff(40,plain,
% 3.78/2.71 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(X!50)) | (segmentP(nil, X!50) <=> (nil = X!50)))),
% 3.78/2.71 inference(quant_inst,[status(thm)],[])).
% 3.78/2.71 tff(41,plain,
% 3.78/2.71 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(X!50)) | (segmentP(nil, X!50) <=> (nil = X!50))),
% 3.78/2.71 inference(modus_ponens,[status(thm)],[40, 39])).
% 3.78/2.71 tff(42,plain,
% 3.78/2.71 (segmentP(nil, X!50) <=> (nil = X!50)),
% 3.78/2.71 inference(unit_resolution,[status(thm)],[41, 38, 28])).
% 3.78/2.71 tff(43,plain,
% 3.78/2.71 (^[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))))))),
% 3.88/2.71 inference(bind,[status(th)],[])).
% 3.88/2.71 tff(44,plain,
% 3.88/2.71 (![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)))))),
% 3.88/2.71 inference(quant_intro,[status(thm)],[43])).
% 3.88/2.71 tff(45,plain,
% 3.88/2.71 (^[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))))))),
% 3.88/2.71 inference(bind,[status(th)],[])).
% 3.88/2.71 tff(46,plain,
% 3.88/2.71 (![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)))))),
% 3.88/2.71 inference(quant_intro,[status(thm)],[45])).
% 3.88/2.71 tff(47,plain,
% 3.88/2.71 (![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)))))),
% 3.88/2.71 inference(transitivity,[status(thm)],[46, 44])).
% 3.88/2.71 tff(48,plain,
% 3.88/2.71 (![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)))))),
% 3.88/2.71 inference(rewrite,[status(thm)],[])).
% 3.88/2.71 tff(49,plain,
% 3.88/2.71 (^[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)))))))),
% 3.88/2.71 inference(bind,[status(th)],[])).
% 3.88/2.71 tff(50,plain,
% 3.88/2.71 (![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)))))),
% 3.88/2.71 inference(quant_intro,[status(thm)],[49])).
% 3.88/2.71 tff(51,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax15')).
% 3.88/2.71 tff(52,plain,
% 3.88/2.71 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 3.88/2.71 inference(modus_ponens,[status(thm)],[51, 50])).
% 3.88/2.71 tff(53,plain,
% 3.88/2.71 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 3.88/2.71 inference(modus_ponens,[status(thm)],[52, 48])).
% 3.88/2.71 tff(54,plain,(
% 3.88/2.71 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 3.88/2.71 inference(skolemize,[status(sab)],[53])).
% 3.88/2.71 tff(55,plain,
% 3.88/2.71 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 3.88/2.71 inference(modus_ponens,[status(thm)],[54, 47])).
% 3.88/2.71 tff(56,plain,
% 3.88/2.71 (((~![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)))))),
% 3.88/2.71 inference(rewrite,[status(thm)],[])).
% 3.88/2.71 tff(57,plain,
% 3.88/2.71 ((~![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)))))),
% 3.88/2.71 inference(quant_inst,[status(thm)],[])).
% 3.88/2.71 tff(58,plain,
% 3.88/2.71 ((~![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))))),
% 3.88/2.71 inference(modus_ponens,[status(thm)],[57, 56])).
% 3.88/2.71 tff(59,plain,
% 3.88/2.71 (![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))),
% 3.88/2.72 inference(unit_resolution,[status(thm)],[58, 55, 28])).
% 3.88/2.72 tff(60,plain,
% 3.88/2.72 (ssList(nil) <=> ssList(nil)),
% 3.88/2.72 inference(rewrite,[status(thm)],[])).
% 3.88/2.72 tff(61,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 3.88/2.72 tff(62,plain,
% 3.88/2.72 (ssList(nil)),
% 3.88/2.72 inference(modus_ponens,[status(thm)],[61, 60])).
% 3.88/2.72 tff(63,plain,
% 3.88/2.72 (((~![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))))),
% 3.88/2.72 inference(rewrite,[status(thm)],[])).
% 3.88/2.72 tff(64,plain,
% 3.88/2.72 ((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | ((~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil))))),
% 3.88/2.72 inference(quant_inst,[status(thm)],[])).
% 3.88/2.72 tff(65,plain,
% 3.88/2.72 ((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | (~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil)))),
% 3.88/2.72 inference(modus_ponens,[status(thm)],[64, 63])).
% 3.88/2.72 tff(66,plain,
% 3.88/2.72 (neq(X!50, nil) <=> (~(X!50 = nil))),
% 3.88/2.72 inference(unit_resolution,[status(thm)],[65, 62, 59])).
% 3.88/2.72 tff(67,plain,
% 3.88/2.72 (V!48 = X!50),
% 3.88/2.72 inference(and_elim,[status(thm)],[24])).
% 3.88/2.72 tff(68,plain,
% 3.88/2.72 (X!50 = V!48),
% 3.88/2.72 inference(symmetry,[status(thm)],[67])).
% 3.88/2.72 tff(69,plain,
% 3.88/2.72 (neq(X!50, nil) <=> neq(V!48, nil)),
% 3.88/2.72 inference(monotonicity,[status(thm)],[68])).
% 3.88/2.72 tff(70,plain,
% 3.88/2.72 (neq(V!48, nil) <=> neq(X!50, nil)),
% 3.88/2.72 inference(symmetry,[status(thm)],[69])).
% 3.88/2.72 tff(71,plain,
% 3.88/2.72 (neq(V!48, nil)),
% 3.88/2.72 inference(and_elim,[status(thm)],[24])).
% 3.88/2.72 tff(72,plain,
% 3.88/2.72 (neq(X!50, nil)),
% 3.88/2.72 inference(modus_ponens,[status(thm)],[71, 70])).
% 3.88/2.72 tff(73,plain,
% 3.88/2.72 ((~(neq(X!50, nil) <=> (~(X!50 = nil)))) | (~neq(X!50, nil)) | (~(X!50 = nil))),
% 3.88/2.72 inference(tautology,[status(thm)],[])).
% 3.88/2.72 tff(74,plain,
% 3.88/2.72 ((~(neq(X!50, nil) <=> (~(X!50 = nil)))) | (~(X!50 = nil))),
% 3.88/2.72 inference(unit_resolution,[status(thm)],[73, 72])).
% 3.88/2.72 tff(75,plain,
% 3.88/2.72 (~(X!50 = nil)),
% 3.88/2.72 inference(unit_resolution,[status(thm)],[74, 66])).
% 3.88/2.72 tff(76,plain,
% 3.88/2.72 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 3.88/2.72 inference(bind,[status(th)],[])).
% 3.88/2.72 tff(77,plain,
% 3.88/2.72 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 3.88/2.72 inference(quant_intro,[status(thm)],[76])).
% 3.88/2.72 tff(78,plain,
% 3.88/2.72 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 3.88/2.72 inference(bind,[status(th)],[])).
% 3.88/2.72 tff(79,plain,
% 3.88/2.72 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 3.88/2.72 inference(quant_intro,[status(thm)],[78])).
% 3.88/2.72 tff(80,plain,
% 3.88/2.72 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 3.88/2.72 inference(transitivity,[status(thm)],[79, 77])).
% 3.88/2.72 tff(81,plain,
% 3.88/2.72 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 3.88/2.72 inference(bind,[status(th)],[])).
% 3.88/2.72 tff(82,plain,
% 3.88/2.72 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 3.88/2.72 inference(quant_intro,[status(thm)],[81])).
% 3.88/2.72 tff(83,plain,
% 3.88/2.72 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 3.88/2.72 inference(rewrite,[status(thm)],[])).
% 3.88/2.72 tff(84,plain,
% 3.88/2.72 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite(((segmentP(U, V) & segmentP(V, U)) => (U = V)) <=> ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))), ((ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> (ssList(V) => ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))))), rewrite((ssList(V) => ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))) <=> ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))), ((ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))))), (![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> (ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))))), rewrite((ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))))),
% 3.88/2.72 inference(bind,[status(th)],[])).
% 3.88/2.72 tff(85,plain,
% 3.88/2.72 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 3.88/2.72 inference(quant_intro,[status(thm)],[84])).
% 3.88/2.72 tff(86,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax54')).
% 3.88/2.72 tff(87,plain,
% 3.88/2.72 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 3.88/2.72 inference(modus_ponens,[status(thm)],[86, 85])).
% 3.88/2.72 tff(88,plain,
% 3.88/2.72 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 3.88/2.72 inference(modus_ponens,[status(thm)],[87, 83])).
% 3.88/2.72 tff(89,plain,(
% 3.88/2.72 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 3.88/2.72 inference(skolemize,[status(sab)],[88])).
% 3.88/2.72 tff(90,plain,
% 3.88/2.72 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 3.88/2.72 inference(modus_ponens,[status(thm)],[89, 82])).
% 3.88/2.72 tff(91,plain,
% 3.88/2.72 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 3.88/2.72 inference(modus_ponens,[status(thm)],[90, 80])).
% 3.88/2.72 tff(92,plain,
% 3.88/2.72 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))),
% 3.88/2.72 inference(rewrite,[status(thm)],[])).
% 3.88/2.72 tff(93,plain,
% 3.88/2.72 (((~ssList(X!50)) | ![V: $i] : ((X!50 = V) | (~ssList(V)) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) <=> ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))),
% 3.88/2.72 inference(rewrite,[status(thm)],[])).
% 3.88/2.72 tff(94,plain,
% 3.88/2.72 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(X!50)) | ![V: $i] : ((X!50 = V) | (~ssList(V)) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))))),
% 3.88/2.72 inference(monotonicity,[status(thm)],[93])).
% 3.88/2.72 tff(95,plain,
% 3.88/2.72 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(X!50)) | ![V: $i] : ((X!50 = V) | (~ssList(V)) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))),
% 3.88/2.72 inference(transitivity,[status(thm)],[94, 92])).
% 3.88/2.72 tff(96,plain,
% 3.88/2.72 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(X!50)) | ![V: $i] : ((X!50 = V) | (~ssList(V)) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))),
% 3.88/2.72 inference(quant_inst,[status(thm)],[])).
% 3.88/2.72 tff(97,plain,
% 3.88/2.72 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))),
% 3.88/2.72 inference(modus_ponens,[status(thm)],[96, 95])).
% 3.88/2.72 tff(98,plain,
% 3.88/2.72 (![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))),
% 3.88/2.72 inference(unit_resolution,[status(thm)],[97, 91, 28])).
% 3.88/2.72 tff(99,plain,
% 3.88/2.72 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 3.88/2.72 inference(bind,[status(th)],[])).
% 3.88/2.72 tff(100,plain,
% 3.88/2.72 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 3.88/2.72 inference(quant_intro,[status(thm)],[99])).
% 3.88/2.72 tff(101,plain,
% 3.88/2.72 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 3.88/2.72 inference(rewrite,[status(thm)],[])).
% 3.88/2.72 tff(102,plain,
% 3.88/2.72 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 3.88/2.72 inference(bind,[status(th)],[])).
% 3.88/2.72 tff(103,plain,
% 3.88/2.72 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 3.88/2.72 inference(quant_intro,[status(thm)],[102])).
% 3.88/2.72 tff(104,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax57')).
% 3.88/2.72 tff(105,plain,
% 3.88/2.72 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 3.88/2.72 inference(modus_ponens,[status(thm)],[104, 103])).
% 3.88/2.72 tff(106,plain,
% 3.88/2.72 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 3.88/2.72 inference(modus_ponens,[status(thm)],[105, 101])).
% 3.88/2.72 tff(107,plain,(
% 3.88/2.72 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 3.88/2.72 inference(skolemize,[status(sab)],[106])).
% 3.88/2.72 tff(108,plain,
% 3.88/2.72 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 3.88/2.72 inference(modus_ponens,[status(thm)],[107, 100])).
% 3.88/2.72 tff(109,plain,
% 3.88/2.72 (((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(X!50)) | segmentP(X!50, nil))) <=> ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(X!50)) | segmentP(X!50, nil))),
% 3.88/2.72 inference(rewrite,[status(thm)],[])).
% 3.88/2.72 tff(110,plain,
% 3.88/2.72 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(X!50)) | segmentP(X!50, nil))),
% 3.88/2.72 inference(quant_inst,[status(thm)],[])).
% 3.88/2.72 tff(111,plain,
% 3.88/2.72 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(X!50)) | segmentP(X!50, nil)),
% 3.88/2.72 inference(modus_ponens,[status(thm)],[110, 109])).
% 3.88/2.72 tff(112,plain,
% 3.88/2.72 (segmentP(X!50, nil)),
% 3.88/2.72 inference(unit_resolution,[status(thm)],[111, 108, 28])).
% 3.88/2.72 tff(113,plain,
% 3.88/2.72 (((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | ((~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil)))) <=> ((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | (~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil)))),
% 3.88/2.72 inference(rewrite,[status(thm)],[])).
% 3.88/2.72 tff(114,plain,
% 3.88/2.72 (((~ssList(nil)) | (X!50 = nil) | (~segmentP(X!50, nil)) | (~segmentP(nil, X!50))) <=> ((~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil)))),
% 3.88/2.72 inference(rewrite,[status(thm)],[])).
% 3.88/2.72 tff(115,plain,
% 3.88/2.72 (((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | ((~ssList(nil)) | (X!50 = nil) | (~segmentP(X!50, nil)) | (~segmentP(nil, X!50)))) <=> ((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | ((~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil))))),
% 3.88/2.72 inference(monotonicity,[status(thm)],[114])).
% 3.88/2.72 tff(116,plain,
% 3.88/2.72 (((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | ((~ssList(nil)) | (X!50 = nil) | (~segmentP(X!50, nil)) | (~segmentP(nil, X!50)))) <=> ((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | (~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil)))),
% 3.88/2.72 inference(transitivity,[status(thm)],[115, 113])).
% 3.88/2.72 tff(117,plain,
% 3.88/2.72 ((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | ((~ssList(nil)) | (X!50 = nil) | (~segmentP(X!50, nil)) | (~segmentP(nil, X!50)))),
% 3.88/2.72 inference(quant_inst,[status(thm)],[])).
% 3.88/2.72 tff(118,plain,
% 3.88/2.72 ((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | (~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil))),
% 3.88/2.72 inference(modus_ponens,[status(thm)],[117, 116])).
% 3.88/2.72 tff(119,plain,
% 3.88/2.72 ((~segmentP(nil, X!50)) | (X!50 = nil)),
% 3.88/2.72 inference(unit_resolution,[status(thm)],[118, 62, 112, 98])).
% 3.88/2.72 tff(120,plain,
% 3.88/2.72 (~segmentP(nil, X!50)),
% 3.88/2.72 inference(unit_resolution,[status(thm)],[119, 75])).
% 3.88/2.72 tff(121,plain,
% 3.88/2.72 ((~(segmentP(nil, X!50) <=> (nil = X!50))) | segmentP(nil, X!50) | (~(nil = X!50))),
% 3.88/2.72 inference(tautology,[status(thm)],[])).
% 3.88/2.72 tff(122,plain,
% 3.88/2.72 (~(nil = X!50)),
% 3.88/2.72 inference(unit_resolution,[status(thm)],[121, 120, 42])).
% 3.88/2.72 tff(123,plain,
% 3.88/2.72 (((~(nil = W!49)) | (~(nil = X!50))) | (nil = X!50)),
% 3.88/2.72 inference(tautology,[status(thm)],[])).
% 3.88/2.72 tff(124,plain,
% 3.88/2.72 ((~(nil = W!49)) | (~(nil = X!50))),
% 3.88/2.72 inference(unit_resolution,[status(thm)],[123, 122])).
% 3.88/2.72 tff(125,plain,
% 3.88/2.72 ((~((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))),
% 3.88/2.72 inference(and_elim,[status(thm)],[24])).
% 3.88/2.72 tff(126,plain,
% 3.88/2.72 (~((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51)))),
% 3.88/2.72 inference(unit_resolution,[status(thm)],[125, 124])).
% 3.88/2.72 tff(127,plain,
% 3.88/2.72 (((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51))) | frontsegP(W!49, Z!51)),
% 3.88/2.72 inference(tautology,[status(thm)],[])).
% 3.88/2.72 tff(128,plain,
% 3.88/2.72 (frontsegP(W!49, Z!51)),
% 3.88/2.72 inference(unit_resolution,[status(thm)],[127, 126])).
% 3.88/2.72 tff(129,plain,
% 3.88/2.72 (frontsegP(U!47, Z!51)),
% 3.88/2.72 inference(modus_ponens,[status(thm)],[128, 27])).
% 3.88/2.72 tff(130,plain,
% 3.88/2.72 (frontsegP(V!48, Z!51) <=> frontsegP(X!50, Z!51)),
% 3.88/2.72 inference(monotonicity,[status(thm)],[67])).
% 3.88/2.72 tff(131,plain,
% 3.88/2.72 (frontsegP(X!50, Z!51) <=> frontsegP(V!48, Z!51)),
% 3.88/2.72 inference(symmetry,[status(thm)],[130])).
% 3.88/2.72 tff(132,plain,
% 3.88/2.72 (((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51))) | frontsegP(X!50, Z!51)),
% 3.88/2.72 inference(tautology,[status(thm)],[])).
% 3.88/2.72 tff(133,plain,
% 3.88/2.72 (frontsegP(X!50, Z!51)),
% 3.88/2.72 inference(unit_resolution,[status(thm)],[132, 126])).
% 3.88/2.72 tff(134,plain,
% 3.88/2.72 (frontsegP(V!48, Z!51)),
% 3.88/2.72 inference(modus_ponens,[status(thm)],[133, 131])).
% 3.88/2.72 tff(135,plain,
% 3.88/2.72 (((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51))) | ssList(Z!51)),
% 3.88/2.72 inference(tautology,[status(thm)],[])).
% 3.88/2.72 tff(136,plain,
% 3.88/2.72 (ssList(Z!51)),
% 3.88/2.72 inference(unit_resolution,[status(thm)],[135, 126])).
% 3.88/2.72 tff(137,plain,
% 3.88/2.72 (((~frontsegP(W!49, Z!51)) | (~frontsegP(X!50, Z!51)) | (~neq(Z!51, nil)) | (~ssList(Z!51))) | neq(Z!51, nil)),
% 3.88/2.72 inference(tautology,[status(thm)],[])).
% 3.88/2.72 tff(138,plain,
% 3.88/2.72 (neq(Z!51, nil)),
% 3.88/2.72 inference(unit_resolution,[status(thm)],[137, 126])).
% 3.88/2.72 tff(139,plain,
% 3.88/2.72 (^[Y: $i] : refl(((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y))) <=> ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y))))),
% 3.88/2.72 inference(bind,[status(th)],[])).
% 3.88/2.72 tff(140,plain,
% 3.88/2.72 (![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y))) <=> ![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))),
% 3.88/2.72 inference(quant_intro,[status(thm)],[139])).
% 3.88/2.72 tff(141,plain,
% 3.88/2.72 (^[Y: $i] : trans(monotonicity(rewrite((ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y)) <=> (~((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y))))), ((~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) <=> (~(~((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y))))))), rewrite((~(~((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y))))) <=> ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))), ((~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) <=> ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))))),
% 3.88/2.72 inference(bind,[status(th)],[])).
% 3.88/2.72 tff(142,plain,
% 3.88/2.72 (![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y))) <=> ![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))),
% 3.88/2.72 inference(quant_intro,[status(thm)],[141])).
% 3.88/2.72 tff(143,plain,
% 3.88/2.72 (![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!48, Y) & frontsegP(U!47, Y)))),
% 3.88/2.72 inference(and_elim,[status(thm)],[24])).
% 3.88/2.72 tff(144,plain,
% 3.88/2.72 (![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))),
% 3.88/2.72 inference(modus_ponens,[status(thm)],[143, 142])).
% 3.88/2.72 tff(145,plain,
% 3.88/2.72 (![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))),
% 3.88/2.72 inference(modus_ponens,[status(thm)],[144, 140])).
% 3.88/2.72 tff(146,plain,
% 3.88/2.72 (((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))) | ((~neq(Z!51, nil)) | (~ssList(Z!51)) | (~frontsegP(U!47, Z!51)) | (~frontsegP(V!48, Z!51)))) <=> ((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))) | (~neq(Z!51, nil)) | (~ssList(Z!51)) | (~frontsegP(U!47, Z!51)) | (~frontsegP(V!48, Z!51)))),
% 3.88/2.72 inference(rewrite,[status(thm)],[])).
% 3.88/2.72 tff(147,plain,
% 3.88/2.72 (((~neq(Z!51, nil)) | (~ssList(Z!51)) | (~frontsegP(V!48, Z!51)) | (~frontsegP(U!47, Z!51))) <=> ((~neq(Z!51, nil)) | (~ssList(Z!51)) | (~frontsegP(U!47, Z!51)) | (~frontsegP(V!48, Z!51)))),
% 3.88/2.72 inference(rewrite,[status(thm)],[])).
% 3.88/2.72 tff(148,plain,
% 3.88/2.72 (((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))) | ((~neq(Z!51, nil)) | (~ssList(Z!51)) | (~frontsegP(V!48, Z!51)) | (~frontsegP(U!47, Z!51)))) <=> ((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))) | ((~neq(Z!51, nil)) | (~ssList(Z!51)) | (~frontsegP(U!47, Z!51)) | (~frontsegP(V!48, Z!51))))),
% 3.88/2.72 inference(monotonicity,[status(thm)],[147])).
% 3.88/2.72 tff(149,plain,
% 3.88/2.72 (((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))) | ((~neq(Z!51, nil)) | (~ssList(Z!51)) | (~frontsegP(V!48, Z!51)) | (~frontsegP(U!47, Z!51)))) <=> ((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))) | (~neq(Z!51, nil)) | (~ssList(Z!51)) | (~frontsegP(U!47, Z!51)) | (~frontsegP(V!48, Z!51)))),
% 3.88/2.72 inference(transitivity,[status(thm)],[148, 146])).
% 3.88/2.72 tff(150,plain,
% 3.88/2.72 ((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))) | ((~neq(Z!51, nil)) | (~ssList(Z!51)) | (~frontsegP(V!48, Z!51)) | (~frontsegP(U!47, Z!51)))),
% 3.88/2.72 inference(quant_inst,[status(thm)],[])).
% 3.88/2.72 tff(151,plain,
% 3.88/2.72 ((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(V!48, Y)) | (~frontsegP(U!47, Y)))) | (~neq(Z!51, nil)) | (~ssList(Z!51)) | (~frontsegP(U!47, Z!51)) | (~frontsegP(V!48, Z!51))),
% 3.88/2.72 inference(modus_ponens,[status(thm)],[150, 149])).
% 3.88/2.72 tff(152,plain,
% 3.88/2.72 ((~frontsegP(U!47, Z!51)) | (~frontsegP(V!48, Z!51))),
% 3.88/2.72 inference(unit_resolution,[status(thm)],[151, 145, 138, 136])).
% 3.88/2.74 tff(153,plain,
% 3.88/2.74 ($false),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[152, 134, 129])).
% 3.88/2.74 % SZS output end Proof
%------------------------------------------------------------------------------