TSTP Solution File: SWC206+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC206+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 11:56:07 EDT 2022
% Result : Theorem 0.96s 0.87s
% Output : Proof 0.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC206+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Sep 3 22:38:15 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.96/0.87 % SZS status Theorem
% 0.96/0.87 % SZS output start Proof
% 0.96/0.87 tff(app_type, type, (
% 0.96/0.87 app: ( $i * $i ) > $i)).
% 0.96/0.87 tff(tptp_fun_W_49_type, type, (
% 0.96/0.87 tptp_fun_W_49: $i)).
% 0.96/0.87 tff(nil_type, type, (
% 0.96/0.87 nil: $i)).
% 0.96/0.87 tff(ssList_type, type, (
% 0.96/0.87 ssList: $i > $o)).
% 0.96/0.87 tff(neq_type, type, (
% 0.96/0.87 neq: ( $i * $i ) > $o)).
% 0.96/0.87 tff(tptp_fun_X_50_type, type, (
% 0.96/0.87 tptp_fun_X_50: $i)).
% 0.96/0.87 tff(tptp_fun_Y_51_type, type, (
% 0.96/0.87 tptp_fun_Y_51: $i)).
% 0.96/0.87 tff(segmentP_type, type, (
% 0.96/0.87 segmentP: ( $i * $i ) > $o)).
% 0.96/0.87 tff(tptp_fun_V_48_type, type, (
% 0.96/0.87 tptp_fun_V_48: $i)).
% 0.96/0.87 tff(tptp_fun_U_47_type, type, (
% 0.96/0.87 tptp_fun_U_47: $i)).
% 0.96/0.87 tff(1,plain,
% 0.96/0.87 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~neq(X!50, nil))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~neq(X!50, nil))))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(2,plain,
% 0.96/0.87 ((ssList(V!48) & (ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~neq(X!50, nil))))) <=> (ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~neq(X!50, nil))))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(3,plain,
% 0.96/0.87 ((ssList(W!49) & ((~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~neq(X!50, nil))))) <=> (ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~neq(X!50, nil))))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(4,plain,
% 0.96/0.87 (((~neq(U!47, nil)) & (~(~neq(V!48, nil))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~neq(X!50, nil)))) <=> ((~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~neq(X!50, nil))))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(5,plain,
% 0.96/0.87 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(6,plain,
% 0.96/0.87 (((~(~ssList(W!49))) & ((~neq(U!47, nil)) & (~(~neq(V!48, nil))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~neq(X!50, nil))))) <=> (ssList(W!49) & ((~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~neq(X!50, nil)))))),
% 0.96/0.87 inference(monotonicity,[status(thm)],[5, 4])).
% 0.96/0.87 tff(7,plain,
% 0.96/0.87 (((~(~ssList(W!49))) & ((~neq(U!47, nil)) & (~(~neq(V!48, nil))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~neq(X!50, nil))))) <=> (ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~neq(X!50, nil))))),
% 0.96/0.87 inference(transitivity,[status(thm)],[6, 3])).
% 0.96/0.87 tff(8,plain,
% 0.96/0.87 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(9,plain,
% 0.96/0.87 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~neq(U!47, nil)) & (~(~neq(V!48, nil))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~neq(X!50, nil)))))) <=> (ssList(V!48) & (ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~neq(X!50, nil)))))),
% 0.96/0.87 inference(monotonicity,[status(thm)],[8, 7])).
% 0.96/0.87 tff(10,plain,
% 0.96/0.87 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~neq(U!47, nil)) & (~(~neq(V!48, nil))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~neq(X!50, nil)))))) <=> (ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~neq(X!50, nil))))),
% 0.96/0.87 inference(transitivity,[status(thm)],[9, 2])).
% 0.96/0.87 tff(11,plain,
% 0.96/0.87 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(12,plain,
% 0.96/0.87 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~neq(U!47, nil)) & (~(~neq(V!48, nil))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~neq(X!50, nil))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~neq(X!50, nil)))))),
% 0.96/0.87 inference(monotonicity,[status(thm)],[11, 10])).
% 0.96/0.87 tff(13,plain,
% 0.96/0.87 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~neq(U!47, nil)) & (~(~neq(V!48, nil))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~neq(X!50, nil))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~neq(X!50, nil))))),
% 0.96/0.87 inference(transitivity,[status(thm)],[12, 1])).
% 0.96/0.87 tff(14,plain,
% 0.96/0.87 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~segmentP(W, Y)) | (~segmentP(X, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & neq(X, nil))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~segmentP(W, Y)) | (~segmentP(X, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & neq(X, nil)))))))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(15,plain,
% 0.96/0.87 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | neq(U, nil)) | ((~(nil = W)) & (nil = X))) | (![Y: $i] : (ssList(Y) => (((~neq(Y, nil)) | (~segmentP(X, Y))) | (~segmentP(W, Y)))) & neq(X, nil)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~segmentP(W, Y)) | (~segmentP(X, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & neq(X, nil)))))))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 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))) | neq(U, nil)) | ((~(nil = W)) & (nil = X))) | (![Y: $i] : (ssList(Y) => (((~neq(Y, nil)) | (~segmentP(X, Y))) | (~segmentP(W, Y)))) & neq(X, nil)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.96/0.87 tff(17,plain,
% 0.96/0.87 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~segmentP(W, Y)) | (~segmentP(X, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & neq(X, nil))))))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.96/0.87 tff(18,plain,
% 0.96/0.87 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~segmentP(W, Y)) | (~segmentP(X, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & neq(X, nil))))))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.96/0.87 tff(19,plain,
% 0.96/0.87 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~segmentP(W, Y)) | (~segmentP(X, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & neq(X, nil))))))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.96/0.87 tff(20,plain,
% 0.96/0.87 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~segmentP(W, Y)) | (~segmentP(X, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & neq(X, nil))))))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.96/0.87 tff(21,plain,
% 0.96/0.87 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~segmentP(W, Y)) | (~segmentP(X, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & neq(X, nil))))))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.96/0.87 tff(22,plain,
% 0.96/0.87 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~segmentP(W, Y)) | (~segmentP(X, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & neq(X, nil))))))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.96/0.87 tff(23,plain,
% 0.96/0.87 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~segmentP(W, Y)) | (~segmentP(X, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & neq(X, nil))))))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[22, 14])).
% 0.96/0.87 tff(24,plain,
% 0.96/0.87 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~neq(X!50, nil)))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.96/0.87 tff(25,plain,
% 0.96/0.87 (ssList(W!49)),
% 0.96/0.87 inference(and_elim,[status(thm)],[24])).
% 0.96/0.87 tff(26,plain,
% 0.96/0.87 (^[U: $i] : refl(((~ssList(U)) | (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 0.96/0.87 inference(bind,[status(th)],[])).
% 0.96/0.87 tff(27,plain,
% 0.96/0.87 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.96/0.87 inference(quant_intro,[status(thm)],[26])).
% 0.96/0.87 tff(28,plain,
% 0.96/0.87 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(29,plain,
% 0.96/0.87 (^[U: $i] : rewrite((ssList(U) => (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 0.96/0.87 inference(bind,[status(th)],[])).
% 0.96/0.87 tff(30,plain,
% 0.96/0.87 (![U: $i] : (ssList(U) => (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.96/0.87 inference(quant_intro,[status(thm)],[29])).
% 0.96/0.87 tff(31,axiom,(![U: $i] : (ssList(U) => (app(nil, U) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax28')).
% 0.96/0.87 tff(32,plain,
% 0.96/0.87 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.96/0.87 tff(33,plain,
% 0.96/0.87 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.96/0.87 tff(34,plain,(
% 0.96/0.87 ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.96/0.87 inference(skolemize,[status(sab)],[33])).
% 0.96/0.87 tff(35,plain,
% 0.96/0.87 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.96/0.87 tff(36,plain,
% 0.96/0.87 (((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(W!49)) | (app(nil, W!49) = W!49))) <=> ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(W!49)) | (app(nil, W!49) = W!49))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(37,plain,
% 0.96/0.87 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(W!49)) | (app(nil, W!49) = W!49))),
% 0.96/0.87 inference(quant_inst,[status(thm)],[])).
% 0.96/0.87 tff(38,plain,
% 0.96/0.87 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(W!49)) | (app(nil, W!49) = W!49)),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.96/0.87 tff(39,plain,
% 0.96/0.87 (app(nil, W!49) = W!49),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[38, 35, 25])).
% 0.96/0.87 tff(40,plain,
% 0.96/0.87 ((nil = app(nil, W!49)) <=> (nil = W!49)),
% 0.96/0.87 inference(monotonicity,[status(thm)],[39])).
% 0.96/0.87 tff(41,plain,
% 0.96/0.87 ((nil = W!49) <=> (nil = app(nil, W!49))),
% 0.96/0.87 inference(symmetry,[status(thm)],[40])).
% 0.96/0.87 tff(42,plain,
% 0.96/0.87 ((W!49 = nil) <=> (nil = W!49)),
% 0.96/0.87 inference(commutativity,[status(thm)],[])).
% 0.96/0.87 tff(43,plain,
% 0.96/0.87 ((W!49 = nil) <=> (nil = app(nil, W!49))),
% 0.96/0.87 inference(transitivity,[status(thm)],[42, 41])).
% 0.96/0.87 tff(44,plain,
% 0.96/0.87 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))))),
% 0.96/0.87 inference(bind,[status(th)],[])).
% 0.96/0.87 tff(45,plain,
% 0.96/0.87 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.96/0.87 inference(quant_intro,[status(thm)],[44])).
% 0.96/0.87 tff(46,plain,
% 0.96/0.87 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))))),
% 0.96/0.87 inference(bind,[status(th)],[])).
% 0.96/0.87 tff(47,plain,
% 0.96/0.87 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.96/0.87 inference(quant_intro,[status(thm)],[46])).
% 0.96/0.87 tff(48,plain,
% 0.96/0.87 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.96/0.87 inference(transitivity,[status(thm)],[47, 45])).
% 0.96/0.87 tff(49,plain,
% 0.96/0.87 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(50,plain,
% 0.96/0.87 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))), (![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))))),
% 0.96/0.87 inference(bind,[status(th)],[])).
% 0.96/0.87 tff(51,plain,
% 0.96/0.87 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.96/0.87 inference(quant_intro,[status(thm)],[50])).
% 0.96/0.87 tff(52,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax15')).
% 0.96/0.87 tff(53,plain,
% 0.96/0.87 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.96/0.87 tff(54,plain,
% 0.96/0.87 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.96/0.87 tff(55,plain,(
% 0.96/0.87 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.96/0.87 inference(skolemize,[status(sab)],[54])).
% 0.96/0.87 tff(56,plain,
% 0.96/0.87 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.96/0.87 tff(57,plain,
% 0.96/0.87 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V)))))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(58,plain,
% 0.96/0.87 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V)))))),
% 0.96/0.87 inference(quant_inst,[status(thm)],[])).
% 0.96/0.87 tff(59,plain,
% 0.96/0.87 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.96/0.87 tff(60,plain,
% 0.96/0.87 (![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[59, 56, 25])).
% 0.96/0.87 tff(61,plain,
% 0.96/0.87 (ssList(nil) <=> ssList(nil)),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(62,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.96/0.87 tff(63,plain,
% 0.96/0.87 (ssList(nil)),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.96/0.87 tff(64,plain,
% 0.96/0.87 (((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | ((~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | (~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil))))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(65,plain,
% 0.96/0.87 ((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | ((~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil))))),
% 0.96/0.87 inference(quant_inst,[status(thm)],[])).
% 0.96/0.87 tff(66,plain,
% 0.96/0.87 ((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | (~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil)))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.96/0.87 tff(67,plain,
% 0.96/0.87 (neq(W!49, nil) <=> (~(W!49 = nil))),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[66, 63, 60])).
% 0.96/0.87 tff(68,plain,
% 0.96/0.87 (U!47 = W!49),
% 0.96/0.87 inference(and_elim,[status(thm)],[24])).
% 0.96/0.87 tff(69,plain,
% 0.96/0.87 (W!49 = U!47),
% 0.96/0.87 inference(symmetry,[status(thm)],[68])).
% 0.96/0.87 tff(70,plain,
% 0.96/0.87 (neq(W!49, nil) <=> neq(U!47, nil)),
% 0.96/0.87 inference(monotonicity,[status(thm)],[69])).
% 0.96/0.87 tff(71,plain,
% 0.96/0.87 (neq(U!47, nil) <=> neq(W!49, nil)),
% 0.96/0.87 inference(symmetry,[status(thm)],[70])).
% 0.96/0.87 tff(72,plain,
% 0.96/0.87 ((~neq(U!47, nil)) <=> (~neq(W!49, nil))),
% 0.96/0.87 inference(monotonicity,[status(thm)],[71])).
% 0.96/0.87 tff(73,plain,
% 0.96/0.87 (~neq(U!47, nil)),
% 0.96/0.87 inference(and_elim,[status(thm)],[24])).
% 0.96/0.87 tff(74,plain,
% 0.96/0.87 (~neq(W!49, nil)),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.96/0.87 tff(75,plain,
% 0.96/0.87 ((~(neq(W!49, nil) <=> (~(W!49 = nil)))) | neq(W!49, nil) | (W!49 = nil)),
% 0.96/0.88 inference(tautology,[status(thm)],[])).
% 0.96/0.88 tff(76,plain,
% 0.96/0.88 (W!49 = nil),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[75, 74, 67])).
% 0.96/0.88 tff(77,plain,
% 0.96/0.88 (nil = app(nil, W!49)),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[76, 43])).
% 0.96/0.88 tff(78,plain,
% 0.96/0.88 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))))),
% 0.96/0.88 inference(bind,[status(th)],[])).
% 0.96/0.88 tff(79,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 0.96/0.88 inference(quant_intro,[status(thm)],[78])).
% 0.96/0.88 tff(80,plain,
% 0.96/0.88 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))))),
% 0.96/0.88 inference(bind,[status(th)],[])).
% 0.96/0.88 tff(81,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 0.96/0.88 inference(quant_intro,[status(thm)],[80])).
% 0.96/0.88 tff(82,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 0.96/0.88 inference(transitivity,[status(thm)],[81, 79])).
% 0.96/0.88 tff(83,plain,
% 0.96/0.88 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))))),
% 0.96/0.88 inference(bind,[status(th)],[])).
% 0.96/0.88 tff(84,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 0.96/0.88 inference(quant_intro,[status(thm)],[83])).
% 0.96/0.88 tff(85,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(86,plain,
% 0.96/0.88 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))) <=> ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), (![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))) <=> ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))))),
% 0.96/0.88 inference(bind,[status(th)],[])).
% 0.96/0.88 tff(87,plain,
% 0.96/0.88 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 0.96/0.88 inference(quant_intro,[status(thm)],[86])).
% 0.96/0.88 tff(88,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax83')).
% 0.96/0.88 tff(89,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.96/0.88 tff(90,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.96/0.88 tff(91,plain,(
% 0.96/0.88 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 0.96/0.88 inference(skolemize,[status(sab)],[90])).
% 0.96/0.88 tff(92,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.96/0.88 tff(93,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[92, 82])).
% 0.96/0.88 tff(94,plain,
% 0.96/0.88 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V))))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(95,plain,
% 0.96/0.88 (((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (~((~(nil = V)) | (~(nil = nil))))))) <=> ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V))))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(96,plain,
% 0.96/0.88 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (~((~(nil = V)) | (~(nil = nil)))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V)))))),
% 0.96/0.88 inference(monotonicity,[status(thm)],[95])).
% 0.96/0.88 tff(97,plain,
% 0.96/0.88 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (~((~(nil = V)) | (~(nil = nil)))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V))))),
% 0.96/0.88 inference(transitivity,[status(thm)],[96, 94])).
% 0.96/0.88 tff(98,plain,
% 0.96/0.88 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (~((~(nil = V)) | (~(nil = nil)))))))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(99,plain,
% 0.96/0.88 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V)))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.96/0.88 tff(100,plain,
% 0.96/0.88 (![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V)))),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[99, 63, 93])).
% 0.96/0.88 tff(101,plain,
% 0.96/0.88 (((~![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V)))) | ((~ssList(W!49)) | ((nil = app(nil, W!49)) <=> (nil = W!49)))) <=> ((~![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V)))) | (~ssList(W!49)) | ((nil = app(nil, W!49)) <=> (nil = W!49)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(102,plain,
% 0.96/0.88 ((~![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V)))) | ((~ssList(W!49)) | ((nil = app(nil, W!49)) <=> (nil = W!49)))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(103,plain,
% 0.96/0.88 ((~![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V)))) | (~ssList(W!49)) | ((nil = app(nil, W!49)) <=> (nil = W!49))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.96/0.88 tff(104,plain,
% 0.96/0.88 ((nil = app(nil, W!49)) <=> (nil = W!49)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[103, 25, 100])).
% 0.96/0.88 tff(105,plain,
% 0.96/0.88 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.96/0.88 inference(bind,[status(th)],[])).
% 0.96/0.88 tff(106,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.96/0.88 inference(quant_intro,[status(thm)],[105])).
% 0.96/0.88 tff(107,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(108,plain,
% 0.96/0.88 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.96/0.88 inference(bind,[status(th)],[])).
% 0.96/0.88 tff(109,plain,
% 0.96/0.88 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.96/0.88 inference(quant_intro,[status(thm)],[108])).
% 0.96/0.88 tff(110,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax58')).
% 0.96/0.88 tff(111,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.96/0.88 tff(112,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.96/0.88 tff(113,plain,(
% 0.96/0.88 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.96/0.88 inference(skolemize,[status(sab)],[112])).
% 0.96/0.88 tff(114,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[113, 106])).
% 0.96/0.88 tff(115,plain,
% 0.96/0.88 (((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(W!49)) | (segmentP(nil, W!49) <=> (nil = W!49)))) <=> ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(W!49)) | (segmentP(nil, W!49) <=> (nil = W!49)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(116,plain,
% 0.96/0.88 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(W!49)) | (segmentP(nil, W!49) <=> (nil = W!49)))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(117,plain,
% 0.96/0.88 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(W!49)) | (segmentP(nil, W!49) <=> (nil = W!49))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.96/0.88 tff(118,plain,
% 0.96/0.88 (segmentP(nil, W!49) <=> (nil = W!49)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[117, 114, 25])).
% 0.96/0.88 tff(119,plain,
% 0.96/0.88 (V!48 = X!50),
% 0.96/0.88 inference(and_elim,[status(thm)],[24])).
% 0.96/0.88 tff(120,plain,
% 0.96/0.88 (neq(V!48, nil) <=> neq(X!50, nil)),
% 0.96/0.88 inference(monotonicity,[status(thm)],[119])).
% 0.96/0.88 tff(121,plain,
% 0.96/0.88 (neq(V!48, nil)),
% 0.96/0.88 inference(and_elim,[status(thm)],[24])).
% 0.96/0.88 tff(122,plain,
% 0.96/0.88 (neq(X!50, nil)),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.96/0.88 tff(123,plain,
% 0.96/0.88 ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~neq(X!50, nil))),
% 0.96/0.88 inference(and_elim,[status(thm)],[24])).
% 0.96/0.88 tff(124,plain,
% 0.96/0.88 (~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.96/0.88 tff(125,plain,
% 0.96/0.88 (((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51))) | ssList(Y!51)),
% 0.96/0.88 inference(tautology,[status(thm)],[])).
% 0.96/0.88 tff(126,plain,
% 0.96/0.88 (ssList(Y!51)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.96/0.88 tff(127,plain,
% 0.96/0.88 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | ((~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | (neq(Y!51, V) <=> (~(Y!51 = V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | (~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | (neq(Y!51, V) <=> (~(Y!51 = V)))))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(128,plain,
% 0.96/0.88 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | ((~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | (neq(Y!51, V) <=> (~(Y!51 = V)))))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(129,plain,
% 0.96/0.88 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | (~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | (neq(Y!51, V) <=> (~(Y!51 = V))))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.96/0.88 tff(130,plain,
% 0.96/0.88 (![V: $i] : ((~ssList(V)) | (neq(Y!51, V) <=> (~(Y!51 = V))))),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[129, 56, 126])).
% 0.96/0.88 tff(131,plain,
% 0.96/0.88 (((~![V: $i] : ((~ssList(V)) | (neq(Y!51, V) <=> (~(Y!51 = V))))) | ((~ssList(nil)) | (neq(Y!51, nil) <=> (~(Y!51 = nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (neq(Y!51, V) <=> (~(Y!51 = V))))) | (~ssList(nil)) | (neq(Y!51, nil) <=> (~(Y!51 = nil))))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(132,plain,
% 0.96/0.88 ((~![V: $i] : ((~ssList(V)) | (neq(Y!51, V) <=> (~(Y!51 = V))))) | ((~ssList(nil)) | (neq(Y!51, nil) <=> (~(Y!51 = nil))))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(133,plain,
% 0.96/0.88 ((~![V: $i] : ((~ssList(V)) | (neq(Y!51, V) <=> (~(Y!51 = V))))) | (~ssList(nil)) | (neq(Y!51, nil) <=> (~(Y!51 = nil)))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.96/0.88 tff(134,plain,
% 0.96/0.88 (neq(Y!51, nil) <=> (~(Y!51 = nil))),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[133, 63, 130])).
% 0.96/0.88 tff(135,plain,
% 0.96/0.88 (((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51))) | neq(Y!51, nil)),
% 0.96/0.88 inference(tautology,[status(thm)],[])).
% 0.96/0.88 tff(136,plain,
% 0.96/0.88 (neq(Y!51, nil)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[135, 124])).
% 0.96/0.88 tff(137,plain,
% 0.96/0.88 ((~(neq(Y!51, nil) <=> (~(Y!51 = nil)))) | (~neq(Y!51, nil)) | (~(Y!51 = nil))),
% 0.96/0.88 inference(tautology,[status(thm)],[])).
% 0.96/0.88 tff(138,plain,
% 0.96/0.88 ((~(neq(Y!51, nil) <=> (~(Y!51 = nil)))) | (~(Y!51 = nil))),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.96/0.88 tff(139,plain,
% 0.96/0.88 (~(Y!51 = nil)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[138, 134])).
% 0.96/0.88 tff(140,plain,
% 0.96/0.88 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U)))))),
% 0.96/0.88 inference(bind,[status(th)],[])).
% 0.96/0.88 tff(141,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))),
% 0.96/0.88 inference(quant_intro,[status(thm)],[140])).
% 0.96/0.88 tff(142,plain,
% 0.96/0.88 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U)))))),
% 0.96/0.88 inference(bind,[status(th)],[])).
% 0.96/0.88 tff(143,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))),
% 0.96/0.88 inference(quant_intro,[status(thm)],[142])).
% 0.96/0.88 tff(144,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))),
% 0.96/0.88 inference(transitivity,[status(thm)],[143, 141])).
% 0.96/0.88 tff(145,plain,
% 0.96/0.88 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U)))))),
% 0.96/0.88 inference(bind,[status(th)],[])).
% 0.96/0.88 tff(146,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))),
% 0.96/0.88 inference(quant_intro,[status(thm)],[145])).
% 0.96/0.88 tff(147,plain,
% 0.96/0.88 (![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)))))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(148,plain,
% 0.96/0.88 (^[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)))))))),
% 0.96/0.88 inference(bind,[status(th)],[])).
% 0.96/0.88 tff(149,plain,
% 0.96/0.88 (![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)))))),
% 0.96/0.88 inference(quant_intro,[status(thm)],[148])).
% 0.96/0.88 tff(150,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax54')).
% 0.96/0.88 tff(151,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.96/0.88 tff(152,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[151, 147])).
% 0.96/0.88 tff(153,plain,(
% 0.96/0.88 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.96/0.88 inference(skolemize,[status(sab)],[152])).
% 0.96/0.88 tff(154,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[153, 146])).
% 0.96/0.88 tff(155,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[154, 144])).
% 0.96/0.88 tff(156,plain,
% 0.96/0.88 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))) | ((~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))) | (~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51))))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(157,plain,
% 0.96/0.88 (((~ssList(Y!51)) | ![V: $i] : ((Y!51 = V) | (~segmentP(Y!51, V)) | (~ssList(V)) | (~segmentP(V, Y!51)))) <=> ((~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51))))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(158,plain,
% 0.96/0.88 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))) | ((~ssList(Y!51)) | ![V: $i] : ((Y!51 = V) | (~segmentP(Y!51, V)) | (~ssList(V)) | (~segmentP(V, Y!51))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))) | ((~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51)))))),
% 0.96/0.88 inference(monotonicity,[status(thm)],[157])).
% 0.96/0.88 tff(159,plain,
% 0.96/0.88 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))) | ((~ssList(Y!51)) | ![V: $i] : ((Y!51 = V) | (~segmentP(Y!51, V)) | (~ssList(V)) | (~segmentP(V, Y!51))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))) | (~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51))))),
% 0.96/0.88 inference(transitivity,[status(thm)],[158, 156])).
% 0.96/0.88 tff(160,plain,
% 0.96/0.88 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))) | ((~ssList(Y!51)) | ![V: $i] : ((Y!51 = V) | (~segmentP(Y!51, V)) | (~ssList(V)) | (~segmentP(V, Y!51))))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(161,plain,
% 0.96/0.88 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))) | (~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51)))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.96/0.88 tff(162,plain,
% 0.96/0.88 (![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51)))),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[161, 155, 126])).
% 0.96/0.88 tff(163,plain,
% 0.96/0.88 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.96/0.88 inference(bind,[status(th)],[])).
% 0.96/0.88 tff(164,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.96/0.88 inference(quant_intro,[status(thm)],[163])).
% 0.96/0.88 tff(165,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(166,plain,
% 0.96/0.88 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.96/0.88 inference(bind,[status(th)],[])).
% 0.96/0.88 tff(167,plain,
% 0.96/0.88 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.96/0.88 inference(quant_intro,[status(thm)],[166])).
% 0.96/0.88 tff(168,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax57')).
% 0.96/0.88 tff(169,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.96/0.88 tff(170,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[169, 165])).
% 0.96/0.88 tff(171,plain,(
% 0.96/0.88 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.96/0.88 inference(skolemize,[status(sab)],[170])).
% 0.96/0.88 tff(172,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[171, 164])).
% 0.96/0.88 tff(173,plain,
% 0.96/0.88 (((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(Y!51)) | segmentP(Y!51, nil))) <=> ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(Y!51)) | segmentP(Y!51, nil))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(174,plain,
% 0.96/0.88 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(Y!51)) | segmentP(Y!51, nil))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(175,plain,
% 0.96/0.88 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(Y!51)) | segmentP(Y!51, nil)),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.96/0.88 tff(176,plain,
% 0.96/0.88 (segmentP(Y!51, nil)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[175, 172, 126])).
% 0.96/0.88 tff(177,plain,
% 0.96/0.88 (((~![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51)))) | ((~ssList(nil)) | (~segmentP(nil, Y!51)) | (Y!51 = nil) | (~segmentP(Y!51, nil)))) <=> ((~![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51)))) | (~ssList(nil)) | (~segmentP(nil, Y!51)) | (Y!51 = nil) | (~segmentP(Y!51, nil)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(178,plain,
% 0.96/0.88 (((~ssList(nil)) | (~segmentP(Y!51, nil)) | (Y!51 = nil) | (~segmentP(nil, Y!51))) <=> ((~ssList(nil)) | (~segmentP(nil, Y!51)) | (Y!51 = nil) | (~segmentP(Y!51, nil)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(179,plain,
% 0.96/0.88 (((~![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51)))) | ((~ssList(nil)) | (~segmentP(Y!51, nil)) | (Y!51 = nil) | (~segmentP(nil, Y!51)))) <=> ((~![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51)))) | ((~ssList(nil)) | (~segmentP(nil, Y!51)) | (Y!51 = nil) | (~segmentP(Y!51, nil))))),
% 0.96/0.88 inference(monotonicity,[status(thm)],[178])).
% 0.96/0.88 tff(180,plain,
% 0.96/0.88 (((~![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51)))) | ((~ssList(nil)) | (~segmentP(Y!51, nil)) | (Y!51 = nil) | (~segmentP(nil, Y!51)))) <=> ((~![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51)))) | (~ssList(nil)) | (~segmentP(nil, Y!51)) | (Y!51 = nil) | (~segmentP(Y!51, nil)))),
% 0.96/0.88 inference(transitivity,[status(thm)],[179, 177])).
% 0.96/0.88 tff(181,plain,
% 0.96/0.88 ((~![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51)))) | ((~ssList(nil)) | (~segmentP(Y!51, nil)) | (Y!51 = nil) | (~segmentP(nil, Y!51)))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(182,plain,
% 0.96/0.88 ((~![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51)))) | (~ssList(nil)) | (~segmentP(nil, Y!51)) | (Y!51 = nil) | (~segmentP(Y!51, nil))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.96/0.88 tff(183,plain,
% 0.96/0.88 ((~segmentP(nil, Y!51)) | (Y!51 = nil)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[182, 63, 176, 162])).
% 0.96/0.88 tff(184,plain,
% 0.96/0.88 (~segmentP(nil, Y!51)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[183, 139])).
% 0.96/0.88 tff(185,plain,
% 0.96/0.88 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(U, V))))))),
% 0.96/0.88 inference(bind,[status(th)],[])).
% 0.96/0.88 tff(186,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(U, V)))))),
% 0.96/0.88 inference(quant_intro,[status(thm)],[185])).
% 0.96/0.88 tff(187,plain,
% 0.96/0.88 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(U, V))))))),
% 0.96/0.88 inference(bind,[status(th)],[])).
% 0.96/0.88 tff(188,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(U, V)))))),
% 0.96/0.88 inference(quant_intro,[status(thm)],[187])).
% 0.96/0.88 tff(189,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(U, V)))))),
% 0.96/0.88 inference(transitivity,[status(thm)],[188, 186])).
% 0.96/0.88 tff(190,plain,
% 0.96/0.88 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~ssList(W)) | (~(segmentP(U, V) & segmentP(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(U, V))))))),
% 0.96/0.88 inference(bind,[status(th)],[])).
% 0.96/0.88 tff(191,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~ssList(W)) | (~(segmentP(U, V) & segmentP(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(U, V)))))),
% 0.96/0.88 inference(quant_intro,[status(thm)],[190])).
% 0.96/0.88 tff(192,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~ssList(W)) | (~(segmentP(U, V) & segmentP(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~ssList(W)) | (~(segmentP(U, V) & segmentP(V, W))))))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(193,plain,
% 0.96/0.88 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : trans(monotonicity(rewrite(((segmentP(U, V) & segmentP(V, W)) => segmentP(U, W)) <=> ((~(segmentP(U, V) & segmentP(V, W))) | segmentP(U, W))), ((ssList(W) => ((segmentP(U, V) & segmentP(V, W)) => segmentP(U, W))) <=> (ssList(W) => ((~(segmentP(U, V) & segmentP(V, W))) | segmentP(U, W))))), rewrite((ssList(W) => ((~(segmentP(U, V) & segmentP(V, W))) | segmentP(U, W))) <=> (segmentP(U, W) | (~ssList(W)) | (~(segmentP(U, V) & segmentP(V, W))))), ((ssList(W) => ((segmentP(U, V) & segmentP(V, W)) => segmentP(U, W))) <=> (segmentP(U, W) | (~ssList(W)) | (~(segmentP(U, V) & segmentP(V, W))))))), (![W: $i] : (ssList(W) => ((segmentP(U, V) & segmentP(V, W)) => segmentP(U, W))) <=> ![W: $i] : (segmentP(U, W) | (~ssList(W)) | (~(segmentP(U, V) & segmentP(V, W)))))), ((ssList(V) => ![W: $i] : (ssList(W) => ((segmentP(U, V) & segmentP(V, W)) => segmentP(U, W)))) <=> (ssList(V) => ![W: $i] : (segmentP(U, W) | (~ssList(W)) | (~(segmentP(U, V) & segmentP(V, W))))))), rewrite((ssList(V) => ![W: $i] : (segmentP(U, W) | (~ssList(W)) | (~(segmentP(U, V) & segmentP(V, W))))) <=> ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~ssList(W)) | (~(segmentP(U, V) & segmentP(V, W)))))), ((ssList(V) => ![W: $i] : (ssList(W) => ((segmentP(U, V) & segmentP(V, W)) => segmentP(U, W)))) <=> ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~ssList(W)) | (~(segmentP(U, V) & segmentP(V, W)))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((segmentP(U, V) & segmentP(V, W)) => segmentP(U, W)))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~ssList(W)) | (~(segmentP(U, V) & segmentP(V, W))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((segmentP(U, V) & segmentP(V, W)) => segmentP(U, W))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~ssList(W)) | (~(segmentP(U, V) & segmentP(V, W)))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~ssList(W)) | (~(segmentP(U, V) & segmentP(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~ssList(W)) | (~(segmentP(U, V) & segmentP(V, W))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((segmentP(U, V) & segmentP(V, W)) => segmentP(U, W))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~ssList(W)) | (~(segmentP(U, V) & segmentP(V, W))))))))),
% 0.96/0.88 inference(bind,[status(th)],[])).
% 0.96/0.88 tff(194,plain,
% 0.96/0.88 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((segmentP(U, V) & segmentP(V, W)) => segmentP(U, W))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~ssList(W)) | (~(segmentP(U, V) & segmentP(V, W))))))),
% 0.96/0.88 inference(quant_intro,[status(thm)],[193])).
% 0.96/0.88 tff(195,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((segmentP(U, V) & segmentP(V, W)) => segmentP(U, W)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax53')).
% 0.96/0.88 tff(196,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~ssList(W)) | (~(segmentP(U, V) & segmentP(V, W))))))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.96/0.88 tff(197,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~ssList(W)) | (~(segmentP(U, V) & segmentP(V, W))))))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[196, 192])).
% 0.96/0.88 tff(198,plain,(
% 0.96/0.88 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~ssList(W)) | (~(segmentP(U, V) & segmentP(V, W))))))),
% 0.96/0.88 inference(skolemize,[status(sab)],[197])).
% 0.96/0.88 tff(199,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(U, V)))))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[198, 191])).
% 0.96/0.88 tff(200,plain,
% 0.96/0.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(U, V)))))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[199, 189])).
% 0.96/0.88 tff(201,plain,
% 0.96/0.88 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(U, V)))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(nil, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(nil, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(U, V)))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(nil, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(nil, V)))))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(202,plain,
% 0.96/0.88 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(U, V)))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(nil, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(nil, V)))))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(203,plain,
% 0.96/0.88 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(U, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(U, V)))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(nil, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(nil, V))))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.96/0.88 tff(204,plain,
% 0.96/0.88 (![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(nil, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(nil, V))))),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[203, 63, 200])).
% 0.96/0.88 tff(205,plain,
% 0.96/0.88 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(nil, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(nil, V))))) | ((~ssList(W!49)) | ![W: $i] : (segmentP(nil, W) | (~ssList(W)) | (~segmentP(W!49, W)) | (~segmentP(nil, W!49))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(nil, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(nil, V))))) | (~ssList(W!49)) | ![W: $i] : (segmentP(nil, W) | (~ssList(W)) | (~segmentP(W!49, W)) | (~segmentP(nil, W!49))))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(206,plain,
% 0.96/0.88 (((~ssList(W!49)) | ![W: $i] : (segmentP(nil, W) | (~segmentP(W!49, W)) | (~ssList(W)) | (~segmentP(nil, W!49)))) <=> ((~ssList(W!49)) | ![W: $i] : (segmentP(nil, W) | (~ssList(W)) | (~segmentP(W!49, W)) | (~segmentP(nil, W!49))))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(207,plain,
% 0.96/0.88 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(nil, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(nil, V))))) | ((~ssList(W!49)) | ![W: $i] : (segmentP(nil, W) | (~segmentP(W!49, W)) | (~ssList(W)) | (~segmentP(nil, W!49))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(nil, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(nil, V))))) | ((~ssList(W!49)) | ![W: $i] : (segmentP(nil, W) | (~ssList(W)) | (~segmentP(W!49, W)) | (~segmentP(nil, W!49)))))),
% 0.96/0.88 inference(monotonicity,[status(thm)],[206])).
% 0.96/0.88 tff(208,plain,
% 0.96/0.88 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(nil, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(nil, V))))) | ((~ssList(W!49)) | ![W: $i] : (segmentP(nil, W) | (~segmentP(W!49, W)) | (~ssList(W)) | (~segmentP(nil, W!49))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(nil, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(nil, V))))) | (~ssList(W!49)) | ![W: $i] : (segmentP(nil, W) | (~ssList(W)) | (~segmentP(W!49, W)) | (~segmentP(nil, W!49))))),
% 0.96/0.88 inference(transitivity,[status(thm)],[207, 205])).
% 0.96/0.88 tff(209,plain,
% 0.96/0.88 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(nil, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(nil, V))))) | ((~ssList(W!49)) | ![W: $i] : (segmentP(nil, W) | (~segmentP(W!49, W)) | (~ssList(W)) | (~segmentP(nil, W!49))))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(210,plain,
% 0.96/0.88 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : (segmentP(nil, W) | (~segmentP(V, W)) | (~ssList(W)) | (~segmentP(nil, V))))) | (~ssList(W!49)) | ![W: $i] : (segmentP(nil, W) | (~ssList(W)) | (~segmentP(W!49, W)) | (~segmentP(nil, W!49)))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.96/0.89 tff(211,plain,
% 0.96/0.89 (![W: $i] : (segmentP(nil, W) | (~ssList(W)) | (~segmentP(W!49, W)) | (~segmentP(nil, W!49)))),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[210, 25, 204])).
% 0.96/0.89 tff(212,plain,
% 0.96/0.89 (((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51))) | segmentP(W!49, Y!51)),
% 0.96/0.89 inference(tautology,[status(thm)],[])).
% 0.96/0.89 tff(213,plain,
% 0.96/0.89 (segmentP(W!49, Y!51)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[212, 124])).
% 0.96/0.89 tff(214,plain,
% 0.96/0.89 (((~![W: $i] : (segmentP(nil, W) | (~ssList(W)) | (~segmentP(W!49, W)) | (~segmentP(nil, W!49)))) | ((~segmentP(W!49, Y!51)) | (~ssList(Y!51)) | (~segmentP(nil, W!49)) | segmentP(nil, Y!51))) <=> ((~![W: $i] : (segmentP(nil, W) | (~ssList(W)) | (~segmentP(W!49, W)) | (~segmentP(nil, W!49)))) | (~segmentP(W!49, Y!51)) | (~ssList(Y!51)) | (~segmentP(nil, W!49)) | segmentP(nil, Y!51))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(215,plain,
% 0.96/0.89 ((segmentP(nil, Y!51) | (~ssList(Y!51)) | (~segmentP(W!49, Y!51)) | (~segmentP(nil, W!49))) <=> ((~segmentP(W!49, Y!51)) | (~ssList(Y!51)) | (~segmentP(nil, W!49)) | segmentP(nil, Y!51))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(216,plain,
% 0.96/0.89 (((~![W: $i] : (segmentP(nil, W) | (~ssList(W)) | (~segmentP(W!49, W)) | (~segmentP(nil, W!49)))) | (segmentP(nil, Y!51) | (~ssList(Y!51)) | (~segmentP(W!49, Y!51)) | (~segmentP(nil, W!49)))) <=> ((~![W: $i] : (segmentP(nil, W) | (~ssList(W)) | (~segmentP(W!49, W)) | (~segmentP(nil, W!49)))) | ((~segmentP(W!49, Y!51)) | (~ssList(Y!51)) | (~segmentP(nil, W!49)) | segmentP(nil, Y!51)))),
% 0.96/0.89 inference(monotonicity,[status(thm)],[215])).
% 0.96/0.89 tff(217,plain,
% 0.96/0.89 (((~![W: $i] : (segmentP(nil, W) | (~ssList(W)) | (~segmentP(W!49, W)) | (~segmentP(nil, W!49)))) | (segmentP(nil, Y!51) | (~ssList(Y!51)) | (~segmentP(W!49, Y!51)) | (~segmentP(nil, W!49)))) <=> ((~![W: $i] : (segmentP(nil, W) | (~ssList(W)) | (~segmentP(W!49, W)) | (~segmentP(nil, W!49)))) | (~segmentP(W!49, Y!51)) | (~ssList(Y!51)) | (~segmentP(nil, W!49)) | segmentP(nil, Y!51))),
% 0.96/0.89 inference(transitivity,[status(thm)],[216, 214])).
% 0.96/0.89 tff(218,plain,
% 0.96/0.89 ((~![W: $i] : (segmentP(nil, W) | (~ssList(W)) | (~segmentP(W!49, W)) | (~segmentP(nil, W!49)))) | (segmentP(nil, Y!51) | (~ssList(Y!51)) | (~segmentP(W!49, Y!51)) | (~segmentP(nil, W!49)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(219,plain,
% 0.96/0.89 ((~![W: $i] : (segmentP(nil, W) | (~ssList(W)) | (~segmentP(W!49, W)) | (~segmentP(nil, W!49)))) | (~segmentP(W!49, Y!51)) | (~ssList(Y!51)) | (~segmentP(nil, W!49)) | segmentP(nil, Y!51)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.96/0.89 tff(220,plain,
% 0.96/0.89 ((~segmentP(nil, W!49)) | segmentP(nil, Y!51)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[219, 213, 126, 211])).
% 0.96/0.89 tff(221,plain,
% 0.96/0.89 (~segmentP(nil, W!49)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[220, 184])).
% 0.96/0.89 tff(222,plain,
% 0.96/0.89 ((~(segmentP(nil, W!49) <=> (nil = W!49))) | segmentP(nil, W!49) | (~(nil = W!49))),
% 0.96/0.89 inference(tautology,[status(thm)],[])).
% 0.96/0.89 tff(223,plain,
% 0.96/0.89 (~(nil = W!49)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[222, 221, 118])).
% 0.96/0.89 tff(224,plain,
% 0.96/0.89 ((~((nil = app(nil, W!49)) <=> (nil = W!49))) | (~(nil = app(nil, W!49))) | (nil = W!49)),
% 0.96/0.89 inference(tautology,[status(thm)],[])).
% 0.96/0.89 tff(225,plain,
% 0.96/0.89 (~(nil = app(nil, W!49))),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[224, 223, 104])).
% 0.96/0.89 tff(226,plain,
% 0.96/0.89 ($false),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[225, 77])).
% 0.96/0.89 % SZS output end Proof
%------------------------------------------------------------------------------