TSTP Solution File: SWC256+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC256+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 11:56:35 EDT 2022
% Result : Theorem 4.50s 3.07s
% Output : Proof 4.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC256+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 : n010.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
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 3 23:05:12 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.
% 4.50/3.07 % SZS status Theorem
% 4.50/3.07 % SZS output start Proof
% 4.50/3.07 tff(tptp_fun_W_49_type, type, (
% 4.50/3.07 tptp_fun_W_49: $i)).
% 4.50/3.07 tff(cons_type, type, (
% 4.50/3.07 cons: ( $i * $i ) > $i)).
% 4.50/3.07 tff(nil_type, type, (
% 4.50/3.07 nil: $i)).
% 4.50/3.07 tff(ssItem_type, type, (
% 4.50/3.07 ssItem: $i > $o)).
% 4.50/3.07 tff(singletonP_type, type, (
% 4.50/3.07 singletonP: $i > $o)).
% 4.50/3.07 tff(tptp_fun_V_4_type, type, (
% 4.50/3.07 tptp_fun_V_4: $i > $i)).
% 4.50/3.07 tff(ssList_type, type, (
% 4.50/3.07 ssList: $i > $o)).
% 4.50/3.07 tff(tptp_fun_X_50_type, type, (
% 4.50/3.07 tptp_fun_X_50: $i)).
% 4.50/3.07 tff(tptp_fun_Y_51_type, type, (
% 4.50/3.07 tptp_fun_Y_51: $i)).
% 4.50/3.07 tff(memberP_type, type, (
% 4.50/3.07 memberP: ( $i * $i ) > $o)).
% 4.50/3.07 tff(tptp_fun_V_48_type, type, (
% 4.50/3.07 tptp_fun_V_48: $i)).
% 4.50/3.07 tff(tptp_fun_U_47_type, type, (
% 4.50/3.07 tptp_fun_U_47: $i)).
% 4.50/3.07 tff(neq_type, type, (
% 4.50/3.07 neq: ( $i * $i ) > $o)).
% 4.50/3.07 tff(segmentP_type, type, (
% 4.50/3.07 segmentP: ( $i * $i ) > $o)).
% 4.50/3.07 tff(1,plain,
% 4.50/3.07 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~singletonP(U!47)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~singletonP(U!47)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 4.50/3.07 inference(rewrite,[status(thm)],[])).
% 4.50/3.07 tff(2,plain,
% 4.50/3.07 ((ssList(V!48) & (ssList(W!49) & (~singletonP(U!47)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))) <=> (ssList(V!48) & ssList(W!49) & (~singletonP(U!47)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 4.50/3.07 inference(rewrite,[status(thm)],[])).
% 4.50/3.07 tff(3,plain,
% 4.50/3.07 ((ssList(W!49) & ((~singletonP(U!47)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))) <=> (ssList(W!49) & (~singletonP(U!47)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 4.50/3.07 inference(rewrite,[status(thm)],[])).
% 4.50/3.07 tff(4,plain,
% 4.50/3.07 (((~singletonP(U!47)) & (~(~neq(V!48, nil))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~((~(nil = X!50)) | (~(nil = W!49)))))) <=> ((~singletonP(U!47)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 4.50/3.07 inference(rewrite,[status(thm)],[])).
% 4.50/3.07 tff(5,plain,
% 4.50/3.07 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 4.50/3.07 inference(rewrite,[status(thm)],[])).
% 4.50/3.07 tff(6,plain,
% 4.50/3.07 (((~(~ssList(W!49))) & ((~singletonP(U!47)) & (~(~neq(V!48, nil))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~((~(nil = X!50)) | (~(nil = W!49))))))) <=> (ssList(W!49) & ((~singletonP(U!47)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50)))))))),
% 4.50/3.07 inference(monotonicity,[status(thm)],[5, 4])).
% 4.50/3.07 tff(7,plain,
% 4.50/3.07 (((~(~ssList(W!49))) & ((~singletonP(U!47)) & (~(~neq(V!48, nil))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~((~(nil = X!50)) | (~(nil = W!49))))))) <=> (ssList(W!49) & (~singletonP(U!47)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 4.50/3.07 inference(transitivity,[status(thm)],[6, 3])).
% 4.50/3.07 tff(8,plain,
% 4.50/3.07 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 4.50/3.07 inference(rewrite,[status(thm)],[])).
% 4.50/3.07 tff(9,plain,
% 4.50/3.07 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~singletonP(U!47)) & (~(~neq(V!48, nil))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~((~(nil = X!50)) | (~(nil = W!49)))))))) <=> (ssList(V!48) & (ssList(W!49) & (~singletonP(U!47)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50)))))))),
% 4.50/3.07 inference(monotonicity,[status(thm)],[8, 7])).
% 4.50/3.07 tff(10,plain,
% 4.50/3.07 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~singletonP(U!47)) & (~(~neq(V!48, nil))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~((~(nil = X!50)) | (~(nil = W!49)))))))) <=> (ssList(V!48) & ssList(W!49) & (~singletonP(U!47)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 4.50/3.07 inference(transitivity,[status(thm)],[9, 2])).
% 4.50/3.07 tff(11,plain,
% 4.50/3.07 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 4.50/3.07 inference(rewrite,[status(thm)],[])).
% 4.50/3.07 tff(12,plain,
% 4.50/3.07 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~singletonP(U!47)) & (~(~neq(V!48, nil))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~((~(nil = X!50)) | (~(nil = W!49))))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~singletonP(U!47)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50)))))))),
% 4.50/3.07 inference(monotonicity,[status(thm)],[11, 10])).
% 4.50/3.07 tff(13,plain,
% 4.50/3.07 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~singletonP(U!47)) & (~(~neq(V!48, nil))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~((~(nil = X!50)) | (~(nil = W!49))))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~singletonP(U!47)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 4.50/3.07 inference(transitivity,[status(thm)],[12, 1])).
% 4.50/3.07 tff(14,plain,
% 4.50/3.07 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (singletonP(U) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & ((~(nil = X)) | (~(nil = W))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (singletonP(U) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & ((~(nil = X)) | (~(nil = W)))))))))),
% 4.50/3.07 inference(rewrite,[status(thm)],[])).
% 4.50/3.07 tff(15,plain,
% 4.50/3.07 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | singletonP(U)) | (![Y: $i] : (ssItem(Y) => ((~(cons(Y, nil) = W)) | (~memberP(X, Y)))) & ((~(nil = X)) | (~(nil = W)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (singletonP(U) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & ((~(nil = X)) | (~(nil = W)))))))))),
% 4.50/3.07 inference(rewrite,[status(thm)],[])).
% 4.50/3.07 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))) | singletonP(U)) | (![Y: $i] : (ssItem(Y) => ((~(cons(Y, nil) = W)) | (~memberP(X, Y)))) & ((~(nil = X)) | (~(nil = W)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 4.50/3.08 tff(17,plain,
% 4.50/3.08 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (singletonP(U) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & ((~(nil = X)) | (~(nil = W))))))))),
% 4.50/3.08 inference(modus_ponens,[status(thm)],[16, 15])).
% 4.50/3.08 tff(18,plain,
% 4.50/3.08 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (singletonP(U) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & ((~(nil = X)) | (~(nil = W))))))))),
% 4.50/3.08 inference(modus_ponens,[status(thm)],[17, 14])).
% 4.50/3.08 tff(19,plain,
% 4.50/3.08 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (singletonP(U) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & ((~(nil = X)) | (~(nil = W))))))))),
% 4.50/3.08 inference(modus_ponens,[status(thm)],[18, 14])).
% 4.50/3.08 tff(20,plain,
% 4.50/3.08 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (singletonP(U) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & ((~(nil = X)) | (~(nil = W))))))))),
% 4.50/3.08 inference(modus_ponens,[status(thm)],[19, 14])).
% 4.50/3.08 tff(21,plain,
% 4.50/3.08 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (singletonP(U) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & ((~(nil = X)) | (~(nil = W))))))))),
% 4.50/3.08 inference(modus_ponens,[status(thm)],[20, 14])).
% 4.50/3.08 tff(22,plain,
% 4.50/3.08 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (singletonP(U) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & ((~(nil = X)) | (~(nil = W))))))))),
% 4.50/3.08 inference(modus_ponens,[status(thm)],[21, 14])).
% 4.50/3.08 tff(23,plain,
% 4.50/3.08 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (singletonP(U) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & ((~(nil = X)) | (~(nil = W))))))))),
% 4.50/3.08 inference(modus_ponens,[status(thm)],[22, 14])).
% 4.50/3.08 tff(24,plain,
% 4.50/3.08 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~singletonP(U!47)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50)))))),
% 4.50/3.08 inference(modus_ponens,[status(thm)],[23, 13])).
% 4.50/3.08 tff(25,plain,
% 4.50/3.08 (ssList(W!49)),
% 4.50/3.08 inference(and_elim,[status(thm)],[24])).
% 4.50/3.08 tff(26,plain,
% 4.50/3.08 (^[U: $i] : refl(((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))) <=> ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))))),
% 4.50/3.08 inference(bind,[status(th)],[])).
% 4.50/3.08 tff(27,plain,
% 4.50/3.08 (![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))),
% 4.50/3.08 inference(quant_intro,[status(thm)],[26])).
% 4.50/3.08 tff(28,plain,
% 4.50/3.08 (^[U: $i] : rewrite(((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))) <=> ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))))),
% 4.50/3.08 inference(bind,[status(th)],[])).
% 4.50/3.08 tff(29,plain,
% 4.50/3.08 (![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))),
% 4.50/3.08 inference(quant_intro,[status(thm)],[28])).
% 4.50/3.08 tff(30,plain,
% 4.50/3.08 (![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))),
% 4.50/3.08 inference(transitivity,[status(thm)],[29, 27])).
% 4.50/3.08 tff(31,plain,
% 4.50/3.08 (^[U: $i] : rewrite(((~ssList(U)) | (((~singletonP(U)) | (ssItem(tptp_fun_V_4(U)) & (cons(tptp_fun_V_4(U), nil) = U))) & (singletonP(U) | ![V: $i] : (~(ssItem(V) & (cons(V, nil) = U)))))) <=> ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))))),
% 4.50/3.08 inference(bind,[status(th)],[])).
% 4.50/3.08 tff(32,plain,
% 4.50/3.08 (![U: $i] : ((~ssList(U)) | (((~singletonP(U)) | (ssItem(tptp_fun_V_4(U)) & (cons(tptp_fun_V_4(U), nil) = U))) & (singletonP(U) | ![V: $i] : (~(ssItem(V) & (cons(V, nil) = U)))))) <=> ![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))),
% 4.50/3.08 inference(quant_intro,[status(thm)],[31])).
% 4.50/3.08 tff(33,plain,
% 4.50/3.08 (![U: $i] : ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))) <=> ![U: $i] : ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))),
% 4.50/3.08 inference(rewrite,[status(thm)],[])).
% 4.50/3.08 tff(34,plain,
% 4.50/3.08 (^[U: $i] : trans(monotonicity(rewrite((singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))) <=> (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))), ((ssList(U) => (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))) <=> (ssList(U) => (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))))), rewrite((ssList(U) => (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))) <=> ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))), ((ssList(U) => (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))) <=> ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))))),
% 4.50/3.08 inference(bind,[status(th)],[])).
% 4.50/3.08 tff(35,plain,
% 4.50/3.08 (![U: $i] : (ssList(U) => (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))) <=> ![U: $i] : ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))),
% 4.50/3.08 inference(quant_intro,[status(thm)],[34])).
% 4.50/3.08 tff(36,axiom,(![U: $i] : (ssList(U) => (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax4')).
% 4.50/3.08 tff(37,plain,
% 4.50/3.08 (![U: $i] : ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))),
% 4.50/3.08 inference(modus_ponens,[status(thm)],[36, 35])).
% 4.50/3.08 tff(38,plain,
% 4.50/3.08 (![U: $i] : ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))),
% 4.50/3.08 inference(modus_ponens,[status(thm)],[37, 33])).
% 4.50/3.08 tff(39,plain,(
% 4.50/3.08 ![U: $i] : ((~ssList(U)) | (((~singletonP(U)) | (ssItem(tptp_fun_V_4(U)) & (cons(tptp_fun_V_4(U), nil) = U))) & (singletonP(U) | ![V: $i] : (~(ssItem(V) & (cons(V, nil) = U))))))),
% 4.50/3.08 inference(skolemize,[status(sab)],[38])).
% 4.50/3.08 tff(40,plain,
% 4.50/3.08 (![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))),
% 4.50/3.08 inference(modus_ponens,[status(thm)],[39, 32])).
% 4.50/3.08 tff(41,plain,
% 4.50/3.08 (![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))),
% 4.50/3.08 inference(modus_ponens,[status(thm)],[40, 30])).
% 4.50/3.08 tff(42,plain,
% 4.50/3.08 (((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | ((~ssList(W!49)) | (~((~((~singletonP(W!49)) | (~((~ssItem(tptp_fun_V_4(W!49))) | (~(cons(tptp_fun_V_4(W!49), nil) = W!49)))))) | (~(singletonP(W!49) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = W!49))))))))) <=> ((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | (~ssList(W!49)) | (~((~((~singletonP(W!49)) | (~((~ssItem(tptp_fun_V_4(W!49))) | (~(cons(tptp_fun_V_4(W!49), nil) = W!49)))))) | (~(singletonP(W!49) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = W!49))))))))),
% 4.50/3.08 inference(rewrite,[status(thm)],[])).
% 4.50/3.08 tff(43,plain,
% 4.50/3.08 ((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | ((~ssList(W!49)) | (~((~((~singletonP(W!49)) | (~((~ssItem(tptp_fun_V_4(W!49))) | (~(cons(tptp_fun_V_4(W!49), nil) = W!49)))))) | (~(singletonP(W!49) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = W!49))))))))),
% 4.50/3.08 inference(quant_inst,[status(thm)],[])).
% 4.50/3.08 tff(44,plain,
% 4.50/3.08 ((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | (~ssList(W!49)) | (~((~((~singletonP(W!49)) | (~((~ssItem(tptp_fun_V_4(W!49))) | (~(cons(tptp_fun_V_4(W!49), nil) = W!49)))))) | (~(singletonP(W!49) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = W!49)))))))),
% 4.50/3.08 inference(modus_ponens,[status(thm)],[43, 42])).
% 4.50/3.08 tff(45,plain,
% 4.50/3.08 (~((~((~singletonP(W!49)) | (~((~ssItem(tptp_fun_V_4(W!49))) | (~(cons(tptp_fun_V_4(W!49), nil) = W!49)))))) | (~(singletonP(W!49) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = W!49))))))),
% 4.50/3.08 inference(unit_resolution,[status(thm)],[44, 41, 25])).
% 4.50/3.08 tff(46,plain,
% 4.50/3.08 (((~((~singletonP(W!49)) | (~((~ssItem(tptp_fun_V_4(W!49))) | (~(cons(tptp_fun_V_4(W!49), nil) = W!49)))))) | (~(singletonP(W!49) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = W!49)))))) | (singletonP(W!49) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = W!49))))),
% 4.50/3.08 inference(tautology,[status(thm)],[])).
% 4.50/3.08 tff(47,plain,
% 4.50/3.08 (singletonP(W!49) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = W!49)))),
% 4.50/3.08 inference(unit_resolution,[status(thm)],[46, 45])).
% 4.50/3.08 tff(48,plain,
% 4.50/3.08 (U!47 = W!49),
% 4.50/3.08 inference(and_elim,[status(thm)],[24])).
% 4.50/3.08 tff(49,plain,
% 4.50/3.08 (W!49 = U!47),
% 4.50/3.08 inference(symmetry,[status(thm)],[48])).
% 4.50/3.08 tff(50,plain,
% 4.50/3.08 (singletonP(W!49) <=> singletonP(U!47)),
% 4.50/3.08 inference(monotonicity,[status(thm)],[49])).
% 4.50/3.08 tff(51,plain,
% 4.50/3.08 (singletonP(U!47) <=> singletonP(W!49)),
% 4.50/3.08 inference(symmetry,[status(thm)],[50])).
% 4.50/3.08 tff(52,plain,
% 4.50/3.08 ((~singletonP(U!47)) <=> (~singletonP(W!49))),
% 4.50/3.08 inference(monotonicity,[status(thm)],[51])).
% 4.50/3.08 tff(53,plain,
% 4.50/3.08 (~singletonP(U!47)),
% 4.50/3.08 inference(and_elim,[status(thm)],[24])).
% 4.50/3.08 tff(54,plain,
% 4.50/3.08 (~singletonP(W!49)),
% 4.50/3.08 inference(modus_ponens,[status(thm)],[53, 52])).
% 4.50/3.08 tff(55,plain,
% 4.50/3.08 ((~(singletonP(W!49) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = W!49))))) | singletonP(W!49) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = W!49)))),
% 4.50/3.08 inference(tautology,[status(thm)],[])).
% 4.50/3.08 tff(56,plain,
% 4.50/3.08 (![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = W!49)))),
% 4.50/3.08 inference(unit_resolution,[status(thm)],[55, 54, 47])).
% 4.50/3.08 tff(57,plain,
% 4.50/3.08 (ssList(X!50)),
% 4.50/3.08 inference(and_elim,[status(thm)],[24])).
% 4.50/3.08 tff(58,plain,
% 4.50/3.08 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 4.50/3.08 inference(bind,[status(th)],[])).
% 4.50/3.08 tff(59,plain,
% 4.50/3.08 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 4.50/3.08 inference(quant_intro,[status(thm)],[58])).
% 4.50/3.08 tff(60,plain,
% 4.50/3.08 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 4.50/3.08 inference(rewrite,[status(thm)],[])).
% 4.50/3.08 tff(61,plain,
% 4.50/3.08 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 4.50/3.08 inference(bind,[status(th)],[])).
% 4.50/3.08 tff(62,plain,
% 4.50/3.08 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 4.50/3.08 inference(quant_intro,[status(thm)],[61])).
% 4.50/3.08 tff(63,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax58')).
% 4.50/3.08 tff(64,plain,
% 4.50/3.08 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 4.50/3.08 inference(modus_ponens,[status(thm)],[63, 62])).
% 4.50/3.08 tff(65,plain,
% 4.50/3.08 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 4.50/3.08 inference(modus_ponens,[status(thm)],[64, 60])).
% 4.50/3.08 tff(66,plain,(
% 4.50/3.08 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 4.50/3.08 inference(skolemize,[status(sab)],[65])).
% 4.50/3.08 tff(67,plain,
% 4.50/3.08 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 4.50/3.08 inference(modus_ponens,[status(thm)],[66, 59])).
% 4.50/3.08 tff(68,plain,
% 4.50/3.08 (((~![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)))),
% 4.50/3.08 inference(rewrite,[status(thm)],[])).
% 4.50/3.08 tff(69,plain,
% 4.50/3.08 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(X!50)) | (segmentP(nil, X!50) <=> (nil = X!50)))),
% 4.50/3.08 inference(quant_inst,[status(thm)],[])).
% 4.50/3.08 tff(70,plain,
% 4.50/3.08 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(X!50)) | (segmentP(nil, X!50) <=> (nil = X!50))),
% 4.50/3.08 inference(modus_ponens,[status(thm)],[69, 68])).
% 4.50/3.08 tff(71,plain,
% 4.50/3.08 (segmentP(nil, X!50) <=> (nil = X!50)),
% 4.50/3.08 inference(unit_resolution,[status(thm)],[70, 67, 57])).
% 4.50/3.08 tff(72,plain,
% 4.50/3.08 (^[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))))))),
% 4.50/3.08 inference(bind,[status(th)],[])).
% 4.50/3.08 tff(73,plain,
% 4.50/3.08 (![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)))))),
% 4.50/3.08 inference(quant_intro,[status(thm)],[72])).
% 4.50/3.08 tff(74,plain,
% 4.50/3.08 (^[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))))))),
% 4.50/3.08 inference(bind,[status(th)],[])).
% 4.50/3.08 tff(75,plain,
% 4.50/3.08 (![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)))))),
% 4.50/3.08 inference(quant_intro,[status(thm)],[74])).
% 4.50/3.08 tff(76,plain,
% 4.50/3.08 (![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)))))),
% 4.50/3.08 inference(transitivity,[status(thm)],[75, 73])).
% 4.50/3.08 tff(77,plain,
% 4.50/3.08 (![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)))))),
% 4.50/3.08 inference(rewrite,[status(thm)],[])).
% 4.50/3.08 tff(78,plain,
% 4.50/3.08 (^[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)))))))),
% 4.50/3.09 inference(bind,[status(th)],[])).
% 4.50/3.09 tff(79,plain,
% 4.50/3.09 (![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)))))),
% 4.50/3.09 inference(quant_intro,[status(thm)],[78])).
% 4.50/3.09 tff(80,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax15')).
% 4.50/3.09 tff(81,plain,
% 4.50/3.09 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 4.50/3.09 inference(modus_ponens,[status(thm)],[80, 79])).
% 4.50/3.09 tff(82,plain,
% 4.50/3.09 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 4.50/3.09 inference(modus_ponens,[status(thm)],[81, 77])).
% 4.50/3.09 tff(83,plain,(
% 4.50/3.09 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 4.50/3.09 inference(skolemize,[status(sab)],[82])).
% 4.50/3.09 tff(84,plain,
% 4.50/3.09 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 4.50/3.09 inference(modus_ponens,[status(thm)],[83, 76])).
% 4.50/3.09 tff(85,plain,
% 4.50/3.09 (((~![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)))))),
% 4.50/3.09 inference(rewrite,[status(thm)],[])).
% 4.50/3.09 tff(86,plain,
% 4.50/3.09 ((~![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)))))),
% 4.50/3.09 inference(quant_inst,[status(thm)],[])).
% 4.50/3.09 tff(87,plain,
% 4.50/3.09 ((~![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))))),
% 4.50/3.09 inference(modus_ponens,[status(thm)],[86, 85])).
% 4.50/3.09 tff(88,plain,
% 4.50/3.09 (![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))),
% 4.50/3.09 inference(unit_resolution,[status(thm)],[87, 84, 57])).
% 4.50/3.09 tff(89,plain,
% 4.50/3.09 (ssList(nil) <=> ssList(nil)),
% 4.50/3.09 inference(rewrite,[status(thm)],[])).
% 4.50/3.09 tff(90,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 4.50/3.09 tff(91,plain,
% 4.50/3.09 (ssList(nil)),
% 4.50/3.09 inference(modus_ponens,[status(thm)],[90, 89])).
% 4.50/3.09 tff(92,plain,
% 4.50/3.09 (((~![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))))),
% 4.50/3.09 inference(rewrite,[status(thm)],[])).
% 4.50/3.09 tff(93,plain,
% 4.50/3.09 ((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | ((~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil))))),
% 4.50/3.09 inference(quant_inst,[status(thm)],[])).
% 4.50/3.09 tff(94,plain,
% 4.50/3.09 ((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | (~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil)))),
% 4.50/3.09 inference(modus_ponens,[status(thm)],[93, 92])).
% 4.50/3.09 tff(95,plain,
% 4.50/3.09 (neq(X!50, nil) <=> (~(X!50 = nil))),
% 4.50/3.09 inference(unit_resolution,[status(thm)],[94, 91, 88])).
% 4.50/3.09 tff(96,plain,
% 4.50/3.09 (V!48 = X!50),
% 4.50/3.09 inference(and_elim,[status(thm)],[24])).
% 4.50/3.09 tff(97,plain,
% 4.50/3.09 (X!50 = V!48),
% 4.50/3.09 inference(symmetry,[status(thm)],[96])).
% 4.50/3.09 tff(98,plain,
% 4.50/3.09 (neq(X!50, nil) <=> neq(V!48, nil)),
% 4.50/3.09 inference(monotonicity,[status(thm)],[97])).
% 4.50/3.09 tff(99,plain,
% 4.50/3.09 (neq(V!48, nil) <=> neq(X!50, nil)),
% 4.50/3.09 inference(symmetry,[status(thm)],[98])).
% 4.50/3.09 tff(100,plain,
% 4.50/3.09 (neq(V!48, nil)),
% 4.50/3.09 inference(and_elim,[status(thm)],[24])).
% 4.50/3.09 tff(101,plain,
% 4.50/3.09 (neq(X!50, nil)),
% 4.50/3.09 inference(modus_ponens,[status(thm)],[100, 99])).
% 4.50/3.09 tff(102,plain,
% 4.50/3.09 ((~(neq(X!50, nil) <=> (~(X!50 = nil)))) | (~neq(X!50, nil)) | (~(X!50 = nil))),
% 4.50/3.09 inference(tautology,[status(thm)],[])).
% 4.50/3.09 tff(103,plain,
% 4.50/3.09 (~(X!50 = nil)),
% 4.50/3.09 inference(unit_resolution,[status(thm)],[102, 101, 95])).
% 4.50/3.09 tff(104,plain,
% 4.50/3.09 (^[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)))))),
% 4.50/3.09 inference(bind,[status(th)],[])).
% 4.50/3.09 tff(105,plain,
% 4.50/3.09 (![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))))),
% 4.50/3.09 inference(quant_intro,[status(thm)],[104])).
% 4.50/3.09 tff(106,plain,
% 4.50/3.09 (^[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)))))),
% 4.50/3.09 inference(bind,[status(th)],[])).
% 4.50/3.09 tff(107,plain,
% 4.50/3.09 (![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))))),
% 4.50/3.09 inference(quant_intro,[status(thm)],[106])).
% 4.50/3.09 tff(108,plain,
% 4.50/3.09 (![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))))),
% 4.50/3.09 inference(transitivity,[status(thm)],[107, 105])).
% 4.50/3.09 tff(109,plain,
% 4.50/3.09 (^[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)))))),
% 4.50/3.09 inference(bind,[status(th)],[])).
% 4.50/3.09 tff(110,plain,
% 4.50/3.09 (![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))))),
% 4.50/3.09 inference(quant_intro,[status(thm)],[109])).
% 4.50/3.09 tff(111,plain,
% 4.50/3.09 (![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)))))),
% 4.50/3.09 inference(rewrite,[status(thm)],[])).
% 4.50/3.09 tff(112,plain,
% 4.50/3.09 (^[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)))))))),
% 4.50/3.09 inference(bind,[status(th)],[])).
% 4.50/3.09 tff(113,plain,
% 4.50/3.09 (![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)))))),
% 4.50/3.09 inference(quant_intro,[status(thm)],[112])).
% 4.50/3.09 tff(114,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')).
% 4.50/3.09 tff(115,plain,
% 4.50/3.09 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 4.50/3.09 inference(modus_ponens,[status(thm)],[114, 113])).
% 4.50/3.09 tff(116,plain,
% 4.50/3.09 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 4.50/3.09 inference(modus_ponens,[status(thm)],[115, 111])).
% 4.50/3.09 tff(117,plain,(
% 4.50/3.09 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 4.50/3.09 inference(skolemize,[status(sab)],[116])).
% 4.50/3.09 tff(118,plain,
% 4.50/3.09 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 4.50/3.09 inference(modus_ponens,[status(thm)],[117, 110])).
% 4.50/3.09 tff(119,plain,
% 4.50/3.09 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 4.50/3.09 inference(modus_ponens,[status(thm)],[118, 108])).
% 4.50/3.09 tff(120,plain,
% 4.50/3.09 (((~![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))))),
% 4.50/3.09 inference(rewrite,[status(thm)],[])).
% 4.50/3.09 tff(121,plain,
% 4.50/3.09 (((~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))))),
% 4.50/3.09 inference(rewrite,[status(thm)],[])).
% 4.50/3.09 tff(122,plain,
% 4.50/3.09 (((~![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)))))),
% 4.50/3.09 inference(monotonicity,[status(thm)],[121])).
% 4.50/3.09 tff(123,plain,
% 4.50/3.09 (((~![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))))),
% 4.50/3.09 inference(transitivity,[status(thm)],[122, 120])).
% 4.50/3.09 tff(124,plain,
% 4.50/3.09 ((~![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))))),
% 4.50/3.09 inference(quant_inst,[status(thm)],[])).
% 4.50/3.09 tff(125,plain,
% 4.50/3.09 ((~![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)))),
% 4.50/3.09 inference(modus_ponens,[status(thm)],[124, 123])).
% 4.50/3.09 tff(126,plain,
% 4.50/3.09 (![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))),
% 4.50/3.09 inference(unit_resolution,[status(thm)],[125, 119, 57])).
% 4.50/3.09 tff(127,plain,
% 4.50/3.09 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 4.50/3.09 inference(bind,[status(th)],[])).
% 4.50/3.09 tff(128,plain,
% 4.50/3.09 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 4.50/3.09 inference(quant_intro,[status(thm)],[127])).
% 4.50/3.09 tff(129,plain,
% 4.50/3.09 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 4.50/3.09 inference(rewrite,[status(thm)],[])).
% 4.50/3.09 tff(130,plain,
% 4.50/3.09 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 4.50/3.09 inference(bind,[status(th)],[])).
% 4.50/3.09 tff(131,plain,
% 4.50/3.09 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 4.50/3.09 inference(quant_intro,[status(thm)],[130])).
% 4.50/3.09 tff(132,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax57')).
% 4.50/3.09 tff(133,plain,
% 4.50/3.09 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 4.50/3.09 inference(modus_ponens,[status(thm)],[132, 131])).
% 4.50/3.09 tff(134,plain,
% 4.50/3.09 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 4.50/3.09 inference(modus_ponens,[status(thm)],[133, 129])).
% 4.50/3.09 tff(135,plain,(
% 4.50/3.09 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 4.50/3.09 inference(skolemize,[status(sab)],[134])).
% 4.50/3.09 tff(136,plain,
% 4.50/3.09 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 4.50/3.09 inference(modus_ponens,[status(thm)],[135, 128])).
% 4.50/3.09 tff(137,plain,
% 4.50/3.09 (((~![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))),
% 4.50/3.09 inference(rewrite,[status(thm)],[])).
% 4.50/3.09 tff(138,plain,
% 4.50/3.09 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(X!50)) | segmentP(X!50, nil))),
% 4.50/3.09 inference(quant_inst,[status(thm)],[])).
% 4.50/3.09 tff(139,plain,
% 4.50/3.09 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(X!50)) | segmentP(X!50, nil)),
% 4.50/3.09 inference(modus_ponens,[status(thm)],[138, 137])).
% 4.50/3.09 tff(140,plain,
% 4.50/3.09 (segmentP(X!50, nil)),
% 4.50/3.09 inference(unit_resolution,[status(thm)],[139, 136, 57])).
% 4.50/3.09 tff(141,plain,
% 4.50/3.09 (((~![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)))),
% 4.50/3.09 inference(rewrite,[status(thm)],[])).
% 4.50/3.09 tff(142,plain,
% 4.50/3.09 (((~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)))),
% 4.50/3.09 inference(rewrite,[status(thm)],[])).
% 4.50/3.09 tff(143,plain,
% 4.50/3.09 (((~![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))))),
% 4.50/3.09 inference(monotonicity,[status(thm)],[142])).
% 4.50/3.09 tff(144,plain,
% 4.50/3.09 (((~![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)))),
% 4.50/3.09 inference(transitivity,[status(thm)],[143, 141])).
% 4.50/3.09 tff(145,plain,
% 4.50/3.09 ((~![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)))),
% 4.50/3.09 inference(quant_inst,[status(thm)],[])).
% 4.50/3.09 tff(146,plain,
% 4.50/3.09 ((~![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))),
% 4.50/3.09 inference(modus_ponens,[status(thm)],[145, 144])).
% 4.50/3.09 tff(147,plain,
% 4.50/3.09 ((~segmentP(nil, X!50)) | (X!50 = nil)),
% 4.50/3.09 inference(unit_resolution,[status(thm)],[146, 91, 140, 126])).
% 4.50/3.09 tff(148,plain,
% 4.50/3.09 (~segmentP(nil, X!50)),
% 4.50/3.09 inference(unit_resolution,[status(thm)],[147, 103])).
% 4.62/3.11 tff(149,plain,
% 4.62/3.11 ((~(segmentP(nil, X!50) <=> (nil = X!50))) | segmentP(nil, X!50) | (~(nil = X!50))),
% 4.62/3.11 inference(tautology,[status(thm)],[])).
% 4.62/3.11 tff(150,plain,
% 4.62/3.11 (~(nil = X!50)),
% 4.62/3.11 inference(unit_resolution,[status(thm)],[149, 148, 71])).
% 4.62/3.11 tff(151,plain,
% 4.62/3.11 (((~(nil = W!49)) | (~(nil = X!50))) | (nil = X!50)),
% 4.62/3.11 inference(tautology,[status(thm)],[])).
% 4.62/3.11 tff(152,plain,
% 4.62/3.11 ((~(nil = W!49)) | (~(nil = X!50))),
% 4.62/3.11 inference(unit_resolution,[status(thm)],[151, 150])).
% 4.62/3.11 tff(153,plain,
% 4.62/3.11 ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))),
% 4.62/3.11 inference(and_elim,[status(thm)],[24])).
% 4.62/3.11 tff(154,plain,
% 4.62/3.11 (~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))),
% 4.62/3.11 inference(unit_resolution,[status(thm)],[153, 152])).
% 4.62/3.11 tff(155,plain,
% 4.62/3.11 (((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51))) | ssItem(Y!51)),
% 4.62/3.11 inference(tautology,[status(thm)],[])).
% 4.62/3.11 tff(156,plain,
% 4.62/3.11 (ssItem(Y!51)),
% 4.62/3.11 inference(unit_resolution,[status(thm)],[155, 154])).
% 4.62/3.11 tff(157,plain,
% 4.62/3.11 (((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51))) | (cons(Y!51, nil) = W!49)),
% 4.62/3.11 inference(tautology,[status(thm)],[])).
% 4.62/3.11 tff(158,plain,
% 4.62/3.11 (cons(Y!51, nil) = W!49),
% 4.62/3.11 inference(unit_resolution,[status(thm)],[157, 154])).
% 4.62/3.11 tff(159,plain,
% 4.62/3.11 (((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = W!49)))) | ((~ssItem(Y!51)) | (~(cons(Y!51, nil) = W!49)))) <=> ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = W!49)))) | (~ssItem(Y!51)) | (~(cons(Y!51, nil) = W!49)))),
% 4.62/3.11 inference(rewrite,[status(thm)],[])).
% 4.62/3.11 tff(160,plain,
% 4.62/3.11 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = W!49)))) | ((~ssItem(Y!51)) | (~(cons(Y!51, nil) = W!49)))),
% 4.62/3.11 inference(quant_inst,[status(thm)],[])).
% 4.62/3.11 tff(161,plain,
% 4.62/3.11 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = W!49)))) | (~ssItem(Y!51)) | (~(cons(Y!51, nil) = W!49))),
% 4.62/3.11 inference(modus_ponens,[status(thm)],[160, 159])).
% 4.62/3.11 tff(162,plain,
% 4.62/3.11 ($false),
% 4.62/3.11 inference(unit_resolution,[status(thm)],[161, 158, 156, 56])).
% 4.62/3.11 % SZS output end Proof
%------------------------------------------------------------------------------