TSTP Solution File: SWC217+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC217+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 11:56:13 EDT 2022
% Result : Theorem 0.84s 0.82s
% Output : Proof 0.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC217+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.35 % Computer : n005.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat Sep 3 22:43:48 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.35 Usage: tptp [options] [-file:]file
% 0.15/0.35 -h, -? prints this message.
% 0.15/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.35 -m, -model generate model.
% 0.15/0.35 -p, -proof generate proof.
% 0.15/0.35 -c, -core generate unsat core of named formulas.
% 0.15/0.35 -st, -statistics display statistics.
% 0.15/0.35 -t:timeout set timeout (in second).
% 0.15/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.35 -<param>:<value> configuration parameter and value.
% 0.15/0.35 -o:<output-file> file to place output in.
% 0.84/0.82 % SZS status Theorem
% 0.84/0.82 % SZS output start Proof
% 0.84/0.82 tff(nil_type, type, (
% 0.84/0.82 nil: $i)).
% 0.84/0.82 tff(tptp_fun_W_49_type, type, (
% 0.84/0.82 tptp_fun_W_49: $i)).
% 0.84/0.82 tff(neq_type, type, (
% 0.84/0.82 neq: ( $i * $i ) > $o)).
% 0.84/0.82 tff(ssList_type, type, (
% 0.84/0.82 ssList: $i > $o)).
% 0.84/0.82 tff(tptp_fun_X_50_type, type, (
% 0.84/0.82 tptp_fun_X_50: $i)).
% 0.84/0.82 tff(ssItem_type, type, (
% 0.84/0.82 ssItem: $i > $o)).
% 0.84/0.82 tff(tptp_fun_Y_51_type, type, (
% 0.84/0.82 tptp_fun_Y_51: $i)).
% 0.84/0.82 tff(memberP_type, type, (
% 0.84/0.82 memberP: ( $i * $i ) > $o)).
% 0.84/0.82 tff(cons_type, type, (
% 0.84/0.82 cons: ( $i * $i ) > $i)).
% 0.84/0.82 tff(tptp_fun_V_48_type, type, (
% 0.84/0.82 tptp_fun_V_48: $i)).
% 0.84/0.82 tff(tptp_fun_U_47_type, type, (
% 0.84/0.82 tptp_fun_U_47: $i)).
% 0.84/0.82 tff(1,plain,
% 0.84/0.82 ((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) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(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) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil))))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(2,plain,
% 0.84/0.83 ((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) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(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) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil))))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(3,plain,
% 0.84/0.83 ((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) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(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) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil))))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(4,plain,
% 0.84/0.83 (((~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))) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(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) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil))))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(5,plain,
% 0.84/0.83 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(6,plain,
% 0.84/0.83 (((~(~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))) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(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) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil)))))),
% 0.84/0.83 inference(monotonicity,[status(thm)],[5, 4])).
% 0.84/0.83 tff(7,plain,
% 0.84/0.83 (((~(~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))) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(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) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil))))),
% 0.84/0.83 inference(transitivity,[status(thm)],[6, 3])).
% 0.84/0.83 tff(8,plain,
% 0.84/0.83 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(9,plain,
% 0.84/0.83 (((~(~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))) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(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) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil)))))),
% 0.84/0.83 inference(monotonicity,[status(thm)],[8, 7])).
% 0.84/0.83 tff(10,plain,
% 0.84/0.83 (((~(~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))) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(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) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil))))),
% 0.84/0.83 inference(transitivity,[status(thm)],[9, 2])).
% 0.84/0.83 tff(11,plain,
% 0.84/0.83 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(12,plain,
% 0.84/0.83 (((~(~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))) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(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) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil)))))),
% 0.84/0.83 inference(monotonicity,[status(thm)],[11, 10])).
% 0.84/0.83 tff(13,plain,
% 0.84/0.83 (((~(~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))) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(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) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil))))),
% 0.84/0.83 inference(transitivity,[status(thm)],[12, 1])).
% 0.84/0.83 tff(14,plain,
% 0.84/0.83 ((~![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] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(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] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & neq(X, nil)))))))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(15,plain,
% 0.84/0.83 ((~![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] : (ssItem(Y) => ((~(cons(Y, nil) = W)) | (~memberP(X, 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] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & neq(X, nil)))))))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 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] : (ssItem(Y) => ((~(cons(Y, nil) = W)) | (~memberP(X, Y)))) & neq(X, nil)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.84/0.83 tff(17,plain,
% 0.84/0.83 (~![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] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & neq(X, nil))))))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.84/0.83 tff(18,plain,
% 0.84/0.83 (~![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] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & neq(X, nil))))))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.84/0.83 tff(19,plain,
% 0.84/0.83 (~![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] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & neq(X, nil))))))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.84/0.83 tff(20,plain,
% 0.84/0.83 (~![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] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & neq(X, nil))))))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.84/0.83 tff(21,plain,
% 0.84/0.83 (~![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] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & neq(X, nil))))))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.84/0.83 tff(22,plain,
% 0.84/0.83 (~![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] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & neq(X, nil))))))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.84/0.83 tff(23,plain,
% 0.84/0.83 (~![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] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & neq(X, nil))))))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[22, 14])).
% 0.84/0.83 tff(24,plain,
% 0.84/0.83 (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) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil)))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.84/0.83 tff(25,plain,
% 0.84/0.83 (ssList(W!49)),
% 0.84/0.83 inference(and_elim,[status(thm)],[24])).
% 0.84/0.83 tff(26,plain,
% 0.84/0.83 (^[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))))))),
% 0.84/0.83 inference(bind,[status(th)],[])).
% 0.84/0.83 tff(27,plain,
% 0.84/0.83 (![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)))))),
% 0.84/0.83 inference(quant_intro,[status(thm)],[26])).
% 0.84/0.83 tff(28,plain,
% 0.84/0.83 (^[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))))))),
% 0.84/0.83 inference(bind,[status(th)],[])).
% 0.84/0.83 tff(29,plain,
% 0.84/0.83 (![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)))))),
% 0.84/0.83 inference(quant_intro,[status(thm)],[28])).
% 0.84/0.83 tff(30,plain,
% 0.84/0.83 (![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)))))),
% 0.84/0.83 inference(transitivity,[status(thm)],[29, 27])).
% 0.84/0.83 tff(31,plain,
% 0.84/0.83 (![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)))))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(32,plain,
% 0.84/0.83 (^[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)))))))),
% 0.84/0.83 inference(bind,[status(th)],[])).
% 0.84/0.83 tff(33,plain,
% 0.84/0.83 (![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)))))),
% 0.84/0.83 inference(quant_intro,[status(thm)],[32])).
% 0.84/0.83 tff(34,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax15')).
% 0.84/0.83 tff(35,plain,
% 0.84/0.83 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.84/0.83 tff(36,plain,
% 0.84/0.83 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.84/0.83 tff(37,plain,(
% 0.84/0.83 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.84/0.83 inference(skolemize,[status(sab)],[36])).
% 0.84/0.83 tff(38,plain,
% 0.84/0.83 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.84/0.83 tff(39,plain,
% 0.84/0.83 (((~![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)))))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(40,plain,
% 0.84/0.83 ((~![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)))))),
% 0.84/0.83 inference(quant_inst,[status(thm)],[])).
% 0.84/0.83 tff(41,plain,
% 0.84/0.83 ((~![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))))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.84/0.83 tff(42,plain,
% 0.84/0.83 (![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))),
% 0.84/0.83 inference(unit_resolution,[status(thm)],[41, 38, 25])).
% 0.84/0.83 tff(43,plain,
% 0.84/0.83 (ssList(nil) <=> ssList(nil)),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(44,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.84/0.83 tff(45,plain,
% 0.84/0.83 (ssList(nil)),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.84/0.83 tff(46,plain,
% 0.84/0.83 (((~![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))))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(47,plain,
% 0.84/0.83 ((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | ((~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil))))),
% 0.84/0.83 inference(quant_inst,[status(thm)],[])).
% 0.84/0.83 tff(48,plain,
% 0.84/0.83 ((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | (~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil)))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.84/0.83 tff(49,plain,
% 0.84/0.83 (neq(W!49, nil) <=> (~(W!49 = nil))),
% 0.84/0.83 inference(unit_resolution,[status(thm)],[48, 45, 42])).
% 0.84/0.83 tff(50,plain,
% 0.84/0.83 ((W!49 = nil) <=> (nil = W!49)),
% 0.84/0.83 inference(commutativity,[status(thm)],[])).
% 0.84/0.83 tff(51,plain,
% 0.84/0.83 ((nil = W!49) <=> (W!49 = nil)),
% 0.84/0.83 inference(symmetry,[status(thm)],[50])).
% 0.84/0.83 tff(52,plain,
% 0.84/0.83 ((~(nil = W!49)) <=> (~(W!49 = nil))),
% 0.84/0.83 inference(monotonicity,[status(thm)],[51])).
% 0.84/0.83 tff(53,plain,
% 0.84/0.83 (V!48 = X!50),
% 0.84/0.83 inference(and_elim,[status(thm)],[24])).
% 0.84/0.83 tff(54,plain,
% 0.84/0.83 (neq(V!48, nil) <=> neq(X!50, nil)),
% 0.84/0.83 inference(monotonicity,[status(thm)],[53])).
% 0.84/0.83 tff(55,plain,
% 0.84/0.83 (neq(V!48, nil)),
% 0.84/0.83 inference(and_elim,[status(thm)],[24])).
% 0.84/0.83 tff(56,plain,
% 0.84/0.83 (neq(X!50, nil)),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.84/0.83 tff(57,plain,
% 0.84/0.83 ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil))),
% 0.84/0.83 inference(and_elim,[status(thm)],[24])).
% 0.84/0.83 tff(58,plain,
% 0.84/0.83 (~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))),
% 0.84/0.83 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.84/0.83 tff(59,plain,
% 0.84/0.83 (((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51))) | (cons(Y!51, nil) = W!49)),
% 0.84/0.83 inference(tautology,[status(thm)],[])).
% 0.84/0.83 tff(60,plain,
% 0.84/0.83 (cons(Y!51, nil) = W!49),
% 0.84/0.83 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.84/0.83 tff(61,plain,
% 0.84/0.83 ((cons(Y!51, nil) = nil) <=> (W!49 = nil)),
% 0.84/0.83 inference(monotonicity,[status(thm)],[60])).
% 0.84/0.83 tff(62,plain,
% 0.84/0.83 ((cons(Y!51, nil) = nil) <=> (nil = W!49)),
% 0.84/0.83 inference(transitivity,[status(thm)],[61, 50])).
% 0.84/0.83 tff(63,plain,
% 0.84/0.83 ((~(cons(Y!51, nil) = nil)) <=> (~(nil = W!49))),
% 0.84/0.83 inference(monotonicity,[status(thm)],[62])).
% 0.84/0.83 tff(64,plain,
% 0.84/0.83 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))),
% 0.84/0.83 inference(bind,[status(th)],[])).
% 0.84/0.83 tff(65,plain,
% 0.84/0.83 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.84/0.83 inference(quant_intro,[status(thm)],[64])).
% 0.84/0.83 tff(66,plain,
% 0.84/0.83 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))),
% 0.84/0.83 inference(bind,[status(th)],[])).
% 0.84/0.83 tff(67,plain,
% 0.84/0.83 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.84/0.83 inference(quant_intro,[status(thm)],[66])).
% 0.84/0.83 tff(68,plain,
% 0.84/0.83 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.84/0.83 inference(transitivity,[status(thm)],[67, 65])).
% 0.84/0.83 tff(69,plain,
% 0.84/0.83 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(70,plain,
% 0.84/0.83 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (~(cons(V, U) = U))) <=> ((~ssItem(V)) | (~(cons(V, U) = U))))), (![V: $i] : (ssItem(V) => (~(cons(V, U) = U))) <=> ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))))),
% 0.84/0.83 inference(bind,[status(th)],[])).
% 0.84/0.83 tff(71,plain,
% 0.84/0.83 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.84/0.84 inference(quant_intro,[status(thm)],[70])).
% 0.84/0.84 tff(72,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax18')).
% 0.84/0.84 tff(73,plain,
% 0.84/0.84 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.84/0.84 tff(74,plain,
% 0.84/0.84 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.84/0.84 tff(75,plain,(
% 0.84/0.84 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.84/0.84 inference(skolemize,[status(sab)],[74])).
% 0.84/0.84 tff(76,plain,
% 0.84/0.84 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.84/0.84 tff(77,plain,
% 0.84/0.84 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil))))),
% 0.84/0.84 inference(rewrite,[status(thm)],[])).
% 0.84/0.84 tff(78,plain,
% 0.84/0.84 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil))))),
% 0.84/0.84 inference(quant_inst,[status(thm)],[])).
% 0.84/0.84 tff(79,plain,
% 0.84/0.84 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.84/0.84 tff(80,plain,
% 0.84/0.84 (![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))),
% 0.84/0.84 inference(unit_resolution,[status(thm)],[79, 45, 76])).
% 0.84/0.84 tff(81,plain,
% 0.84/0.84 (((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51))) | ssItem(Y!51)),
% 0.84/0.84 inference(tautology,[status(thm)],[])).
% 0.84/0.84 tff(82,plain,
% 0.84/0.84 (ssItem(Y!51)),
% 0.84/0.84 inference(unit_resolution,[status(thm)],[81, 58])).
% 0.84/0.84 tff(83,plain,
% 0.84/0.84 (((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | ((~ssItem(Y!51)) | (~(cons(Y!51, nil) = nil)))) <=> ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | (~ssItem(Y!51)) | (~(cons(Y!51, nil) = nil)))),
% 0.84/0.84 inference(rewrite,[status(thm)],[])).
% 0.84/0.84 tff(84,plain,
% 0.84/0.84 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | ((~ssItem(Y!51)) | (~(cons(Y!51, nil) = nil)))),
% 0.84/0.84 inference(quant_inst,[status(thm)],[])).
% 0.84/0.84 tff(85,plain,
% 0.84/0.84 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | (~ssItem(Y!51)) | (~(cons(Y!51, nil) = nil))),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.84/0.84 tff(86,plain,
% 0.84/0.84 (~(cons(Y!51, nil) = nil)),
% 0.84/0.84 inference(unit_resolution,[status(thm)],[85, 82, 80])).
% 0.84/0.84 tff(87,plain,
% 0.84/0.84 (~(nil = W!49)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[86, 63])).
% 0.84/0.84 tff(88,plain,
% 0.84/0.84 (~(W!49 = nil)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[87, 52])).
% 0.84/0.84 tff(89,plain,
% 0.84/0.84 (U!47 = W!49),
% 0.84/0.84 inference(and_elim,[status(thm)],[24])).
% 0.84/0.84 tff(90,plain,
% 0.84/0.84 (W!49 = U!47),
% 0.84/0.84 inference(symmetry,[status(thm)],[89])).
% 0.84/0.84 tff(91,plain,
% 0.84/0.84 (neq(W!49, nil) <=> neq(U!47, nil)),
% 0.84/0.84 inference(monotonicity,[status(thm)],[90])).
% 0.84/0.84 tff(92,plain,
% 0.84/0.84 (neq(U!47, nil) <=> neq(W!49, nil)),
% 0.84/0.84 inference(symmetry,[status(thm)],[91])).
% 0.84/0.84 tff(93,plain,
% 0.84/0.84 ((~neq(U!47, nil)) <=> (~neq(W!49, nil))),
% 0.84/0.84 inference(monotonicity,[status(thm)],[92])).
% 0.84/0.84 tff(94,plain,
% 0.84/0.84 (~neq(U!47, nil)),
% 0.84/0.84 inference(and_elim,[status(thm)],[24])).
% 0.84/0.84 tff(95,plain,
% 0.84/0.84 (~neq(W!49, nil)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.84/0.84 tff(96,plain,
% 0.84/0.84 ((~(neq(W!49, nil) <=> (~(W!49 = nil)))) | neq(W!49, nil) | (W!49 = nil)),
% 0.84/0.84 inference(tautology,[status(thm)],[])).
% 0.84/0.84 tff(97,plain,
% 0.84/0.84 ($false),
% 0.84/0.84 inference(unit_resolution,[status(thm)],[96, 95, 88, 49])).
% 0.84/0.84 % SZS output end Proof
%------------------------------------------------------------------------------