TSTP Solution File: SWC408+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC408+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 11:57:47 EDT 2022
% Result : Theorem 0.90s 0.81s
% Output : Proof 0.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC408+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 : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 00:47:39 EDT 2022
% 0.13/0.34 % 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.
% 0.90/0.81 % SZS status Theorem
% 0.90/0.81 % SZS output start Proof
% 0.90/0.81 tff(memberP_type, type, (
% 0.90/0.81 memberP: ( $i * $i ) > $o)).
% 0.90/0.81 tff(tptp_fun_Y_51_type, type, (
% 0.90/0.81 tptp_fun_Y_51: $i)).
% 0.90/0.81 tff(app_type, type, (
% 0.90/0.81 app: ( $i * $i ) > $i)).
% 0.90/0.81 tff(tptp_fun_X_50_type, type, (
% 0.90/0.81 tptp_fun_X_50: $i)).
% 0.90/0.81 tff(tptp_fun_U_47_type, type, (
% 0.90/0.81 tptp_fun_U_47: $i)).
% 0.90/0.81 tff(tptp_fun_W_49_type, type, (
% 0.90/0.81 tptp_fun_W_49: $i)).
% 0.90/0.81 tff(ssItem_type, type, (
% 0.90/0.81 ssItem: $i > $o)).
% 0.90/0.81 tff(tptp_fun_V_48_type, type, (
% 0.90/0.81 tptp_fun_V_48: $i)).
% 0.90/0.81 tff(ssList_type, type, (
% 0.90/0.81 ssList: $i > $o)).
% 0.90/0.81 tff(1,plain,
% 0.90/0.81 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (app(X!50, X!50) = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(U!47, Y!51) | (~memberP(V!48, Y!51)) | (~ssItem(Y!51)))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (app(X!50, X!50) = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(U!47, Y!51) | (~memberP(V!48, Y!51)) | (~ssItem(Y!51)))))),
% 0.90/0.81 inference(rewrite,[status(thm)],[])).
% 0.90/0.81 tff(2,plain,
% 0.90/0.81 ((ssList(V!48) & (ssList(W!49) & (app(X!50, X!50) = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(U!47, Y!51) | (~memberP(V!48, Y!51)) | (~ssItem(Y!51)))))) <=> (ssList(V!48) & ssList(W!49) & (app(X!50, X!50) = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(U!47, Y!51) | (~memberP(V!48, Y!51)) | (~ssItem(Y!51)))))),
% 0.90/0.81 inference(rewrite,[status(thm)],[])).
% 0.90/0.81 tff(3,plain,
% 0.90/0.81 ((ssList(W!49) & ((app(X!50, X!50) = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(U!47, Y!51) | (~memberP(V!48, Y!51)) | (~ssItem(Y!51)))))) <=> (ssList(W!49) & (app(X!50, X!50) = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(U!47, Y!51) | (~memberP(V!48, Y!51)) | (~ssItem(Y!51)))))),
% 0.90/0.81 inference(rewrite,[status(thm)],[])).
% 0.90/0.81 tff(4,plain,
% 0.90/0.81 (((~(~(app(X!50, X!50) = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (~(memberP(U!47, Y!51) | (~memberP(V!48, Y!51)) | (~ssItem(Y!51))))) <=> ((app(X!50, X!50) = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(U!47, Y!51) | (~memberP(V!48, Y!51)) | (~ssItem(Y!51)))))),
% 0.90/0.81 inference(rewrite,[status(thm)],[])).
% 0.90/0.81 tff(5,plain,
% 0.90/0.81 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 0.90/0.81 inference(rewrite,[status(thm)],[])).
% 0.90/0.81 tff(6,plain,
% 0.90/0.81 (((~(~ssList(W!49))) & ((~(~(app(X!50, X!50) = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (~(memberP(U!47, Y!51) | (~memberP(V!48, Y!51)) | (~ssItem(Y!51)))))) <=> (ssList(W!49) & ((app(X!50, X!50) = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(U!47, Y!51) | (~memberP(V!48, Y!51)) | (~ssItem(Y!51))))))),
% 0.90/0.81 inference(monotonicity,[status(thm)],[5, 4])).
% 0.90/0.81 tff(7,plain,
% 0.90/0.81 (((~(~ssList(W!49))) & ((~(~(app(X!50, X!50) = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (~(memberP(U!47, Y!51) | (~memberP(V!48, Y!51)) | (~ssItem(Y!51)))))) <=> (ssList(W!49) & (app(X!50, X!50) = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(U!47, Y!51) | (~memberP(V!48, Y!51)) | (~ssItem(Y!51)))))),
% 0.90/0.81 inference(transitivity,[status(thm)],[6, 3])).
% 0.90/0.81 tff(8,plain,
% 0.90/0.81 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 0.90/0.81 inference(rewrite,[status(thm)],[])).
% 0.90/0.81 tff(9,plain,
% 0.90/0.81 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(app(X!50, X!50) = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (~(memberP(U!47, Y!51) | (~memberP(V!48, Y!51)) | (~ssItem(Y!51))))))) <=> (ssList(V!48) & (ssList(W!49) & (app(X!50, X!50) = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(U!47, Y!51) | (~memberP(V!48, Y!51)) | (~ssItem(Y!51))))))),
% 0.90/0.81 inference(monotonicity,[status(thm)],[8, 7])).
% 0.90/0.81 tff(10,plain,
% 0.90/0.81 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(app(X!50, X!50) = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (~(memberP(U!47, Y!51) | (~memberP(V!48, Y!51)) | (~ssItem(Y!51))))))) <=> (ssList(V!48) & ssList(W!49) & (app(X!50, X!50) = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(U!47, Y!51) | (~memberP(V!48, Y!51)) | (~ssItem(Y!51)))))),
% 0.90/0.81 inference(transitivity,[status(thm)],[9, 2])).
% 0.90/0.82 tff(11,plain,
% 0.90/0.82 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 0.90/0.82 inference(rewrite,[status(thm)],[])).
% 0.90/0.82 tff(12,plain,
% 0.90/0.82 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(app(X!50, X!50) = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (~(memberP(U!47, Y!51) | (~memberP(V!48, Y!51)) | (~ssItem(Y!51)))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (app(X!50, X!50) = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(U!47, Y!51) | (~memberP(V!48, Y!51)) | (~ssItem(Y!51))))))),
% 0.90/0.82 inference(monotonicity,[status(thm)],[11, 10])).
% 0.90/0.82 tff(13,plain,
% 0.90/0.82 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(app(X!50, X!50) = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (~(memberP(U!47, Y!51) | (~memberP(V!48, Y!51)) | (~ssItem(Y!51)))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (app(X!50, X!50) = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(U!47, Y!51) | (~memberP(V!48, Y!51)) | (~ssItem(Y!51)))))),
% 0.90/0.82 inference(transitivity,[status(thm)],[12, 1])).
% 0.90/0.82 tff(14,plain,
% 0.90/0.82 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(app(X, X) = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : (memberP(U, Y) | (~memberP(V, Y)) | (~ssItem(Y)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(app(X, X) = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : (memberP(U, Y) | (~memberP(V, Y)) | (~ssItem(Y))))))))),
% 0.90/0.82 inference(rewrite,[status(thm)],[])).
% 0.90/0.82 tff(15,plain,
% 0.90/0.82 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(app(X, X) = W)) | (~(V = X))) | (~(U = W))) | ![Y: $i] : (ssItem(Y) => ((~memberP(V, Y)) | memberP(U, Y))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(app(X, X) = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : (memberP(U, Y) | (~memberP(V, Y)) | (~ssItem(Y))))))))),
% 0.90/0.82 inference(rewrite,[status(thm)],[])).
% 0.90/0.82 tff(16,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(app(X, X) = W)) | (~(V = X))) | (~(U = W))) | ![Y: $i] : (ssItem(Y) => ((~memberP(V, Y)) | memberP(U, Y))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.90/0.82 tff(17,plain,
% 0.90/0.82 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(app(X, X) = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : (memberP(U, Y) | (~memberP(V, Y)) | (~ssItem(Y)))))))),
% 0.90/0.82 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.90/0.82 tff(18,plain,
% 0.90/0.82 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(app(X, X) = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : (memberP(U, Y) | (~memberP(V, Y)) | (~ssItem(Y)))))))),
% 0.90/0.82 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.90/0.82 tff(19,plain,
% 0.90/0.82 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(app(X, X) = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : (memberP(U, Y) | (~memberP(V, Y)) | (~ssItem(Y)))))))),
% 0.90/0.82 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.90/0.82 tff(20,plain,
% 0.90/0.82 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(app(X, X) = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : (memberP(U, Y) | (~memberP(V, Y)) | (~ssItem(Y)))))))),
% 0.90/0.82 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.90/0.82 tff(21,plain,
% 0.90/0.82 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(app(X, X) = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : (memberP(U, Y) | (~memberP(V, Y)) | (~ssItem(Y)))))))),
% 0.90/0.82 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.90/0.82 tff(22,plain,
% 0.90/0.82 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(app(X, X) = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : (memberP(U, Y) | (~memberP(V, Y)) | (~ssItem(Y)))))))),
% 0.90/0.82 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.90/0.82 tff(23,plain,
% 0.90/0.82 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(app(X, X) = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : (memberP(U, Y) | (~memberP(V, Y)) | (~ssItem(Y)))))))),
% 0.90/0.82 inference(modus_ponens,[status(thm)],[22, 14])).
% 0.90/0.82 tff(24,plain,
% 0.90/0.82 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (app(X!50, X!50) = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(U!47, Y!51) | (~memberP(V!48, Y!51)) | (~ssItem(Y!51))))),
% 0.90/0.82 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.90/0.82 tff(25,plain,
% 0.90/0.82 (U!47 = W!49),
% 0.90/0.82 inference(and_elim,[status(thm)],[24])).
% 0.90/0.82 tff(26,plain,
% 0.90/0.82 (W!49 = U!47),
% 0.90/0.82 inference(symmetry,[status(thm)],[25])).
% 0.90/0.82 tff(27,plain,
% 0.90/0.82 (app(X!50, X!50) = W!49),
% 0.90/0.82 inference(and_elim,[status(thm)],[24])).
% 0.90/0.82 tff(28,plain,
% 0.90/0.82 (app(X!50, X!50) = U!47),
% 0.90/0.82 inference(transitivity,[status(thm)],[27, 26])).
% 0.90/0.82 tff(29,plain,
% 0.90/0.82 (memberP(app(X!50, X!50), Y!51) <=> memberP(U!47, Y!51)),
% 0.90/0.82 inference(monotonicity,[status(thm)],[28])).
% 0.90/0.82 tff(30,plain,
% 0.90/0.82 (memberP(U!47, Y!51) <=> memberP(app(X!50, X!50), Y!51)),
% 0.90/0.82 inference(symmetry,[status(thm)],[29])).
% 0.90/0.82 tff(31,plain,
% 0.90/0.82 ((~memberP(U!47, Y!51)) <=> (~memberP(app(X!50, X!50), Y!51))),
% 0.90/0.82 inference(monotonicity,[status(thm)],[30])).
% 0.90/0.82 tff(32,plain,
% 0.90/0.82 (~(memberP(U!47, Y!51) | (~memberP(V!48, Y!51)) | (~ssItem(Y!51)))),
% 0.90/0.82 inference(and_elim,[status(thm)],[24])).
% 0.90/0.82 tff(33,plain,
% 0.90/0.82 (~memberP(U!47, Y!51)),
% 0.90/0.82 inference(or_elim,[status(thm)],[32])).
% 0.90/0.82 tff(34,plain,
% 0.90/0.82 (~memberP(app(X!50, X!50), Y!51)),
% 0.90/0.82 inference(modus_ponens,[status(thm)],[33, 31])).
% 0.90/0.82 tff(35,plain,
% 0.90/0.82 (ssItem(Y!51)),
% 0.90/0.82 inference(or_elim,[status(thm)],[32])).
% 0.90/0.82 tff(36,plain,
% 0.90/0.82 (^[U: $i] : refl(((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))))),
% 0.90/0.82 inference(bind,[status(th)],[])).
% 0.90/0.82 tff(37,plain,
% 0.90/0.82 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.90/0.82 inference(quant_intro,[status(thm)],[36])).
% 0.90/0.82 tff(38,plain,
% 0.90/0.82 (^[U: $i] : rewrite(((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))))),
% 0.90/0.82 inference(bind,[status(th)],[])).
% 0.90/0.82 tff(39,plain,
% 0.90/0.82 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.90/0.82 inference(quant_intro,[status(thm)],[38])).
% 0.90/0.82 tff(40,plain,
% 0.90/0.82 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.90/0.82 inference(transitivity,[status(thm)],[39, 37])).
% 0.90/0.82 tff(41,plain,
% 0.90/0.82 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.90/0.82 inference(rewrite,[status(thm)],[])).
% 0.90/0.82 tff(42,plain,
% 0.90/0.82 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : trans(monotonicity(rewrite((memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))) <=> (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))), ((ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))) <=> (ssList(W) => (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))), rewrite((ssList(W) => (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))) <=> ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))), ((ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))) <=> ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))), (![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))) <=> ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))), ((ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))))) <=> (ssList(V) => ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))), rewrite((ssList(V) => ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))), ((ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))), ((ssItem(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))))) <=> (ssItem(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))))), rewrite((ssItem(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))), ((ssItem(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))))),
% 0.90/0.82 inference(bind,[status(th)],[])).
% 0.90/0.82 tff(43,plain,
% 0.90/0.82 (![U: $i] : (ssItem(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.90/0.82 inference(quant_intro,[status(thm)],[42])).
% 0.90/0.82 tff(44,axiom,(![U: $i] : (ssItem(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax36')).
% 0.90/0.82 tff(45,plain,
% 0.90/0.82 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.90/0.82 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.90/0.82 tff(46,plain,
% 0.90/0.82 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.90/0.82 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.90/0.82 tff(47,plain,(
% 0.90/0.82 ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.90/0.82 inference(skolemize,[status(sab)],[46])).
% 0.90/0.82 tff(48,plain,
% 0.90/0.82 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.90/0.82 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.90/0.82 tff(49,plain,
% 0.90/0.82 (((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))) | ((~ssItem(Y!51)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), Y!51) <=> (memberP(W, Y!51) | memberP(V, Y!51))))))) <=> ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))) | (~ssItem(Y!51)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), Y!51) <=> (memberP(W, Y!51) | memberP(V, Y!51))))))),
% 0.90/0.82 inference(rewrite,[status(thm)],[])).
% 0.90/0.82 tff(50,plain,
% 0.90/0.82 ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))) | ((~ssItem(Y!51)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), Y!51) <=> (memberP(W, Y!51) | memberP(V, Y!51))))))),
% 0.90/0.82 inference(quant_inst,[status(thm)],[])).
% 0.90/0.82 tff(51,plain,
% 0.90/0.82 ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))) | (~ssItem(Y!51)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), Y!51) <=> (memberP(W, Y!51) | memberP(V, Y!51)))))),
% 0.90/0.82 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.90/0.82 tff(52,plain,
% 0.90/0.82 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), Y!51) <=> (memberP(W, Y!51) | memberP(V, Y!51)))))),
% 0.90/0.82 inference(unit_resolution,[status(thm)],[51, 48, 35])).
% 0.90/0.82 tff(53,plain,
% 0.90/0.82 (ssList(X!50)),
% 0.90/0.82 inference(and_elim,[status(thm)],[24])).
% 0.90/0.82 tff(54,plain,
% 0.90/0.82 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), Y!51) <=> (memberP(W, Y!51) | memberP(V, Y!51)))))) | ((~ssList(X!50)) | ![W: $i] : ((~ssList(W)) | (memberP(app(X!50, W), Y!51) <=> (memberP(W, Y!51) | memberP(X!50, Y!51)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), Y!51) <=> (memberP(W, Y!51) | memberP(V, Y!51)))))) | (~ssList(X!50)) | ![W: $i] : ((~ssList(W)) | (memberP(app(X!50, W), Y!51) <=> (memberP(W, Y!51) | memberP(X!50, Y!51)))))),
% 0.90/0.82 inference(rewrite,[status(thm)],[])).
% 0.90/0.82 tff(55,plain,
% 0.90/0.82 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), Y!51) <=> (memberP(W, Y!51) | memberP(V, Y!51)))))) | ((~ssList(X!50)) | ![W: $i] : ((~ssList(W)) | (memberP(app(X!50, W), Y!51) <=> (memberP(W, Y!51) | memberP(X!50, Y!51)))))),
% 0.90/0.82 inference(quant_inst,[status(thm)],[])).
% 0.90/0.82 tff(56,plain,
% 0.90/0.82 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), Y!51) <=> (memberP(W, Y!51) | memberP(V, Y!51)))))) | (~ssList(X!50)) | ![W: $i] : ((~ssList(W)) | (memberP(app(X!50, W), Y!51) <=> (memberP(W, Y!51) | memberP(X!50, Y!51))))),
% 0.90/0.82 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.90/0.82 tff(57,plain,
% 0.90/0.82 (![W: $i] : ((~ssList(W)) | (memberP(app(X!50, W), Y!51) <=> (memberP(W, Y!51) | memberP(X!50, Y!51))))),
% 0.90/0.82 inference(unit_resolution,[status(thm)],[56, 53, 52])).
% 0.90/0.82 tff(58,plain,
% 0.90/0.82 (((~![W: $i] : ((~ssList(W)) | (memberP(app(X!50, W), Y!51) <=> (memberP(W, Y!51) | memberP(X!50, Y!51))))) | ((~ssList(X!50)) | (memberP(app(X!50, X!50), Y!51) <=> memberP(X!50, Y!51)))) <=> ((~![W: $i] : ((~ssList(W)) | (memberP(app(X!50, W), Y!51) <=> (memberP(W, Y!51) | memberP(X!50, Y!51))))) | (~ssList(X!50)) | (memberP(app(X!50, X!50), Y!51) <=> memberP(X!50, Y!51)))),
% 0.90/0.82 inference(rewrite,[status(thm)],[])).
% 0.90/0.82 tff(59,plain,
% 0.90/0.82 (((~ssList(X!50)) | (memberP(app(X!50, X!50), Y!51) <=> (memberP(X!50, Y!51) | memberP(X!50, Y!51)))) <=> ((~ssList(X!50)) | (memberP(app(X!50, X!50), Y!51) <=> memberP(X!50, Y!51)))),
% 0.90/0.82 inference(rewrite,[status(thm)],[])).
% 0.90/0.82 tff(60,plain,
% 0.90/0.82 (((~![W: $i] : ((~ssList(W)) | (memberP(app(X!50, W), Y!51) <=> (memberP(W, Y!51) | memberP(X!50, Y!51))))) | ((~ssList(X!50)) | (memberP(app(X!50, X!50), Y!51) <=> (memberP(X!50, Y!51) | memberP(X!50, Y!51))))) <=> ((~![W: $i] : ((~ssList(W)) | (memberP(app(X!50, W), Y!51) <=> (memberP(W, Y!51) | memberP(X!50, Y!51))))) | ((~ssList(X!50)) | (memberP(app(X!50, X!50), Y!51) <=> memberP(X!50, Y!51))))),
% 0.90/0.82 inference(monotonicity,[status(thm)],[59])).
% 0.90/0.83 tff(61,plain,
% 0.90/0.83 (((~![W: $i] : ((~ssList(W)) | (memberP(app(X!50, W), Y!51) <=> (memberP(W, Y!51) | memberP(X!50, Y!51))))) | ((~ssList(X!50)) | (memberP(app(X!50, X!50), Y!51) <=> (memberP(X!50, Y!51) | memberP(X!50, Y!51))))) <=> ((~![W: $i] : ((~ssList(W)) | (memberP(app(X!50, W), Y!51) <=> (memberP(W, Y!51) | memberP(X!50, Y!51))))) | (~ssList(X!50)) | (memberP(app(X!50, X!50), Y!51) <=> memberP(X!50, Y!51)))),
% 0.90/0.83 inference(transitivity,[status(thm)],[60, 58])).
% 0.90/0.83 tff(62,plain,
% 0.90/0.83 ((~![W: $i] : ((~ssList(W)) | (memberP(app(X!50, W), Y!51) <=> (memberP(W, Y!51) | memberP(X!50, Y!51))))) | ((~ssList(X!50)) | (memberP(app(X!50, X!50), Y!51) <=> (memberP(X!50, Y!51) | memberP(X!50, Y!51))))),
% 0.90/0.83 inference(quant_inst,[status(thm)],[])).
% 0.90/0.83 tff(63,plain,
% 0.90/0.83 ((~![W: $i] : ((~ssList(W)) | (memberP(app(X!50, W), Y!51) <=> (memberP(W, Y!51) | memberP(X!50, Y!51))))) | (~ssList(X!50)) | (memberP(app(X!50, X!50), Y!51) <=> memberP(X!50, Y!51))),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.90/0.83 tff(64,plain,
% 0.90/0.83 (memberP(app(X!50, X!50), Y!51) <=> memberP(X!50, Y!51)),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[63, 53, 57])).
% 0.90/0.83 tff(65,plain,
% 0.90/0.83 (V!48 = X!50),
% 0.90/0.83 inference(and_elim,[status(thm)],[24])).
% 0.90/0.83 tff(66,plain,
% 0.90/0.83 (X!50 = V!48),
% 0.90/0.83 inference(symmetry,[status(thm)],[65])).
% 0.90/0.83 tff(67,plain,
% 0.90/0.83 (memberP(X!50, Y!51) <=> memberP(V!48, Y!51)),
% 0.90/0.83 inference(monotonicity,[status(thm)],[66])).
% 0.90/0.83 tff(68,plain,
% 0.90/0.83 (memberP(V!48, Y!51) <=> memberP(X!50, Y!51)),
% 0.90/0.83 inference(symmetry,[status(thm)],[67])).
% 0.90/0.83 tff(69,plain,
% 0.90/0.83 (memberP(V!48, Y!51)),
% 0.90/0.83 inference(or_elim,[status(thm)],[32])).
% 0.90/0.83 tff(70,plain,
% 0.90/0.83 (memberP(X!50, Y!51)),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.90/0.83 tff(71,plain,
% 0.90/0.83 ((~(memberP(app(X!50, X!50), Y!51) <=> memberP(X!50, Y!51))) | memberP(app(X!50, X!50), Y!51) | (~memberP(X!50, Y!51))),
% 0.90/0.83 inference(tautology,[status(thm)],[])).
% 0.90/0.83 tff(72,plain,
% 0.90/0.83 ((~(memberP(app(X!50, X!50), Y!51) <=> memberP(X!50, Y!51))) | memberP(app(X!50, X!50), Y!51)),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.90/0.83 tff(73,plain,
% 0.90/0.83 (memberP(app(X!50, X!50), Y!51)),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[72, 64])).
% 0.90/0.83 tff(74,plain,
% 0.90/0.83 ($false),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[73, 34])).
% 0.90/0.83 % SZS output end Proof
%------------------------------------------------------------------------------