TSTP Solution File: SWC405+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC405+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 11:57:45 EDT 2022
% Result : Theorem 0.19s 0.48s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWC405+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Sep 4 00:46:24 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 % SZS output start Proof
% 0.19/0.48 tff(memberP_type, type, (
% 0.19/0.48 memberP: ( $i * $i ) > $o)).
% 0.19/0.48 tff(tptp_fun_Z_51_type, type, (
% 0.19/0.48 tptp_fun_Z_51: $i)).
% 0.19/0.48 tff(tptp_fun_X_50_type, type, (
% 0.19/0.48 tptp_fun_X_50: $i)).
% 0.19/0.48 tff(tptp_fun_W_49_type, type, (
% 0.19/0.48 tptp_fun_W_49: $i)).
% 0.19/0.48 tff(ssItem_type, type, (
% 0.19/0.48 ssItem: $i > $o)).
% 0.19/0.48 tff(tptp_fun_U_47_type, type, (
% 0.19/0.48 tptp_fun_U_47: $i)).
% 0.19/0.48 tff(tptp_fun_V_48_type, type, (
% 0.19/0.48 tptp_fun_V_48: $i)).
% 0.19/0.48 tff(ssList_type, type, (
% 0.19/0.48 ssList: $i > $o)).
% 0.19/0.48 tff(1,plain,
% 0.19/0.48 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (V!48 = X!50) & ![Y: $i] : (~(ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y))))) & (U!47 = W!49) & ssList(X!50) & (~(memberP(V!48, Z!51) | (~memberP(U!47, Z!51)) | (~ssItem(Z!51)))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (V!48 = X!50) & ![Y: $i] : (~(ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y))))) & (U!47 = W!49) & ssList(X!50) & (~(memberP(V!48, Z!51) | (~memberP(U!47, Z!51)) | (~ssItem(Z!51)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(2,plain,
% 0.19/0.48 ((ssList(V!48) & (ssList(W!49) & (V!48 = X!50) & ![Y: $i] : (~(ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y))))) & (U!47 = W!49) & ssList(X!50) & (~(memberP(V!48, Z!51) | (~memberP(U!47, Z!51)) | (~ssItem(Z!51)))))) <=> (ssList(V!48) & ssList(W!49) & (V!48 = X!50) & ![Y: $i] : (~(ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y))))) & (U!47 = W!49) & ssList(X!50) & (~(memberP(V!48, Z!51) | (~memberP(U!47, Z!51)) | (~ssItem(Z!51)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(3,plain,
% 0.19/0.48 ((ssList(W!49) & ((V!48 = X!50) & ![Y: $i] : (~(ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y))))) & (U!47 = W!49) & ssList(X!50) & (~(memberP(V!48, Z!51) | (~memberP(U!47, Z!51)) | (~ssItem(Z!51)))))) <=> (ssList(W!49) & (V!48 = X!50) & ![Y: $i] : (~(ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y))))) & (U!47 = W!49) & ssList(X!50) & (~(memberP(V!48, Z!51) | (~memberP(U!47, Z!51)) | (~ssItem(Z!51)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(4,plain,
% 0.19/0.48 (((~(~(V!48 = X!50))) & ![Y: $i] : (~(ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y))))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & (~(memberP(V!48, Z!51) | (~memberP(U!47, Z!51)) | (~ssItem(Z!51))))) <=> ((V!48 = X!50) & ![Y: $i] : (~(ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y))))) & (U!47 = W!49) & ssList(X!50) & (~(memberP(V!48, Z!51) | (~memberP(U!47, Z!51)) | (~ssItem(Z!51)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(5,plain,
% 0.19/0.48 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(6,plain,
% 0.19/0.48 (((~(~ssList(W!49))) & ((~(~(V!48 = X!50))) & ![Y: $i] : (~(ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y))))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & (~(memberP(V!48, Z!51) | (~memberP(U!47, Z!51)) | (~ssItem(Z!51)))))) <=> (ssList(W!49) & ((V!48 = X!50) & ![Y: $i] : (~(ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y))))) & (U!47 = W!49) & ssList(X!50) & (~(memberP(V!48, Z!51) | (~memberP(U!47, Z!51)) | (~ssItem(Z!51))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[5, 4])).
% 0.19/0.48 tff(7,plain,
% 0.19/0.48 (((~(~ssList(W!49))) & ((~(~(V!48 = X!50))) & ![Y: $i] : (~(ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y))))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & (~(memberP(V!48, Z!51) | (~memberP(U!47, Z!51)) | (~ssItem(Z!51)))))) <=> (ssList(W!49) & (V!48 = X!50) & ![Y: $i] : (~(ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y))))) & (U!47 = W!49) & ssList(X!50) & (~(memberP(V!48, Z!51) | (~memberP(U!47, Z!51)) | (~ssItem(Z!51)))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[6, 3])).
% 0.19/0.48 tff(8,plain,
% 0.19/0.48 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(9,plain,
% 0.19/0.48 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(V!48 = X!50))) & ![Y: $i] : (~(ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y))))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & (~(memberP(V!48, Z!51) | (~memberP(U!47, Z!51)) | (~ssItem(Z!51))))))) <=> (ssList(V!48) & (ssList(W!49) & (V!48 = X!50) & ![Y: $i] : (~(ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y))))) & (U!47 = W!49) & ssList(X!50) & (~(memberP(V!48, Z!51) | (~memberP(U!47, Z!51)) | (~ssItem(Z!51))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[8, 7])).
% 0.19/0.48 tff(10,plain,
% 0.19/0.48 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(V!48 = X!50))) & ![Y: $i] : (~(ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y))))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & (~(memberP(V!48, Z!51) | (~memberP(U!47, Z!51)) | (~ssItem(Z!51))))))) <=> (ssList(V!48) & ssList(W!49) & (V!48 = X!50) & ![Y: $i] : (~(ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y))))) & (U!47 = W!49) & ssList(X!50) & (~(memberP(V!48, Z!51) | (~memberP(U!47, Z!51)) | (~ssItem(Z!51)))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[9, 2])).
% 0.19/0.48 tff(11,plain,
% 0.19/0.48 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(12,plain,
% 0.19/0.48 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(V!48 = X!50))) & ![Y: $i] : (~(ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y))))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & (~(memberP(V!48, Z!51) | (~memberP(U!47, Z!51)) | (~ssItem(Z!51)))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (V!48 = X!50) & ![Y: $i] : (~(ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y))))) & (U!47 = W!49) & ssList(X!50) & (~(memberP(V!48, Z!51) | (~memberP(U!47, Z!51)) | (~ssItem(Z!51))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[11, 10])).
% 0.19/0.48 tff(13,plain,
% 0.19/0.48 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(V!48 = X!50))) & ![Y: $i] : (~(ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y))))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & (~(memberP(V!48, Z!51) | (~memberP(U!47, Z!51)) | (~ssItem(Z!51)))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (V!48 = X!50) & ![Y: $i] : (~(ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y))))) & (U!47 = W!49) & ssList(X!50) & (~(memberP(V!48, Z!51) | (~memberP(U!47, Z!51)) | (~ssItem(Z!51)))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[12, 1])).
% 0.19/0.48 tff(14,plain,
% 0.19/0.48 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(V = X)) | ?[Y: $i] : (ssItem(Y) & (((~memberP(X, Y)) & memberP(W, Y)) | ((~memberP(W, Y)) & memberP(X, Y)))) | (~(U = W)) | (~ssList(X)) | ![Z: $i] : (memberP(V, Z) | (~memberP(U, Z)) | (~ssItem(Z)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(V = X)) | ?[Y: $i] : (ssItem(Y) & (((~memberP(X, Y)) & memberP(W, Y)) | ((~memberP(W, Y)) & memberP(X, Y)))) | (~(U = W)) | (~ssList(X)) | ![Z: $i] : (memberP(V, Z) | (~memberP(U, Z)) | (~ssItem(Z))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(15,plain,
% 0.19/0.48 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(V = X)) | (~(U = W))) | ?[Y: $i] : (ssItem(Y) & (((~memberP(X, Y)) & memberP(W, Y)) | ((~memberP(W, Y)) & memberP(X, Y))))) | ![Z: $i] : (ssItem(Z) => ((~memberP(U, Z)) | memberP(V, Z))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(V = X)) | ?[Y: $i] : (ssItem(Y) & (((~memberP(X, Y)) & memberP(W, Y)) | ((~memberP(W, Y)) & memberP(X, Y)))) | (~(U = W)) | (~ssList(X)) | ![Z: $i] : (memberP(V, Z) | (~memberP(U, Z)) | (~ssItem(Z))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(16,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(V = X)) | (~(U = W))) | ?[Y: $i] : (ssItem(Y) & (((~memberP(X, Y)) & memberP(W, Y)) | ((~memberP(W, Y)) & memberP(X, Y))))) | ![Z: $i] : (ssItem(Z) => ((~memberP(U, Z)) | memberP(V, Z))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.19/0.48 tff(17,plain,
% 0.19/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(V = X)) | ?[Y: $i] : (ssItem(Y) & (((~memberP(X, Y)) & memberP(W, Y)) | ((~memberP(W, Y)) & memberP(X, Y)))) | (~(U = W)) | (~ssList(X)) | ![Z: $i] : (memberP(V, Z) | (~memberP(U, Z)) | (~ssItem(Z)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.48 tff(18,plain,
% 0.19/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(V = X)) | ?[Y: $i] : (ssItem(Y) & (((~memberP(X, Y)) & memberP(W, Y)) | ((~memberP(W, Y)) & memberP(X, Y)))) | (~(U = W)) | (~ssList(X)) | ![Z: $i] : (memberP(V, Z) | (~memberP(U, Z)) | (~ssItem(Z)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.19/0.48 tff(19,plain,
% 0.19/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(V = X)) | ?[Y: $i] : (ssItem(Y) & (((~memberP(X, Y)) & memberP(W, Y)) | ((~memberP(W, Y)) & memberP(X, Y)))) | (~(U = W)) | (~ssList(X)) | ![Z: $i] : (memberP(V, Z) | (~memberP(U, Z)) | (~ssItem(Z)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.48 tff(20,plain,
% 0.19/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(V = X)) | ?[Y: $i] : (ssItem(Y) & (((~memberP(X, Y)) & memberP(W, Y)) | ((~memberP(W, Y)) & memberP(X, Y)))) | (~(U = W)) | (~ssList(X)) | ![Z: $i] : (memberP(V, Z) | (~memberP(U, Z)) | (~ssItem(Z)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.19/0.48 tff(21,plain,
% 0.19/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(V = X)) | ?[Y: $i] : (ssItem(Y) & (((~memberP(X, Y)) & memberP(W, Y)) | ((~memberP(W, Y)) & memberP(X, Y)))) | (~(U = W)) | (~ssList(X)) | ![Z: $i] : (memberP(V, Z) | (~memberP(U, Z)) | (~ssItem(Z)))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.19/0.49 tff(22,plain,
% 0.19/0.49 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(V = X)) | ?[Y: $i] : (ssItem(Y) & (((~memberP(X, Y)) & memberP(W, Y)) | ((~memberP(W, Y)) & memberP(X, Y)))) | (~(U = W)) | (~ssList(X)) | ![Z: $i] : (memberP(V, Z) | (~memberP(U, Z)) | (~ssItem(Z)))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.19/0.49 tff(23,plain,
% 0.19/0.49 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(V = X)) | ?[Y: $i] : (ssItem(Y) & (((~memberP(X, Y)) & memberP(W, Y)) | ((~memberP(W, Y)) & memberP(X, Y)))) | (~(U = W)) | (~ssList(X)) | ![Z: $i] : (memberP(V, Z) | (~memberP(U, Z)) | (~ssItem(Z)))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[22, 14])).
% 0.19/0.49 tff(24,plain,
% 0.19/0.49 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (V!48 = X!50) & ![Y: $i] : (~(ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y))))) & (U!47 = W!49) & ssList(X!50) & (~(memberP(V!48, Z!51) | (~memberP(U!47, Z!51)) | (~ssItem(Z!51))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.19/0.49 tff(25,plain,
% 0.19/0.49 (~(memberP(V!48, Z!51) | (~memberP(U!47, Z!51)) | (~ssItem(Z!51)))),
% 0.19/0.49 inference(and_elim,[status(thm)],[24])).
% 0.19/0.49 tff(26,plain,
% 0.19/0.49 (ssItem(Z!51)),
% 0.19/0.49 inference(or_elim,[status(thm)],[25])).
% 0.19/0.49 tff(27,plain,
% 0.19/0.49 (^[Y: $i] : refl(((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | memberP(X!50, Y))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y))))))) <=> ((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | memberP(X!50, Y))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y))))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(28,plain,
% 0.19/0.49 (![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | memberP(X!50, Y))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y))))))) <=> ![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | memberP(X!50, Y))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.49 tff(29,plain,
% 0.19/0.49 (^[Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y))) <=> ((~((~memberP(W!49, Y)) | memberP(X!50, Y))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)))))), ((ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y)))) <=> (ssItem(Y) & ((~((~memberP(W!49, Y)) | memberP(X!50, Y))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)))))))), rewrite((ssItem(Y) & ((~((~memberP(W!49, Y)) | memberP(X!50, Y))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)))))) <=> (~((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | memberP(X!50, Y))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y))))))))), ((ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y)))) <=> (~((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | memberP(X!50, Y))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)))))))))), ((~(ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y))))) <=> (~(~((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | memberP(X!50, Y))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y))))))))))), rewrite((~(~((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | memberP(X!50, Y))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y))))))))) <=> ((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | memberP(X!50, Y))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)))))))), ((~(ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y))))) <=> ((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | memberP(X!50, Y))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)))))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(30,plain,
% 0.19/0.49 (![Y: $i] : (~(ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y))))) <=> ![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | memberP(X!50, Y))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.49 tff(31,plain,
% 0.19/0.49 (![Y: $i] : (~(ssItem(Y) & (((~memberP(X!50, Y)) & memberP(W!49, Y)) | ((~memberP(W!49, Y)) & memberP(X!50, Y)))))),
% 0.19/0.49 inference(and_elim,[status(thm)],[24])).
% 0.19/0.49 tff(32,plain,
% 0.19/0.49 (![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | memberP(X!50, Y))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.49 tff(33,plain,
% 0.19/0.49 (![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | memberP(X!50, Y))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.19/0.49 tff(34,plain,
% 0.19/0.49 (((~![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | memberP(X!50, Y))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)))))))) | ((~ssItem(Z!51)) | (~((~((~memberP(W!49, Z!51)) | memberP(X!50, Z!51))) | (~(memberP(W!49, Z!51) | (~memberP(X!50, Z!51)))))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | memberP(X!50, Y))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)))))))) | (~ssItem(Z!51)) | (~((~((~memberP(W!49, Z!51)) | memberP(X!50, Z!51))) | (~(memberP(W!49, Z!51) | (~memberP(X!50, Z!51)))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(35,plain,
% 0.19/0.49 ((~![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | memberP(X!50, Y))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)))))))) | ((~ssItem(Z!51)) | (~((~((~memberP(W!49, Z!51)) | memberP(X!50, Z!51))) | (~(memberP(W!49, Z!51) | (~memberP(X!50, Z!51)))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(36,plain,
% 0.19/0.49 ((~![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | memberP(X!50, Y))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)))))))) | (~ssItem(Z!51)) | (~((~((~memberP(W!49, Z!51)) | memberP(X!50, Z!51))) | (~(memberP(W!49, Z!51) | (~memberP(X!50, Z!51))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.49 tff(37,plain,
% 0.19/0.49 (~((~((~memberP(W!49, Z!51)) | memberP(X!50, Z!51))) | (~(memberP(W!49, Z!51) | (~memberP(X!50, Z!51)))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[36, 33, 26])).
% 0.19/0.49 tff(38,plain,
% 0.19/0.49 (((~((~memberP(W!49, Z!51)) | memberP(X!50, Z!51))) | (~(memberP(W!49, Z!51) | (~memberP(X!50, Z!51))))) | ((~memberP(W!49, Z!51)) | memberP(X!50, Z!51))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(39,plain,
% 0.19/0.49 ((~memberP(W!49, Z!51)) | memberP(X!50, Z!51)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.19/0.49 tff(40,plain,
% 0.19/0.49 (U!47 = W!49),
% 0.19/0.49 inference(and_elim,[status(thm)],[24])).
% 0.19/0.49 tff(41,plain,
% 0.19/0.49 (W!49 = U!47),
% 0.19/0.49 inference(symmetry,[status(thm)],[40])).
% 0.19/0.49 tff(42,plain,
% 0.19/0.49 (memberP(W!49, Z!51) <=> memberP(U!47, Z!51)),
% 0.19/0.49 inference(monotonicity,[status(thm)],[41])).
% 0.19/0.49 tff(43,plain,
% 0.19/0.49 (memberP(U!47, Z!51) <=> memberP(W!49, Z!51)),
% 0.19/0.49 inference(symmetry,[status(thm)],[42])).
% 0.19/0.49 tff(44,plain,
% 0.19/0.49 (memberP(U!47, Z!51)),
% 0.19/0.49 inference(or_elim,[status(thm)],[25])).
% 0.19/0.49 tff(45,plain,
% 0.19/0.49 (memberP(W!49, Z!51)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.49 tff(46,plain,
% 0.19/0.49 (V!48 = X!50),
% 0.19/0.49 inference(and_elim,[status(thm)],[24])).
% 0.19/0.49 tff(47,plain,
% 0.19/0.49 (X!50 = V!48),
% 0.19/0.49 inference(symmetry,[status(thm)],[46])).
% 0.19/0.49 tff(48,plain,
% 0.19/0.49 (memberP(X!50, Z!51) <=> memberP(V!48, Z!51)),
% 0.19/0.49 inference(monotonicity,[status(thm)],[47])).
% 0.19/0.49 tff(49,plain,
% 0.19/0.49 (memberP(V!48, Z!51) <=> memberP(X!50, Z!51)),
% 0.19/0.49 inference(symmetry,[status(thm)],[48])).
% 0.19/0.49 tff(50,plain,
% 0.19/0.49 ((~memberP(V!48, Z!51)) <=> (~memberP(X!50, Z!51))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[49])).
% 0.19/0.49 tff(51,plain,
% 0.19/0.49 (~memberP(V!48, Z!51)),
% 0.19/0.49 inference(or_elim,[status(thm)],[25])).
% 0.19/0.49 tff(52,plain,
% 0.19/0.49 (~memberP(X!50, Z!51)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.49 tff(53,plain,
% 0.19/0.49 ((~((~memberP(W!49, Z!51)) | memberP(X!50, Z!51))) | (~memberP(W!49, Z!51)) | memberP(X!50, Z!51)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(54,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[53, 52, 45, 39])).
% 0.19/0.49 % SZS output end Proof
%------------------------------------------------------------------------------