TSTP Solution File: SWC406+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC406+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 0.20s 0.51s
% Output : Proof 0.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC406+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 : n027.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 01:00:36 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.
% 0.20/0.51 % SZS status Theorem
% 0.20/0.51 % SZS output start Proof
% 0.20/0.51 tff(memberP_type, type, (
% 0.20/0.51 memberP: ( $i * $i ) > $o)).
% 0.20/0.51 tff(tptp_fun_X1_51_type, type, (
% 0.20/0.51 tptp_fun_X1_51: $i)).
% 0.20/0.51 tff(tptp_fun_X_50_type, type, (
% 0.20/0.51 tptp_fun_X_50: $i)).
% 0.20/0.51 tff(tptp_fun_V_48_type, type, (
% 0.20/0.51 tptp_fun_V_48: $i)).
% 0.20/0.51 tff(leq_type, type, (
% 0.20/0.51 leq: ( $i * $i ) > $o)).
% 0.20/0.51 tff(ssItem_type, type, (
% 0.20/0.51 ssItem: $i > $o)).
% 0.20/0.51 tff(tptp_fun_W_49_type, type, (
% 0.20/0.51 tptp_fun_W_49: $i)).
% 0.20/0.51 tff(tptp_fun_Z_52_type, type, (
% 0.20/0.51 tptp_fun_Z_52: $i > $i)).
% 0.20/0.51 tff(tptp_fun_U_47_type, type, (
% 0.20/0.51 tptp_fun_U_47: $i)).
% 0.20/0.51 tff(ssList_type, type, (
% 0.20/0.51 ssList: $i > $o)).
% 0.20/0.51 tff(1,plain,
% 0.20/0.51 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(V!48, X1!51) | (~ssItem(X1!51)) | (~memberP(U!47, X1!51)))) & ![Y: $i] : ((~ssItem(Y)) | ((memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y)))))) & ((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssItem(Z) & (~(Y = Z)) & memberP(X!50, Z) & leq(Z, Y))))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(V!48, X1!51) | (~ssItem(X1!51)) | (~memberP(U!47, X1!51)))) & ![Y: $i] : ((~ssItem(Y)) | ((memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y)))))) & ((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssItem(Z) & (~(Y = Z)) & memberP(X!50, Z) & leq(Z, Y))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(2,plain,
% 0.20/0.51 ((ssList(V!48) & (ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(V!48, X1!51) | (~ssItem(X1!51)) | (~memberP(U!47, X1!51)))) & ![Y: $i] : ((~ssItem(Y)) | ((memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y)))))) & ((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssItem(Z) & (~(Y = Z)) & memberP(X!50, Z) & leq(Z, Y))))))))) <=> (ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(V!48, X1!51) | (~ssItem(X1!51)) | (~memberP(U!47, X1!51)))) & ![Y: $i] : ((~ssItem(Y)) | ((memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y)))))) & ((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssItem(Z) & (~(Y = Z)) & memberP(X!50, Z) & leq(Z, Y))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(3,plain,
% 0.20/0.51 ((ssList(W!49) & ((U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(V!48, X1!51) | (~ssItem(X1!51)) | (~memberP(U!47, X1!51)))) & ![Y: $i] : ((~ssItem(Y)) | ((memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y)))))) & ((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssItem(Z) & (~(Y = Z)) & memberP(X!50, Z) & leq(Z, Y))))))))) <=> (ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(V!48, X1!51) | (~ssItem(X1!51)) | (~memberP(U!47, X1!51)))) & ![Y: $i] : ((~ssItem(Y)) | ((memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y)))))) & ((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssItem(Z) & (~(Y = Z)) & memberP(X!50, Z) & leq(Z, Y))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(4,plain,
% 0.20/0.51 (((~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (~(memberP(V!48, X1!51) | (~ssItem(X1!51)) | (~memberP(U!47, X1!51)))) & ![Y: $i] : ((~ssItem(Y)) | (((~(~memberP(W!49, Y))) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))) | (~memberP(X!50, Y))) & ((~memberP(W!49, Y)) | ((~(~memberP(X!50, Y))) & ![Z: $i] : (~(ssItem(Z) & (~(Y = Z)) & memberP(X!50, Z) & leq(Z, Y)))))))) <=> ((U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(V!48, X1!51) | (~ssItem(X1!51)) | (~memberP(U!47, X1!51)))) & ![Y: $i] : ((~ssItem(Y)) | ((memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y)))))) & ((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssItem(Z) & (~(Y = Z)) & memberP(X!50, Z) & leq(Z, Y))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(5,plain,
% 0.20/0.51 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(6,plain,
% 0.20/0.51 (((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (~(memberP(V!48, X1!51) | (~ssItem(X1!51)) | (~memberP(U!47, X1!51)))) & ![Y: $i] : ((~ssItem(Y)) | (((~(~memberP(W!49, Y))) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))) | (~memberP(X!50, Y))) & ((~memberP(W!49, Y)) | ((~(~memberP(X!50, Y))) & ![Z: $i] : (~(ssItem(Z) & (~(Y = Z)) & memberP(X!50, Z) & leq(Z, Y))))))))) <=> (ssList(W!49) & ((U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(V!48, X1!51) | (~ssItem(X1!51)) | (~memberP(U!47, X1!51)))) & ![Y: $i] : ((~ssItem(Y)) | ((memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y)))))) & ((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssItem(Z) & (~(Y = Z)) & memberP(X!50, Z) & leq(Z, Y)))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[5, 4])).
% 0.20/0.51 tff(7,plain,
% 0.20/0.51 (((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (~(memberP(V!48, X1!51) | (~ssItem(X1!51)) | (~memberP(U!47, X1!51)))) & ![Y: $i] : ((~ssItem(Y)) | (((~(~memberP(W!49, Y))) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))) | (~memberP(X!50, Y))) & ((~memberP(W!49, Y)) | ((~(~memberP(X!50, Y))) & ![Z: $i] : (~(ssItem(Z) & (~(Y = Z)) & memberP(X!50, Z) & leq(Z, Y))))))))) <=> (ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(V!48, X1!51) | (~ssItem(X1!51)) | (~memberP(U!47, X1!51)))) & ![Y: $i] : ((~ssItem(Y)) | ((memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y)))))) & ((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssItem(Z) & (~(Y = Z)) & memberP(X!50, Z) & leq(Z, Y))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[6, 3])).
% 0.20/0.51 tff(8,plain,
% 0.20/0.51 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(9,plain,
% 0.20/0.51 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (~(memberP(V!48, X1!51) | (~ssItem(X1!51)) | (~memberP(U!47, X1!51)))) & ![Y: $i] : ((~ssItem(Y)) | (((~(~memberP(W!49, Y))) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))) | (~memberP(X!50, Y))) & ((~memberP(W!49, Y)) | ((~(~memberP(X!50, Y))) & ![Z: $i] : (~(ssItem(Z) & (~(Y = Z)) & memberP(X!50, Z) & leq(Z, Y)))))))))) <=> (ssList(V!48) & (ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(V!48, X1!51) | (~ssItem(X1!51)) | (~memberP(U!47, X1!51)))) & ![Y: $i] : ((~ssItem(Y)) | ((memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y)))))) & ((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssItem(Z) & (~(Y = Z)) & memberP(X!50, Z) & leq(Z, Y)))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[8, 7])).
% 0.20/0.51 tff(10,plain,
% 0.20/0.51 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (~(memberP(V!48, X1!51) | (~ssItem(X1!51)) | (~memberP(U!47, X1!51)))) & ![Y: $i] : ((~ssItem(Y)) | (((~(~memberP(W!49, Y))) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))) | (~memberP(X!50, Y))) & ((~memberP(W!49, Y)) | ((~(~memberP(X!50, Y))) & ![Z: $i] : (~(ssItem(Z) & (~(Y = Z)) & memberP(X!50, Z) & leq(Z, Y)))))))))) <=> (ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(V!48, X1!51) | (~ssItem(X1!51)) | (~memberP(U!47, X1!51)))) & ![Y: $i] : ((~ssItem(Y)) | ((memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y)))))) & ((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssItem(Z) & (~(Y = Z)) & memberP(X!50, Z) & leq(Z, Y))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[9, 2])).
% 0.20/0.51 tff(11,plain,
% 0.20/0.51 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(12,plain,
% 0.20/0.51 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (~(memberP(V!48, X1!51) | (~ssItem(X1!51)) | (~memberP(U!47, X1!51)))) & ![Y: $i] : ((~ssItem(Y)) | (((~(~memberP(W!49, Y))) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))) | (~memberP(X!50, Y))) & ((~memberP(W!49, Y)) | ((~(~memberP(X!50, Y))) & ![Z: $i] : (~(ssItem(Z) & (~(Y = Z)) & memberP(X!50, Z) & leq(Z, Y))))))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(V!48, X1!51) | (~ssItem(X1!51)) | (~memberP(U!47, X1!51)))) & ![Y: $i] : ((~ssItem(Y)) | ((memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y)))))) & ((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssItem(Z) & (~(Y = Z)) & memberP(X!50, Z) & leq(Z, Y)))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[11, 10])).
% 0.20/0.51 tff(13,plain,
% 0.20/0.51 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (~(memberP(V!48, X1!51) | (~ssItem(X1!51)) | (~memberP(U!47, X1!51)))) & ![Y: $i] : ((~ssItem(Y)) | (((~(~memberP(W!49, Y))) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))) | (~memberP(X!50, Y))) & ((~memberP(W!49, Y)) | ((~(~memberP(X!50, Y))) & ![Z: $i] : (~(ssItem(Z) & (~(Y = Z)) & memberP(X!50, Z) & leq(Z, Y))))))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(V!48, X1!51) | (~ssItem(X1!51)) | (~memberP(U!47, X1!51)))) & ![Y: $i] : ((~ssItem(Y)) | ((memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y)))))) & ((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssItem(Z) & (~(Y = Z)) & memberP(X!50, Z) & leq(Z, Y))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[12, 1])).
% 0.20/0.51 tff(14,plain,
% 0.20/0.51 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~ssList(X)) | ![X1: $i] : (memberP(V, X1) | (~ssItem(X1)) | (~memberP(U, X1))) | ?[Y: $i] : (ssItem(Y) & (((~memberP(W, Y)) & ![Z: $i] : ((Y = Z) | (~memberP(X, Z)) | (~leq(Z, Y)) | (~ssItem(Z))) & memberP(X, Y)) | (memberP(W, Y) & ((~memberP(X, Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(X, Z) & leq(Z, Y))))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~ssList(X)) | ![X1: $i] : (memberP(V, X1) | (~ssItem(X1)) | (~memberP(U, X1))) | ?[Y: $i] : (ssItem(Y) & (((~memberP(W, Y)) & ![Z: $i] : ((Y = Z) | (~memberP(X, Z)) | (~leq(Z, Y)) | (~ssItem(Z))) & memberP(X, Y)) | (memberP(W, Y) & ((~memberP(X, Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(X, Z) & leq(Z, Y)))))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(15,plain,
% 0.20/0.51 ((~![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(W, Y)) & ![Z: $i] : (ssItem(Z) => (((~memberP(X, Z)) | (~leq(Z, Y))) | (Y = Z)))) & memberP(X, Y)) | (memberP(W, Y) & ((~memberP(X, Y)) | ?[Z: $i] : (((ssItem(Z) & (~(Y = Z))) & memberP(X, Z)) & leq(Z, Y))))))) | ![X1: $i] : (ssItem(X1) => ((~memberP(U, X1)) | memberP(V, X1))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~ssList(X)) | ![X1: $i] : (memberP(V, X1) | (~ssItem(X1)) | (~memberP(U, X1))) | ?[Y: $i] : (ssItem(Y) & (((~memberP(W, Y)) & ![Z: $i] : ((Y = Z) | (~memberP(X, Z)) | (~leq(Z, Y)) | (~ssItem(Z))) & memberP(X, Y)) | (memberP(W, Y) & ((~memberP(X, Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(X, Z) & leq(Z, Y)))))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 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(W, Y)) & ![Z: $i] : (ssItem(Z) => (((~memberP(X, Z)) | (~leq(Z, Y))) | (Y = Z)))) & memberP(X, Y)) | (memberP(W, Y) & ((~memberP(X, Y)) | ?[Z: $i] : (((ssItem(Z) & (~(Y = Z))) & memberP(X, Z)) & leq(Z, Y))))))) | ![X1: $i] : (ssItem(X1) => ((~memberP(U, X1)) | memberP(V, X1))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.20/0.51 tff(17,plain,
% 0.20/0.51 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~ssList(X)) | ![X1: $i] : (memberP(V, X1) | (~ssItem(X1)) | (~memberP(U, X1))) | ?[Y: $i] : (ssItem(Y) & (((~memberP(W, Y)) & ![Z: $i] : ((Y = Z) | (~memberP(X, Z)) | (~leq(Z, Y)) | (~ssItem(Z))) & memberP(X, Y)) | (memberP(W, Y) & ((~memberP(X, Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(X, Z) & leq(Z, Y))))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.51 tff(18,plain,
% 0.20/0.51 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~ssList(X)) | ![X1: $i] : (memberP(V, X1) | (~ssItem(X1)) | (~memberP(U, X1))) | ?[Y: $i] : (ssItem(Y) & (((~memberP(W, Y)) & ![Z: $i] : ((Y = Z) | (~memberP(X, Z)) | (~leq(Z, Y)) | (~ssItem(Z))) & memberP(X, Y)) | (memberP(W, Y) & ((~memberP(X, Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(X, Z) & leq(Z, Y))))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.20/0.51 tff(19,plain,
% 0.20/0.51 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~ssList(X)) | ![X1: $i] : (memberP(V, X1) | (~ssItem(X1)) | (~memberP(U, X1))) | ?[Y: $i] : (ssItem(Y) & (((~memberP(W, Y)) & ![Z: $i] : ((Y = Z) | (~memberP(X, Z)) | (~leq(Z, Y)) | (~ssItem(Z))) & memberP(X, Y)) | (memberP(W, Y) & ((~memberP(X, Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(X, Z) & leq(Z, Y))))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.51 tff(20,plain,
% 0.20/0.51 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~ssList(X)) | ![X1: $i] : (memberP(V, X1) | (~ssItem(X1)) | (~memberP(U, X1))) | ?[Y: $i] : (ssItem(Y) & (((~memberP(W, Y)) & ![Z: $i] : ((Y = Z) | (~memberP(X, Z)) | (~leq(Z, Y)) | (~ssItem(Z))) & memberP(X, Y)) | (memberP(W, Y) & ((~memberP(X, Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(X, Z) & leq(Z, Y))))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.20/0.51 tff(21,plain,
% 0.20/0.51 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~ssList(X)) | ![X1: $i] : (memberP(V, X1) | (~ssItem(X1)) | (~memberP(U, X1))) | ?[Y: $i] : (ssItem(Y) & (((~memberP(W, Y)) & ![Z: $i] : ((Y = Z) | (~memberP(X, Z)) | (~leq(Z, Y)) | (~ssItem(Z))) & memberP(X, Y)) | (memberP(W, Y) & ((~memberP(X, Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(X, Z) & leq(Z, Y))))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.20/0.51 tff(22,plain,
% 0.20/0.51 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~ssList(X)) | ![X1: $i] : (memberP(V, X1) | (~ssItem(X1)) | (~memberP(U, X1))) | ?[Y: $i] : (ssItem(Y) & (((~memberP(W, Y)) & ![Z: $i] : ((Y = Z) | (~memberP(X, Z)) | (~leq(Z, Y)) | (~ssItem(Z))) & memberP(X, Y)) | (memberP(W, Y) & ((~memberP(X, Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(X, Z) & leq(Z, Y))))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.20/0.51 tff(23,plain,
% 0.20/0.51 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~ssList(X)) | ![X1: $i] : (memberP(V, X1) | (~ssItem(X1)) | (~memberP(U, X1))) | ?[Y: $i] : (ssItem(Y) & (((~memberP(W, Y)) & ![Z: $i] : ((Y = Z) | (~memberP(X, Z)) | (~leq(Z, Y)) | (~ssItem(Z))) & memberP(X, Y)) | (memberP(W, Y) & ((~memberP(X, Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(X, Z) & leq(Z, Y))))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[22, 14])).
% 0.20/0.51 tff(24,plain,
% 0.20/0.51 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (~(memberP(V!48, X1!51) | (~ssItem(X1!51)) | (~memberP(U!47, X1!51)))) & ![Y: $i] : ((~ssItem(Y)) | ((memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y)))))) & ((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssItem(Z) & (~(Y = Z)) & memberP(X!50, Z) & leq(Z, Y)))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.20/0.51 tff(25,plain,
% 0.20/0.51 (V!48 = X!50),
% 0.20/0.51 inference(and_elim,[status(thm)],[24])).
% 0.20/0.51 tff(26,plain,
% 0.20/0.51 (X!50 = V!48),
% 0.20/0.51 inference(symmetry,[status(thm)],[25])).
% 0.20/0.51 tff(27,plain,
% 0.20/0.51 (memberP(X!50, X1!51) <=> memberP(V!48, X1!51)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[26])).
% 0.20/0.51 tff(28,plain,
% 0.20/0.51 (memberP(V!48, X1!51) <=> memberP(X!50, X1!51)),
% 0.20/0.51 inference(symmetry,[status(thm)],[27])).
% 0.20/0.51 tff(29,plain,
% 0.20/0.51 ((~memberP(V!48, X1!51)) <=> (~memberP(X!50, X1!51))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[28])).
% 0.20/0.51 tff(30,plain,
% 0.20/0.51 (~(memberP(V!48, X1!51) | (~ssItem(X1!51)) | (~memberP(U!47, X1!51)))),
% 0.20/0.51 inference(and_elim,[status(thm)],[24])).
% 0.20/0.51 tff(31,plain,
% 0.20/0.51 (~memberP(V!48, X1!51)),
% 0.20/0.51 inference(or_elim,[status(thm)],[30])).
% 0.20/0.51 tff(32,plain,
% 0.20/0.51 (~memberP(X!50, X1!51)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[31, 29])).
% 0.20/0.51 tff(33,plain,
% 0.20/0.51 (^[Y: $i] : refl(((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((Y = Z) | (~leq(Z, Y)) | (~ssItem(Z)) | (~memberP(X!50, Z))))))))))) <=> ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((Y = Z) | (~leq(Z, Y)) | (~ssItem(Z)) | (~memberP(X!50, Z))))))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(34,plain,
% 0.20/0.51 (![Y: $i] : ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((Y = Z) | (~leq(Z, Y)) | (~ssItem(Z)) | (~memberP(X!50, Z))))))))))) <=> ![Y: $i] : ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((Y = Z) | (~leq(Z, Y)) | (~ssItem(Z)) | (~memberP(X!50, Z)))))))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.51 tff(35,plain,
% 0.20/0.51 (^[Y: $i] : rewrite(((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((Y = Z) | (~leq(Z, Y)) | (~ssItem(Z)) | (~memberP(X!50, Z))))))))))) <=> ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((Y = Z) | (~leq(Z, Y)) | (~ssItem(Z)) | (~memberP(X!50, Z))))))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(36,plain,
% 0.20/0.51 (![Y: $i] : ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((Y = Z) | (~leq(Z, Y)) | (~ssItem(Z)) | (~memberP(X!50, Z))))))))))) <=> ![Y: $i] : ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((Y = Z) | (~leq(Z, Y)) | (~ssItem(Z)) | (~memberP(X!50, Z)))))))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.51 tff(37,plain,
% 0.20/0.51 (![Y: $i] : ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((Y = Z) | (~leq(Z, Y)) | (~ssItem(Z)) | (~memberP(X!50, Z))))))))))) <=> ![Y: $i] : ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((Y = Z) | (~leq(Z, Y)) | (~ssItem(Z)) | (~memberP(X!50, Z)))))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[36, 34])).
% 0.20/0.51 tff(38,plain,
% 0.20/0.51 (^[Y: $i] : rewrite(((~ssItem(Y)) | ((memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y)))))) & ((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssItem(Z) & (~(Y = Z)) & memberP(X!50, Z) & leq(Z, Y))))))) <=> ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((Y = Z) | (~leq(Z, Y)) | (~ssItem(Z)) | (~memberP(X!50, Z))))))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(39,plain,
% 0.20/0.51 (![Y: $i] : ((~ssItem(Y)) | ((memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y)))))) & ((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssItem(Z) & (~(Y = Z)) & memberP(X!50, Z) & leq(Z, Y))))))) <=> ![Y: $i] : ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((Y = Z) | (~leq(Z, Y)) | (~ssItem(Z)) | (~memberP(X!50, Z)))))))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.51 tff(40,plain,
% 0.20/0.51 (![Y: $i] : ((~ssItem(Y)) | ((memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y)))))) & ((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssItem(Z) & (~(Y = Z)) & memberP(X!50, Z) & leq(Z, Y)))))))),
% 0.20/0.51 inference(and_elim,[status(thm)],[24])).
% 0.20/0.51 tff(41,plain,
% 0.20/0.51 (![Y: $i] : ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((Y = Z) | (~leq(Z, Y)) | (~ssItem(Z)) | (~memberP(X!50, Z)))))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.42/0.52 tff(42,plain,
% 0.42/0.52 (![Y: $i] : ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((Y = Z) | (~leq(Z, Y)) | (~ssItem(Z)) | (~memberP(X!50, Z)))))))))))),
% 0.42/0.52 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.42/0.52 tff(43,plain,
% 0.42/0.52 (ssItem(X1!51)),
% 0.42/0.52 inference(or_elim,[status(thm)],[30])).
% 0.42/0.52 tff(44,plain,
% 0.42/0.52 (((~![Y: $i] : ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((Y = Z) | (~leq(Z, Y)) | (~ssItem(Z)) | (~memberP(X!50, Z)))))))))))) | ((~ssItem(X1!51)) | (~((~(memberP(W!49, X1!51) | (~memberP(X!50, X1!51)) | (~((X1!51 = tptp_fun_Z_52(X1!51)) | (~memberP(X!50, tptp_fun_Z_52(X1!51))) | (~leq(tptp_fun_Z_52(X1!51), X1!51)) | (~ssItem(tptp_fun_Z_52(X1!51))))))) | (~((~memberP(W!49, X1!51)) | (~((~memberP(X!50, X1!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (X1!51 = Z) | (~leq(Z, X1!51)))))))))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((Y = Z) | (~leq(Z, Y)) | (~ssItem(Z)) | (~memberP(X!50, Z)))))))))))) | (~ssItem(X1!51)) | (~((~(memberP(W!49, X1!51) | (~memberP(X!50, X1!51)) | (~((X1!51 = tptp_fun_Z_52(X1!51)) | (~memberP(X!50, tptp_fun_Z_52(X1!51))) | (~leq(tptp_fun_Z_52(X1!51), X1!51)) | (~ssItem(tptp_fun_Z_52(X1!51))))))) | (~((~memberP(W!49, X1!51)) | (~((~memberP(X!50, X1!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (X1!51 = Z) | (~leq(Z, X1!51)))))))))))),
% 0.42/0.52 inference(rewrite,[status(thm)],[])).
% 0.42/0.52 tff(45,plain,
% 0.42/0.52 (((~ssItem(X1!51)) | (~((~(memberP(W!49, X1!51) | (~memberP(X!50, X1!51)) | (~((X1!51 = tptp_fun_Z_52(X1!51)) | (~memberP(X!50, tptp_fun_Z_52(X1!51))) | (~leq(tptp_fun_Z_52(X1!51), X1!51)) | (~ssItem(tptp_fun_Z_52(X1!51))))))) | (~((~memberP(W!49, X1!51)) | (~((~memberP(X!50, X1!51)) | (~![Z: $i] : ((X1!51 = Z) | (~leq(Z, X1!51)) | (~ssItem(Z)) | (~memberP(X!50, Z))))))))))) <=> ((~ssItem(X1!51)) | (~((~(memberP(W!49, X1!51) | (~memberP(X!50, X1!51)) | (~((X1!51 = tptp_fun_Z_52(X1!51)) | (~memberP(X!50, tptp_fun_Z_52(X1!51))) | (~leq(tptp_fun_Z_52(X1!51), X1!51)) | (~ssItem(tptp_fun_Z_52(X1!51))))))) | (~((~memberP(W!49, X1!51)) | (~((~memberP(X!50, X1!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (X1!51 = Z) | (~leq(Z, X1!51)))))))))))),
% 0.42/0.52 inference(rewrite,[status(thm)],[])).
% 0.42/0.52 tff(46,plain,
% 0.42/0.52 (((~![Y: $i] : ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((Y = Z) | (~leq(Z, Y)) | (~ssItem(Z)) | (~memberP(X!50, Z)))))))))))) | ((~ssItem(X1!51)) | (~((~(memberP(W!49, X1!51) | (~memberP(X!50, X1!51)) | (~((X1!51 = tptp_fun_Z_52(X1!51)) | (~memberP(X!50, tptp_fun_Z_52(X1!51))) | (~leq(tptp_fun_Z_52(X1!51), X1!51)) | (~ssItem(tptp_fun_Z_52(X1!51))))))) | (~((~memberP(W!49, X1!51)) | (~((~memberP(X!50, X1!51)) | (~![Z: $i] : ((X1!51 = Z) | (~leq(Z, X1!51)) | (~ssItem(Z)) | (~memberP(X!50, Z)))))))))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((Y = Z) | (~leq(Z, Y)) | (~ssItem(Z)) | (~memberP(X!50, Z)))))))))))) | ((~ssItem(X1!51)) | (~((~(memberP(W!49, X1!51) | (~memberP(X!50, X1!51)) | (~((X1!51 = tptp_fun_Z_52(X1!51)) | (~memberP(X!50, tptp_fun_Z_52(X1!51))) | (~leq(tptp_fun_Z_52(X1!51), X1!51)) | (~ssItem(tptp_fun_Z_52(X1!51))))))) | (~((~memberP(W!49, X1!51)) | (~((~memberP(X!50, X1!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (X1!51 = Z) | (~leq(Z, X1!51))))))))))))),
% 0.42/0.52 inference(monotonicity,[status(thm)],[45])).
% 0.42/0.52 tff(47,plain,
% 0.42/0.52 (((~![Y: $i] : ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((Y = Z) | (~leq(Z, Y)) | (~ssItem(Z)) | (~memberP(X!50, Z)))))))))))) | ((~ssItem(X1!51)) | (~((~(memberP(W!49, X1!51) | (~memberP(X!50, X1!51)) | (~((X1!51 = tptp_fun_Z_52(X1!51)) | (~memberP(X!50, tptp_fun_Z_52(X1!51))) | (~leq(tptp_fun_Z_52(X1!51), X1!51)) | (~ssItem(tptp_fun_Z_52(X1!51))))))) | (~((~memberP(W!49, X1!51)) | (~((~memberP(X!50, X1!51)) | (~![Z: $i] : ((X1!51 = Z) | (~leq(Z, X1!51)) | (~ssItem(Z)) | (~memberP(X!50, Z)))))))))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((Y = Z) | (~leq(Z, Y)) | (~ssItem(Z)) | (~memberP(X!50, Z)))))))))))) | (~ssItem(X1!51)) | (~((~(memberP(W!49, X1!51) | (~memberP(X!50, X1!51)) | (~((X1!51 = tptp_fun_Z_52(X1!51)) | (~memberP(X!50, tptp_fun_Z_52(X1!51))) | (~leq(tptp_fun_Z_52(X1!51), X1!51)) | (~ssItem(tptp_fun_Z_52(X1!51))))))) | (~((~memberP(W!49, X1!51)) | (~((~memberP(X!50, X1!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (X1!51 = Z) | (~leq(Z, X1!51)))))))))))),
% 0.42/0.52 inference(transitivity,[status(thm)],[46, 44])).
% 0.42/0.52 tff(48,plain,
% 0.42/0.52 ((~![Y: $i] : ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((Y = Z) | (~leq(Z, Y)) | (~ssItem(Z)) | (~memberP(X!50, Z)))))))))))) | ((~ssItem(X1!51)) | (~((~(memberP(W!49, X1!51) | (~memberP(X!50, X1!51)) | (~((X1!51 = tptp_fun_Z_52(X1!51)) | (~memberP(X!50, tptp_fun_Z_52(X1!51))) | (~leq(tptp_fun_Z_52(X1!51), X1!51)) | (~ssItem(tptp_fun_Z_52(X1!51))))))) | (~((~memberP(W!49, X1!51)) | (~((~memberP(X!50, X1!51)) | (~![Z: $i] : ((X1!51 = Z) | (~leq(Z, X1!51)) | (~ssItem(Z)) | (~memberP(X!50, Z)))))))))))),
% 0.42/0.52 inference(quant_inst,[status(thm)],[])).
% 0.42/0.52 tff(49,plain,
% 0.42/0.52 ((~![Y: $i] : ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((Y = tptp_fun_Z_52(Y)) | (~memberP(X!50, tptp_fun_Z_52(Y))) | (~leq(tptp_fun_Z_52(Y), Y)) | (~ssItem(tptp_fun_Z_52(Y))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((Y = Z) | (~leq(Z, Y)) | (~ssItem(Z)) | (~memberP(X!50, Z)))))))))))) | (~ssItem(X1!51)) | (~((~(memberP(W!49, X1!51) | (~memberP(X!50, X1!51)) | (~((X1!51 = tptp_fun_Z_52(X1!51)) | (~memberP(X!50, tptp_fun_Z_52(X1!51))) | (~leq(tptp_fun_Z_52(X1!51), X1!51)) | (~ssItem(tptp_fun_Z_52(X1!51))))))) | (~((~memberP(W!49, X1!51)) | (~((~memberP(X!50, X1!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (X1!51 = Z) | (~leq(Z, X1!51))))))))))),
% 0.42/0.52 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.42/0.52 tff(50,plain,
% 0.42/0.52 (~((~(memberP(W!49, X1!51) | (~memberP(X!50, X1!51)) | (~((X1!51 = tptp_fun_Z_52(X1!51)) | (~memberP(X!50, tptp_fun_Z_52(X1!51))) | (~leq(tptp_fun_Z_52(X1!51), X1!51)) | (~ssItem(tptp_fun_Z_52(X1!51))))))) | (~((~memberP(W!49, X1!51)) | (~((~memberP(X!50, X1!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (X1!51 = Z) | (~leq(Z, X1!51)))))))))),
% 0.42/0.52 inference(unit_resolution,[status(thm)],[49, 43, 42])).
% 0.42/0.52 tff(51,plain,
% 0.42/0.52 (((~(memberP(W!49, X1!51) | (~memberP(X!50, X1!51)) | (~((X1!51 = tptp_fun_Z_52(X1!51)) | (~memberP(X!50, tptp_fun_Z_52(X1!51))) | (~leq(tptp_fun_Z_52(X1!51), X1!51)) | (~ssItem(tptp_fun_Z_52(X1!51))))))) | (~((~memberP(W!49, X1!51)) | (~((~memberP(X!50, X1!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (X1!51 = Z) | (~leq(Z, X1!51))))))))) | ((~memberP(W!49, X1!51)) | (~((~memberP(X!50, X1!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (X1!51 = Z) | (~leq(Z, X1!51)))))))),
% 0.42/0.52 inference(tautology,[status(thm)],[])).
% 0.42/0.52 tff(52,plain,
% 0.42/0.52 ((~memberP(W!49, X1!51)) | (~((~memberP(X!50, X1!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (X1!51 = Z) | (~leq(Z, X1!51))))))),
% 0.42/0.52 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.42/0.52 tff(53,plain,
% 0.42/0.52 (U!47 = W!49),
% 0.42/0.52 inference(and_elim,[status(thm)],[24])).
% 0.42/0.52 tff(54,plain,
% 0.42/0.52 (W!49 = U!47),
% 0.42/0.52 inference(symmetry,[status(thm)],[53])).
% 0.42/0.52 tff(55,plain,
% 0.42/0.52 (memberP(W!49, X1!51) <=> memberP(U!47, X1!51)),
% 0.42/0.52 inference(monotonicity,[status(thm)],[54])).
% 0.42/0.52 tff(56,plain,
% 0.42/0.52 (memberP(U!47, X1!51) <=> memberP(W!49, X1!51)),
% 0.42/0.52 inference(symmetry,[status(thm)],[55])).
% 0.42/0.52 tff(57,plain,
% 0.42/0.52 (memberP(U!47, X1!51)),
% 0.42/0.52 inference(or_elim,[status(thm)],[30])).
% 0.42/0.52 tff(58,plain,
% 0.42/0.52 (memberP(W!49, X1!51)),
% 0.42/0.52 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.42/0.52 tff(59,plain,
% 0.42/0.52 ((~((~memberP(W!49, X1!51)) | (~((~memberP(X!50, X1!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (X1!51 = Z) | (~leq(Z, X1!51)))))))) | (~memberP(W!49, X1!51)) | (~((~memberP(X!50, X1!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (X1!51 = Z) | (~leq(Z, X1!51))))))),
% 0.42/0.52 inference(tautology,[status(thm)],[])).
% 0.42/0.52 tff(60,plain,
% 0.42/0.52 (~((~memberP(X!50, X1!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (X1!51 = Z) | (~leq(Z, X1!51)))))),
% 0.42/0.52 inference(unit_resolution,[status(thm)],[59, 58, 52])).
% 0.42/0.52 tff(61,plain,
% 0.42/0.52 (((~memberP(X!50, X1!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (X1!51 = Z) | (~leq(Z, X1!51))))) | memberP(X!50, X1!51)),
% 0.42/0.52 inference(tautology,[status(thm)],[])).
% 0.42/0.52 tff(62,plain,
% 0.42/0.52 ($false),
% 0.42/0.52 inference(unit_resolution,[status(thm)],[61, 60, 32])).
% 0.42/0.52 % SZS output end Proof
%------------------------------------------------------------------------------