TSTP Solution File: SWC398+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC398+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 11:57:41 EDT 2022
% Result : Theorem 1.22s 1.01s
% Output : Proof 1.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC398+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 : n008.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 00:45:10 EDT 2022
% 0.13/0.34 % 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.
% 1.22/1.01 % SZS status Theorem
% 1.22/1.01 % SZS output start Proof
% 1.22/1.01 tff(memberP_type, type, (
% 1.22/1.01 memberP: ( $i * $i ) > $o)).
% 1.22/1.01 tff(tptp_fun_X3_52_type, type, (
% 1.22/1.01 tptp_fun_X3_52: $i)).
% 1.22/1.01 tff(app_type, type, (
% 1.22/1.01 app: ( $i * $i ) > $i)).
% 1.22/1.01 tff(tptp_fun_Y_51_type, type, (
% 1.22/1.01 tptp_fun_Y_51: $i)).
% 1.22/1.01 tff(tptp_fun_W_49_type, type, (
% 1.22/1.01 tptp_fun_W_49: $i)).
% 1.22/1.01 tff(tptp_fun_V_48_type, type, (
% 1.22/1.01 tptp_fun_V_48: $i)).
% 1.22/1.01 tff(tptp_fun_X_50_type, type, (
% 1.22/1.01 tptp_fun_X_50: $i)).
% 1.22/1.01 tff(ssItem_type, type, (
% 1.22/1.01 ssItem: $i > $o)).
% 1.22/1.01 tff(tptp_fun_U_47_type, type, (
% 1.22/1.01 tptp_fun_U_47: $i)).
% 1.22/1.01 tff(cons_type, type, (
% 1.22/1.01 cons: ( $i * $i ) > $i)).
% 1.22/1.01 tff(nil_type, type, (
% 1.22/1.01 nil: $i)).
% 1.22/1.01 tff(ssList_type, type, (
% 1.22/1.01 ssList: $i > $o)).
% 1.22/1.01 tff(equalelemsP_type, type, (
% 1.22/1.01 equalelemsP: $i > $o)).
% 1.22/1.01 tff(1,plain,
% 1.22/1.01 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))) & (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52)))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))) & (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52)))))),
% 1.22/1.01 inference(rewrite,[status(thm)],[])).
% 1.22/1.01 tff(2,plain,
% 1.22/1.01 ((ssList(V!48) & (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))) & (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52)))))) <=> (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))) & (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52)))))),
% 1.22/1.01 inference(rewrite,[status(thm)],[])).
% 1.22/1.01 tff(3,plain,
% 1.22/1.01 ((ssList(W!49) & ((~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))) & (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52)))))) <=> (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))) & (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52)))))),
% 1.22/1.01 inference(rewrite,[status(thm)],[])).
% 1.22/1.01 tff(4,plain,
% 1.22/1.01 (((~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))) & (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52))))) <=> ((~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))) & (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52)))))),
% 1.22/1.02 inference(rewrite,[status(thm)],[])).
% 1.22/1.02 tff(5,plain,
% 1.22/1.02 ((~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52)))) <=> (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52))))),
% 1.22/1.02 inference(rewrite,[status(thm)],[])).
% 1.22/1.02 tff(6,plain,
% 1.22/1.02 (((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))) <=> ((app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))),
% 1.22/1.02 inference(rewrite,[status(thm)],[])).
% 1.22/1.02 tff(7,plain,
% 1.22/1.02 ((~(~ssList(X!50))) <=> ssList(X!50)),
% 1.22/1.02 inference(rewrite,[status(thm)],[])).
% 1.22/1.02 tff(8,plain,
% 1.22/1.02 ((~(~(V!48 = X!50))) <=> (V!48 = X!50)),
% 1.22/1.02 inference(rewrite,[status(thm)],[])).
% 1.22/1.02 tff(9,plain,
% 1.22/1.02 ((~(~(U!47 = W!49))) <=> (U!47 = W!49)),
% 1.22/1.02 inference(rewrite,[status(thm)],[])).
% 1.22/1.02 tff(10,plain,
% 1.22/1.02 (((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))) & (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52))))) <=> ((~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))) & (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52)))))),
% 1.22/1.02 inference(monotonicity,[status(thm)],[9, 8, 7, 6, 5])).
% 1.22/1.02 tff(11,plain,
% 1.22/1.02 (((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))) & (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52))))) <=> ((~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))) & (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52)))))),
% 1.22/1.02 inference(transitivity,[status(thm)],[10, 4])).
% 1.22/1.02 tff(12,plain,
% 1.22/1.02 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 1.22/1.02 inference(rewrite,[status(thm)],[])).
% 1.22/1.02 tff(13,plain,
% 1.22/1.02 (((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))) & (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52)))))) <=> (ssList(W!49) & ((~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))) & (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52))))))),
% 1.22/1.02 inference(monotonicity,[status(thm)],[12, 11])).
% 1.22/1.02 tff(14,plain,
% 1.22/1.02 (((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))) & (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52)))))) <=> (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))) & (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52)))))),
% 1.22/1.02 inference(transitivity,[status(thm)],[13, 3])).
% 1.22/1.02 tff(15,plain,
% 1.22/1.02 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 1.22/1.02 inference(rewrite,[status(thm)],[])).
% 1.22/1.02 tff(16,plain,
% 1.22/1.02 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))) & (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52))))))) <=> (ssList(V!48) & (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))) & (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52))))))),
% 1.22/1.02 inference(monotonicity,[status(thm)],[15, 14])).
% 1.22/1.02 tff(17,plain,
% 1.22/1.02 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))) & (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52))))))) <=> (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))) & (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52)))))),
% 1.22/1.02 inference(transitivity,[status(thm)],[16, 2])).
% 1.22/1.02 tff(18,plain,
% 1.22/1.02 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 1.22/1.02 inference(rewrite,[status(thm)],[])).
% 1.22/1.02 tff(19,plain,
% 1.22/1.02 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))) & (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52)))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))) & (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52))))))),
% 1.22/1.02 inference(monotonicity,[status(thm)],[18, 17])).
% 1.22/1.02 tff(20,plain,
% 1.22/1.02 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))) & (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52)))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))) & (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52)))))),
% 1.22/1.02 inference(transitivity,[status(thm)],[19, 1])).
% 1.22/1.02 tff(21,plain,
% 1.22/1.02 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W))))) | ![X3: $i] : (memberP(V, X3) | (~memberP(U, X3)) | (~ssItem(X3)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W))))) | ![X3: $i] : (memberP(V, X3) | (~memberP(U, X3)) | (~ssItem(X3))))))))),
% 1.22/1.02 inference(rewrite,[status(thm)],[])).
% 1.22/1.02 tff(22,plain,
% 1.22/1.02 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | ![Y: $i] : (ssList(Y) => (((~(app(W, Y) = X)) | (~equalelemsP(W))) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : ((ssList(X1) & (app(cons(Z, nil), X1) = Y)) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W))))))) | ![X3: $i] : (ssItem(X3) => ((~memberP(U, X3)) | memberP(V, X3)))) | ((~(nil = X)) & (nil = W)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W))))) | ![X3: $i] : (memberP(V, X3) | (~memberP(U, X3)) | (~ssItem(X3))))))))),
% 1.22/1.02 inference(rewrite,[status(thm)],[])).
% 1.22/1.02 tff(23,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | ![Y: $i] : (ssList(Y) => (((~(app(W, Y) = X)) | (~equalelemsP(W))) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : ((ssList(X1) & (app(cons(Z, nil), X1) = Y)) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W))))))) | ![X3: $i] : (ssItem(X3) => ((~memberP(U, X3)) | memberP(V, X3)))) | ((~(nil = X)) & (nil = W)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 1.22/1.02 tff(24,plain,
% 1.22/1.02 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W))))) | ![X3: $i] : (memberP(V, X3) | (~memberP(U, X3)) | (~ssItem(X3)))))))),
% 1.22/1.02 inference(modus_ponens,[status(thm)],[23, 22])).
% 1.22/1.02 tff(25,plain,
% 1.22/1.02 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W))))) | ![X3: $i] : (memberP(V, X3) | (~memberP(U, X3)) | (~ssItem(X3)))))))),
% 1.22/1.02 inference(modus_ponens,[status(thm)],[24, 21])).
% 1.22/1.02 tff(26,plain,
% 1.22/1.02 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W))))) | ![X3: $i] : (memberP(V, X3) | (~memberP(U, X3)) | (~ssItem(X3)))))))),
% 1.22/1.02 inference(modus_ponens,[status(thm)],[25, 21])).
% 1.22/1.02 tff(27,plain,
% 1.22/1.02 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W))))) | ![X3: $i] : (memberP(V, X3) | (~memberP(U, X3)) | (~ssItem(X3)))))))),
% 1.22/1.02 inference(modus_ponens,[status(thm)],[26, 21])).
% 1.22/1.02 tff(28,plain,
% 1.22/1.02 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W))))) | ![X3: $i] : (memberP(V, X3) | (~memberP(U, X3)) | (~ssItem(X3)))))))),
% 1.22/1.02 inference(modus_ponens,[status(thm)],[27, 21])).
% 1.22/1.02 tff(29,plain,
% 1.22/1.02 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W))))) | ![X3: $i] : (memberP(V, X3) | (~memberP(U, X3)) | (~ssItem(X3)))))))),
% 1.22/1.02 inference(modus_ponens,[status(thm)],[28, 21])).
% 1.22/1.02 tff(30,plain,
% 1.22/1.02 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W))))) | ![X3: $i] : (memberP(V, X3) | (~memberP(U, X3)) | (~ssItem(X3)))))))),
% 1.22/1.02 inference(modus_ponens,[status(thm)],[29, 21])).
% 1.22/1.02 tff(31,plain,
% 1.22/1.02 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))) & (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52))))),
% 1.22/1.02 inference(modus_ponens,[status(thm)],[30, 20])).
% 1.22/1.02 tff(32,plain,
% 1.22/1.02 (V!48 = X!50),
% 1.22/1.02 inference(and_elim,[status(thm)],[31])).
% 1.22/1.02 tff(33,plain,
% 1.22/1.02 (X!50 = V!48),
% 1.22/1.02 inference(symmetry,[status(thm)],[32])).
% 1.22/1.02 tff(34,plain,
% 1.22/1.02 (app(W!49, Y!51) = X!50),
% 1.22/1.02 inference(and_elim,[status(thm)],[31])).
% 1.22/1.02 tff(35,plain,
% 1.22/1.02 (app(W!49, Y!51) = V!48),
% 1.22/1.02 inference(transitivity,[status(thm)],[34, 33])).
% 1.22/1.02 tff(36,plain,
% 1.22/1.02 (memberP(app(W!49, Y!51), X3!52) <=> memberP(V!48, X3!52)),
% 1.22/1.02 inference(monotonicity,[status(thm)],[35])).
% 1.22/1.02 tff(37,plain,
% 1.22/1.02 (memberP(V!48, X3!52) <=> memberP(app(W!49, Y!51), X3!52)),
% 1.22/1.02 inference(symmetry,[status(thm)],[36])).
% 1.22/1.02 tff(38,plain,
% 1.22/1.02 ((~memberP(V!48, X3!52)) <=> (~memberP(app(W!49, Y!51), X3!52))),
% 1.22/1.02 inference(monotonicity,[status(thm)],[37])).
% 1.22/1.02 tff(39,plain,
% 1.22/1.02 (~(memberP(V!48, X3!52) | (~memberP(U!47, X3!52)) | (~ssItem(X3!52)))),
% 1.22/1.02 inference(and_elim,[status(thm)],[31])).
% 1.22/1.02 tff(40,plain,
% 1.22/1.02 (~memberP(V!48, X3!52)),
% 1.22/1.02 inference(or_elim,[status(thm)],[39])).
% 1.22/1.02 tff(41,plain,
% 1.22/1.02 (~memberP(app(W!49, Y!51), X3!52)),
% 1.22/1.02 inference(modus_ponens,[status(thm)],[40, 38])).
% 1.22/1.02 tff(42,plain,
% 1.22/1.02 (ssItem(X3!52)),
% 1.22/1.02 inference(or_elim,[status(thm)],[39])).
% 1.22/1.02 tff(43,plain,
% 1.22/1.02 (^[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)))))))),
% 1.22/1.02 inference(bind,[status(th)],[])).
% 1.22/1.02 tff(44,plain,
% 1.22/1.02 (![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))))))),
% 1.22/1.02 inference(quant_intro,[status(thm)],[43])).
% 1.22/1.02 tff(45,plain,
% 1.22/1.02 (^[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)))))))),
% 1.22/1.02 inference(bind,[status(th)],[])).
% 1.22/1.02 tff(46,plain,
% 1.22/1.02 (![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))))))),
% 1.22/1.02 inference(quant_intro,[status(thm)],[45])).
% 1.22/1.02 tff(47,plain,
% 1.22/1.02 (![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))))))),
% 1.22/1.02 inference(transitivity,[status(thm)],[46, 44])).
% 1.22/1.02 tff(48,plain,
% 1.22/1.02 (![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))))))),
% 1.22/1.02 inference(rewrite,[status(thm)],[])).
% 1.22/1.02 tff(49,plain,
% 1.22/1.02 (^[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))))))))),
% 1.22/1.02 inference(bind,[status(th)],[])).
% 1.22/1.02 tff(50,plain,
% 1.22/1.02 (![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))))))),
% 1.22/1.02 inference(quant_intro,[status(thm)],[49])).
% 1.22/1.02 tff(51,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')).
% 1.22/1.02 tff(52,plain,
% 1.22/1.02 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 1.22/1.02 inference(modus_ponens,[status(thm)],[51, 50])).
% 1.22/1.02 tff(53,plain,
% 1.22/1.02 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 1.22/1.02 inference(modus_ponens,[status(thm)],[52, 48])).
% 1.22/1.02 tff(54,plain,(
% 1.22/1.02 ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 1.22/1.02 inference(skolemize,[status(sab)],[53])).
% 1.22/1.02 tff(55,plain,
% 1.22/1.02 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 1.22/1.02 inference(modus_ponens,[status(thm)],[54, 47])).
% 1.22/1.02 tff(56,plain,
% 1.22/1.02 (((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))) | ((~ssItem(X3!52)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X3!52) <=> (memberP(W, X3!52) | memberP(V, X3!52))))))) <=> ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))) | (~ssItem(X3!52)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X3!52) <=> (memberP(W, X3!52) | memberP(V, X3!52))))))),
% 1.22/1.02 inference(rewrite,[status(thm)],[])).
% 1.22/1.02 tff(57,plain,
% 1.22/1.02 ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))) | ((~ssItem(X3!52)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X3!52) <=> (memberP(W, X3!52) | memberP(V, X3!52))))))),
% 1.22/1.02 inference(quant_inst,[status(thm)],[])).
% 1.22/1.02 tff(58,plain,
% 1.22/1.02 ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))) | (~ssItem(X3!52)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X3!52) <=> (memberP(W, X3!52) | memberP(V, X3!52)))))),
% 1.22/1.02 inference(modus_ponens,[status(thm)],[57, 56])).
% 1.22/1.02 tff(59,plain,
% 1.22/1.02 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X3!52) <=> (memberP(W, X3!52) | memberP(V, X3!52)))))),
% 1.22/1.02 inference(unit_resolution,[status(thm)],[58, 55, 42])).
% 1.22/1.02 tff(60,plain,
% 1.22/1.02 (ssList(W!49)),
% 1.22/1.02 inference(and_elim,[status(thm)],[31])).
% 1.22/1.02 tff(61,plain,
% 1.22/1.02 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X3!52) <=> (memberP(W, X3!52) | memberP(V, X3!52)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (memberP(app(W!49, W), X3!52) <=> (memberP(W, X3!52) | memberP(W!49, X3!52)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X3!52) <=> (memberP(W, X3!52) | memberP(V, X3!52)))))) | (~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (memberP(app(W!49, W), X3!52) <=> (memberP(W, X3!52) | memberP(W!49, X3!52)))))),
% 1.22/1.03 inference(rewrite,[status(thm)],[])).
% 1.22/1.03 tff(62,plain,
% 1.22/1.03 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X3!52) <=> (memberP(W, X3!52) | memberP(V, X3!52)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (memberP(app(W!49, W), X3!52) <=> (memberP(W, X3!52) | memberP(W!49, X3!52)))))),
% 1.22/1.03 inference(quant_inst,[status(thm)],[])).
% 1.22/1.03 tff(63,plain,
% 1.22/1.03 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X3!52) <=> (memberP(W, X3!52) | memberP(V, X3!52)))))) | (~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (memberP(app(W!49, W), X3!52) <=> (memberP(W, X3!52) | memberP(W!49, X3!52))))),
% 1.22/1.03 inference(modus_ponens,[status(thm)],[62, 61])).
% 1.22/1.03 tff(64,plain,
% 1.22/1.03 (![W: $i] : ((~ssList(W)) | (memberP(app(W!49, W), X3!52) <=> (memberP(W, X3!52) | memberP(W!49, X3!52))))),
% 1.22/1.03 inference(unit_resolution,[status(thm)],[63, 60, 59])).
% 1.22/1.03 tff(65,plain,
% 1.22/1.03 (ssList(Y!51)),
% 1.22/1.03 inference(and_elim,[status(thm)],[31])).
% 1.22/1.03 tff(66,plain,
% 1.22/1.03 (((~![W: $i] : ((~ssList(W)) | (memberP(app(W!49, W), X3!52) <=> (memberP(W, X3!52) | memberP(W!49, X3!52))))) | ((~ssList(Y!51)) | (memberP(app(W!49, Y!51), X3!52) <=> (memberP(W!49, X3!52) | memberP(Y!51, X3!52))))) <=> ((~![W: $i] : ((~ssList(W)) | (memberP(app(W!49, W), X3!52) <=> (memberP(W, X3!52) | memberP(W!49, X3!52))))) | (~ssList(Y!51)) | (memberP(app(W!49, Y!51), X3!52) <=> (memberP(W!49, X3!52) | memberP(Y!51, X3!52))))),
% 1.22/1.03 inference(rewrite,[status(thm)],[])).
% 1.22/1.03 tff(67,plain,
% 1.22/1.03 (((~ssList(Y!51)) | (memberP(app(W!49, Y!51), X3!52) <=> (memberP(Y!51, X3!52) | memberP(W!49, X3!52)))) <=> ((~ssList(Y!51)) | (memberP(app(W!49, Y!51), X3!52) <=> (memberP(W!49, X3!52) | memberP(Y!51, X3!52))))),
% 1.22/1.03 inference(rewrite,[status(thm)],[])).
% 1.22/1.03 tff(68,plain,
% 1.22/1.03 (((~![W: $i] : ((~ssList(W)) | (memberP(app(W!49, W), X3!52) <=> (memberP(W, X3!52) | memberP(W!49, X3!52))))) | ((~ssList(Y!51)) | (memberP(app(W!49, Y!51), X3!52) <=> (memberP(Y!51, X3!52) | memberP(W!49, X3!52))))) <=> ((~![W: $i] : ((~ssList(W)) | (memberP(app(W!49, W), X3!52) <=> (memberP(W, X3!52) | memberP(W!49, X3!52))))) | ((~ssList(Y!51)) | (memberP(app(W!49, Y!51), X3!52) <=> (memberP(W!49, X3!52) | memberP(Y!51, X3!52)))))),
% 1.22/1.03 inference(monotonicity,[status(thm)],[67])).
% 1.22/1.03 tff(69,plain,
% 1.22/1.03 (((~![W: $i] : ((~ssList(W)) | (memberP(app(W!49, W), X3!52) <=> (memberP(W, X3!52) | memberP(W!49, X3!52))))) | ((~ssList(Y!51)) | (memberP(app(W!49, Y!51), X3!52) <=> (memberP(Y!51, X3!52) | memberP(W!49, X3!52))))) <=> ((~![W: $i] : ((~ssList(W)) | (memberP(app(W!49, W), X3!52) <=> (memberP(W, X3!52) | memberP(W!49, X3!52))))) | (~ssList(Y!51)) | (memberP(app(W!49, Y!51), X3!52) <=> (memberP(W!49, X3!52) | memberP(Y!51, X3!52))))),
% 1.22/1.03 inference(transitivity,[status(thm)],[68, 66])).
% 1.22/1.03 tff(70,plain,
% 1.22/1.03 ((~![W: $i] : ((~ssList(W)) | (memberP(app(W!49, W), X3!52) <=> (memberP(W, X3!52) | memberP(W!49, X3!52))))) | ((~ssList(Y!51)) | (memberP(app(W!49, Y!51), X3!52) <=> (memberP(Y!51, X3!52) | memberP(W!49, X3!52))))),
% 1.22/1.03 inference(quant_inst,[status(thm)],[])).
% 1.22/1.03 tff(71,plain,
% 1.22/1.03 ((~![W: $i] : ((~ssList(W)) | (memberP(app(W!49, W), X3!52) <=> (memberP(W, X3!52) | memberP(W!49, X3!52))))) | (~ssList(Y!51)) | (memberP(app(W!49, Y!51), X3!52) <=> (memberP(W!49, X3!52) | memberP(Y!51, X3!52)))),
% 1.22/1.03 inference(modus_ponens,[status(thm)],[70, 69])).
% 1.22/1.03 tff(72,plain,
% 1.22/1.03 (memberP(app(W!49, Y!51), X3!52) <=> (memberP(W!49, X3!52) | memberP(Y!51, X3!52))),
% 1.22/1.03 inference(unit_resolution,[status(thm)],[71, 65, 64])).
% 1.22/1.03 tff(73,plain,
% 1.22/1.03 (U!47 = W!49),
% 1.22/1.03 inference(and_elim,[status(thm)],[31])).
% 1.22/1.03 tff(74,plain,
% 1.22/1.03 (W!49 = U!47),
% 1.22/1.03 inference(symmetry,[status(thm)],[73])).
% 1.22/1.03 tff(75,plain,
% 1.22/1.03 (memberP(W!49, X3!52) <=> memberP(U!47, X3!52)),
% 1.22/1.03 inference(monotonicity,[status(thm)],[74])).
% 1.22/1.03 tff(76,plain,
% 1.22/1.03 (memberP(U!47, X3!52) <=> memberP(W!49, X3!52)),
% 1.22/1.03 inference(symmetry,[status(thm)],[75])).
% 1.22/1.03 tff(77,plain,
% 1.22/1.03 (memberP(U!47, X3!52)),
% 1.22/1.03 inference(or_elim,[status(thm)],[39])).
% 1.22/1.03 tff(78,plain,
% 1.22/1.03 (memberP(W!49, X3!52)),
% 1.22/1.03 inference(modus_ponens,[status(thm)],[77, 76])).
% 1.22/1.03 tff(79,plain,
% 1.22/1.03 ((memberP(W!49, X3!52) | memberP(Y!51, X3!52)) | (~memberP(W!49, X3!52))),
% 1.22/1.03 inference(tautology,[status(thm)],[])).
% 1.22/1.03 tff(80,plain,
% 1.22/1.03 (memberP(W!49, X3!52) | memberP(Y!51, X3!52)),
% 1.22/1.03 inference(unit_resolution,[status(thm)],[79, 78])).
% 1.22/1.03 tff(81,plain,
% 1.22/1.03 ((~(memberP(app(W!49, Y!51), X3!52) <=> (memberP(W!49, X3!52) | memberP(Y!51, X3!52)))) | memberP(app(W!49, Y!51), X3!52) | (~(memberP(W!49, X3!52) | memberP(Y!51, X3!52)))),
% 1.22/1.03 inference(tautology,[status(thm)],[])).
% 1.22/1.03 tff(82,plain,
% 1.22/1.03 ((~(memberP(app(W!49, Y!51), X3!52) <=> (memberP(W!49, X3!52) | memberP(Y!51, X3!52)))) | memberP(app(W!49, Y!51), X3!52)),
% 1.22/1.03 inference(unit_resolution,[status(thm)],[81, 80])).
% 1.22/1.03 tff(83,plain,
% 1.22/1.03 (memberP(app(W!49, Y!51), X3!52)),
% 1.22/1.03 inference(unit_resolution,[status(thm)],[82, 72])).
% 1.22/1.03 tff(84,plain,
% 1.22/1.03 ($false),
% 1.22/1.03 inference(unit_resolution,[status(thm)],[83, 41])).
% 1.22/1.03 % SZS output end Proof
%------------------------------------------------------------------------------