TSTP Solution File: SWC207+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC207+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 11:56:08 EDT 2022
% Result : Theorem 1.82s 1.38s
% Output : Proof 1.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWC207+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.32 % Computer : n011.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Sat Sep 3 22:35:29 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.32 Usage: tptp [options] [-file:]file
% 0.12/0.32 -h, -? prints this message.
% 0.12/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.32 -m, -model generate model.
% 0.12/0.32 -p, -proof generate proof.
% 0.12/0.32 -c, -core generate unsat core of named formulas.
% 0.12/0.32 -st, -statistics display statistics.
% 0.12/0.32 -t:timeout set timeout (in second).
% 0.12/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.32 -<param>:<value> configuration parameter and value.
% 0.12/0.32 -o:<output-file> file to place output in.
% 1.82/1.38 % SZS status Theorem
% 1.82/1.38 % SZS output start Proof
% 1.82/1.38 tff(nil_type, type, (
% 1.82/1.38 nil: $i)).
% 1.82/1.38 tff(cons_type, type, (
% 1.82/1.38 cons: ( $i * $i ) > $i)).
% 1.82/1.38 tff(tptp_fun_Y_51_type, type, (
% 1.82/1.38 tptp_fun_Y_51: $i)).
% 1.82/1.38 tff(tptp_fun_W_49_type, type, (
% 1.82/1.38 tptp_fun_W_49: $i)).
% 1.82/1.38 tff(neq_type, type, (
% 1.82/1.38 neq: ( $i * $i ) > $o)).
% 1.82/1.38 tff(ssList_type, type, (
% 1.82/1.38 ssList: $i > $o)).
% 1.82/1.38 tff(tptp_fun_X_50_type, type, (
% 1.82/1.38 tptp_fun_X_50: $i)).
% 1.82/1.38 tff(leq_type, type, (
% 1.82/1.38 leq: ( $i * $i ) > $o)).
% 1.82/1.38 tff(memberP_type, type, (
% 1.82/1.38 memberP: ( $i * $i ) > $o)).
% 1.82/1.38 tff(ssItem_type, type, (
% 1.82/1.38 ssItem: $i > $o)).
% 1.82/1.38 tff(tptp_fun_V_48_type, type, (
% 1.82/1.38 tptp_fun_V_48: $i)).
% 1.82/1.38 tff(tptp_fun_U_47_type, type, (
% 1.82/1.38 tptp_fun_U_47: $i)).
% 1.82/1.38 tff(segmentP_type, type, (
% 1.82/1.38 segmentP: ( $i * $i ) > $o)).
% 1.82/1.38 tff(1,plain,
% 1.82/1.38 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (((cons(Y!51, nil) = W!49) & ssItem(Y!51) & memberP(X!50, Y!51) & ![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (((cons(Y!51, nil) = W!49) & ssItem(Y!51) & memberP(X!50, Y!51) & ![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 1.82/1.38 inference(rewrite,[status(thm)],[])).
% 1.82/1.38 tff(2,plain,
% 1.82/1.38 ((ssList(V!48) & (ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (((cons(Y!51, nil) = W!49) & ssItem(Y!51) & memberP(X!50, Y!51) & ![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))) <=> (ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (((cons(Y!51, nil) = W!49) & ssItem(Y!51) & memberP(X!50, Y!51) & ![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 1.82/1.38 inference(rewrite,[status(thm)],[])).
% 1.82/1.38 tff(3,plain,
% 1.82/1.38 ((ssList(W!49) & ((~neq(U!47, nil)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (((cons(Y!51, nil) = W!49) & ssItem(Y!51) & memberP(X!50, Y!51) & ![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))) <=> (ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (((cons(Y!51, nil) = W!49) & ssItem(Y!51) & memberP(X!50, Y!51) & ![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 1.82/1.38 inference(rewrite,[status(thm)],[])).
% 1.82/1.38 tff(4,plain,
% 1.82/1.38 (((~neq(U!47, nil)) & (~(~neq(V!48, nil))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (((~(~(cons(Y!51, nil) = W!49))) & (~(~ssItem(Y!51))) & (~(~memberP(X!50, Y!51))) & ![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)))) | (~((~(nil = X!50)) | (~(nil = W!49)))))) <=> ((~neq(U!47, nil)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (((cons(Y!51, nil) = W!49) & ssItem(Y!51) & memberP(X!50, Y!51) & ![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 1.82/1.38 inference(rewrite,[status(thm)],[])).
% 1.82/1.38 tff(5,plain,
% 1.82/1.38 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 1.82/1.38 inference(rewrite,[status(thm)],[])).
% 1.82/1.38 tff(6,plain,
% 1.82/1.38 (((~(~ssList(W!49))) & ((~neq(U!47, nil)) & (~(~neq(V!48, nil))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (((~(~(cons(Y!51, nil) = W!49))) & (~(~ssItem(Y!51))) & (~(~memberP(X!50, Y!51))) & ![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)))) | (~((~(nil = X!50)) | (~(nil = W!49))))))) <=> (ssList(W!49) & ((~neq(U!47, nil)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (((cons(Y!51, nil) = W!49) & ssItem(Y!51) & memberP(X!50, Y!51) & ![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)))) | (~((~(nil = W!49)) | (~(nil = X!50)))))))),
% 1.82/1.38 inference(monotonicity,[status(thm)],[5, 4])).
% 1.82/1.38 tff(7,plain,
% 1.82/1.38 (((~(~ssList(W!49))) & ((~neq(U!47, nil)) & (~(~neq(V!48, nil))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (((~(~(cons(Y!51, nil) = W!49))) & (~(~ssItem(Y!51))) & (~(~memberP(X!50, Y!51))) & ![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)))) | (~((~(nil = X!50)) | (~(nil = W!49))))))) <=> (ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (((cons(Y!51, nil) = W!49) & ssItem(Y!51) & memberP(X!50, Y!51) & ![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 1.82/1.38 inference(transitivity,[status(thm)],[6, 3])).
% 1.82/1.38 tff(8,plain,
% 1.82/1.38 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 1.82/1.38 inference(rewrite,[status(thm)],[])).
% 1.82/1.38 tff(9,plain,
% 1.82/1.38 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~neq(U!47, nil)) & (~(~neq(V!48, nil))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (((~(~(cons(Y!51, nil) = W!49))) & (~(~ssItem(Y!51))) & (~(~memberP(X!50, Y!51))) & ![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)))) | (~((~(nil = X!50)) | (~(nil = W!49)))))))) <=> (ssList(V!48) & (ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (((cons(Y!51, nil) = W!49) & ssItem(Y!51) & memberP(X!50, Y!51) & ![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)))) | (~((~(nil = W!49)) | (~(nil = X!50)))))))),
% 1.82/1.38 inference(monotonicity,[status(thm)],[8, 7])).
% 1.82/1.38 tff(10,plain,
% 1.82/1.38 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~neq(U!47, nil)) & (~(~neq(V!48, nil))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (((~(~(cons(Y!51, nil) = W!49))) & (~(~ssItem(Y!51))) & (~(~memberP(X!50, Y!51))) & ![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)))) | (~((~(nil = X!50)) | (~(nil = W!49)))))))) <=> (ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (((cons(Y!51, nil) = W!49) & ssItem(Y!51) & memberP(X!50, Y!51) & ![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 1.82/1.38 inference(transitivity,[status(thm)],[9, 2])).
% 1.82/1.38 tff(11,plain,
% 1.82/1.38 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 1.82/1.38 inference(rewrite,[status(thm)],[])).
% 1.82/1.38 tff(12,plain,
% 1.82/1.38 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~neq(U!47, nil)) & (~(~neq(V!48, nil))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (((~(~(cons(Y!51, nil) = W!49))) & (~(~ssItem(Y!51))) & (~(~memberP(X!50, Y!51))) & ![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)))) | (~((~(nil = X!50)) | (~(nil = W!49))))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (((cons(Y!51, nil) = W!49) & ssItem(Y!51) & memberP(X!50, Y!51) & ![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)))) | (~((~(nil = W!49)) | (~(nil = X!50)))))))),
% 1.82/1.38 inference(monotonicity,[status(thm)],[11, 10])).
% 1.82/1.38 tff(13,plain,
% 1.82/1.38 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~neq(U!47, nil)) & (~(~neq(V!48, nil))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (((~(~(cons(Y!51, nil) = W!49))) & (~(~ssItem(Y!51))) & (~(~memberP(X!50, Y!51))) & ![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)))) | (~((~(nil = X!50)) | (~(nil = W!49))))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (((cons(Y!51, nil) = W!49) & ssItem(Y!51) & memberP(X!50, Y!51) & ![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 1.82/1.38 inference(transitivity,[status(thm)],[12, 1])).
% 1.82/1.38 tff(14,plain,
% 1.82/1.38 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~ssItem(Y)) | (~memberP(X, Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(X, Z) & leq(Y, Z))) & ((~(nil = X)) | (~(nil = W))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~ssItem(Y)) | (~memberP(X, Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(X, Z) & leq(Y, Z))) & ((~(nil = X)) | (~(nil = W)))))))))),
% 1.82/1.38 inference(rewrite,[status(thm)],[])).
% 1.82/1.38 tff(15,plain,
% 1.82/1.38 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | neq(U, nil)) | (![Y: $i] : (ssItem(Y) => (((~(cons(Y, nil) = W)) | (~memberP(X, Y))) | ?[Z: $i] : (((ssItem(Z) & (~(Y = Z))) & memberP(X, Z)) & leq(Y, Z)))) & ((~(nil = X)) | (~(nil = W)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~ssItem(Y)) | (~memberP(X, Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(X, Z) & leq(Y, Z))) & ((~(nil = X)) | (~(nil = W)))))))))),
% 1.82/1.38 inference(rewrite,[status(thm)],[])).
% 1.82/1.38 tff(16,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | neq(U, nil)) | (![Y: $i] : (ssItem(Y) => (((~(cons(Y, nil) = W)) | (~memberP(X, Y))) | ?[Z: $i] : (((ssItem(Z) & (~(Y = Z))) & memberP(X, Z)) & leq(Y, Z)))) & ((~(nil = X)) | (~(nil = W)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 1.82/1.38 tff(17,plain,
% 1.82/1.38 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~ssItem(Y)) | (~memberP(X, Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(X, Z) & leq(Y, Z))) & ((~(nil = X)) | (~(nil = W))))))))),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 1.82/1.38 tff(18,plain,
% 1.82/1.38 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~ssItem(Y)) | (~memberP(X, Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(X, Z) & leq(Y, Z))) & ((~(nil = X)) | (~(nil = W))))))))),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[17, 14])).
% 1.82/1.38 tff(19,plain,
% 1.82/1.38 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~ssItem(Y)) | (~memberP(X, Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(X, Z) & leq(Y, Z))) & ((~(nil = X)) | (~(nil = W))))))))),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.82/1.38 tff(20,plain,
% 1.82/1.38 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~ssItem(Y)) | (~memberP(X, Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(X, Z) & leq(Y, Z))) & ((~(nil = X)) | (~(nil = W))))))))),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[19, 14])).
% 1.82/1.38 tff(21,plain,
% 1.82/1.38 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~ssItem(Y)) | (~memberP(X, Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(X, Z) & leq(Y, Z))) & ((~(nil = X)) | (~(nil = W))))))))),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[20, 14])).
% 1.82/1.38 tff(22,plain,
% 1.82/1.38 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~ssItem(Y)) | (~memberP(X, Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(X, Z) & leq(Y, Z))) & ((~(nil = X)) | (~(nil = W))))))))),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[21, 14])).
% 1.82/1.38 tff(23,plain,
% 1.82/1.38 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~ssItem(Y)) | (~memberP(X, Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(X, Z) & leq(Y, Z))) & ((~(nil = X)) | (~(nil = W))))))))),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[22, 14])).
% 1.82/1.38 tff(24,plain,
% 1.82/1.38 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (((cons(Y!51, nil) = W!49) & ssItem(Y!51) & memberP(X!50, Y!51) & ![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)))) | (~((~(nil = W!49)) | (~(nil = X!50)))))),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[23, 13])).
% 1.82/1.38 tff(25,plain,
% 1.82/1.38 (ssList(W!49)),
% 1.82/1.38 inference(and_elim,[status(thm)],[24])).
% 1.82/1.38 tff(26,plain,
% 1.82/1.38 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))))),
% 1.82/1.38 inference(bind,[status(th)],[])).
% 1.82/1.38 tff(27,plain,
% 1.82/1.38 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 1.82/1.38 inference(quant_intro,[status(thm)],[26])).
% 1.82/1.38 tff(28,plain,
% 1.82/1.38 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))))),
% 1.82/1.38 inference(bind,[status(th)],[])).
% 1.82/1.38 tff(29,plain,
% 1.82/1.38 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 1.82/1.38 inference(quant_intro,[status(thm)],[28])).
% 1.82/1.38 tff(30,plain,
% 1.82/1.38 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 1.82/1.38 inference(transitivity,[status(thm)],[29, 27])).
% 1.82/1.38 tff(31,plain,
% 1.82/1.38 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 1.82/1.38 inference(rewrite,[status(thm)],[])).
% 1.82/1.38 tff(32,plain,
% 1.82/1.38 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))), (![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))))),
% 1.82/1.38 inference(bind,[status(th)],[])).
% 1.82/1.38 tff(33,plain,
% 1.82/1.38 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 1.82/1.38 inference(quant_intro,[status(thm)],[32])).
% 1.82/1.38 tff(34,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax15')).
% 1.82/1.38 tff(35,plain,
% 1.82/1.38 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[34, 33])).
% 1.82/1.38 tff(36,plain,
% 1.82/1.38 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[35, 31])).
% 1.82/1.38 tff(37,plain,(
% 1.82/1.38 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 1.82/1.38 inference(skolemize,[status(sab)],[36])).
% 1.82/1.38 tff(38,plain,
% 1.82/1.38 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[37, 30])).
% 1.82/1.38 tff(39,plain,
% 1.82/1.38 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V)))))),
% 1.82/1.38 inference(rewrite,[status(thm)],[])).
% 1.82/1.38 tff(40,plain,
% 1.82/1.38 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V)))))),
% 1.82/1.38 inference(quant_inst,[status(thm)],[])).
% 1.82/1.38 tff(41,plain,
% 1.82/1.38 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 1.82/1.38 tff(42,plain,
% 1.82/1.38 (![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))),
% 1.82/1.38 inference(unit_resolution,[status(thm)],[41, 38, 25])).
% 1.82/1.38 tff(43,plain,
% 1.82/1.38 (ssList(nil) <=> ssList(nil)),
% 1.82/1.38 inference(rewrite,[status(thm)],[])).
% 1.82/1.38 tff(44,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 1.82/1.38 tff(45,plain,
% 1.82/1.38 (ssList(nil)),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[44, 43])).
% 1.82/1.38 tff(46,plain,
% 1.82/1.38 (((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | ((~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | (~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil))))),
% 1.82/1.38 inference(rewrite,[status(thm)],[])).
% 1.82/1.38 tff(47,plain,
% 1.82/1.38 ((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | ((~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil))))),
% 1.82/1.38 inference(quant_inst,[status(thm)],[])).
% 1.82/1.38 tff(48,plain,
% 1.82/1.38 ((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | (~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil)))),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[47, 46])).
% 1.82/1.38 tff(49,plain,
% 1.82/1.38 (neq(W!49, nil) <=> (~(W!49 = nil))),
% 1.82/1.38 inference(unit_resolution,[status(thm)],[48, 45, 42])).
% 1.82/1.38 tff(50,plain,
% 1.82/1.38 (U!47 = W!49),
% 1.82/1.38 inference(and_elim,[status(thm)],[24])).
% 1.82/1.38 tff(51,plain,
% 1.82/1.38 (W!49 = U!47),
% 1.82/1.38 inference(symmetry,[status(thm)],[50])).
% 1.82/1.38 tff(52,plain,
% 1.82/1.38 (neq(W!49, nil) <=> neq(U!47, nil)),
% 1.82/1.38 inference(monotonicity,[status(thm)],[51])).
% 1.82/1.38 tff(53,plain,
% 1.82/1.38 (neq(U!47, nil) <=> neq(W!49, nil)),
% 1.82/1.38 inference(symmetry,[status(thm)],[52])).
% 1.82/1.38 tff(54,plain,
% 1.82/1.38 ((~neq(U!47, nil)) <=> (~neq(W!49, nil))),
% 1.82/1.38 inference(monotonicity,[status(thm)],[53])).
% 1.82/1.38 tff(55,plain,
% 1.82/1.38 (~neq(U!47, nil)),
% 1.82/1.38 inference(and_elim,[status(thm)],[24])).
% 1.82/1.38 tff(56,plain,
% 1.82/1.38 (~neq(W!49, nil)),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[55, 54])).
% 1.82/1.38 tff(57,plain,
% 1.82/1.38 ((~(neq(W!49, nil) <=> (~(W!49 = nil)))) | neq(W!49, nil) | (W!49 = nil)),
% 1.82/1.38 inference(tautology,[status(thm)],[])).
% 1.82/1.38 tff(58,plain,
% 1.82/1.38 (W!49 = nil),
% 1.82/1.38 inference(unit_resolution,[status(thm)],[57, 56, 49])).
% 1.82/1.38 tff(59,plain,
% 1.82/1.38 (ssList(X!50)),
% 1.82/1.38 inference(and_elim,[status(thm)],[24])).
% 1.82/1.38 tff(60,plain,
% 1.82/1.38 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 1.82/1.38 inference(bind,[status(th)],[])).
% 1.82/1.38 tff(61,plain,
% 1.82/1.38 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 1.82/1.38 inference(quant_intro,[status(thm)],[60])).
% 1.82/1.38 tff(62,plain,
% 1.82/1.38 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 1.82/1.38 inference(rewrite,[status(thm)],[])).
% 1.82/1.38 tff(63,plain,
% 1.82/1.38 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 1.82/1.38 inference(bind,[status(th)],[])).
% 1.82/1.38 tff(64,plain,
% 1.82/1.38 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 1.82/1.38 inference(quant_intro,[status(thm)],[63])).
% 1.82/1.38 tff(65,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax58')).
% 1.82/1.38 tff(66,plain,
% 1.82/1.38 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[65, 64])).
% 1.82/1.38 tff(67,plain,
% 1.82/1.38 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[66, 62])).
% 1.82/1.38 tff(68,plain,(
% 1.82/1.38 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 1.82/1.38 inference(skolemize,[status(sab)],[67])).
% 1.82/1.38 tff(69,plain,
% 1.82/1.38 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[68, 61])).
% 1.82/1.38 tff(70,plain,
% 1.82/1.38 (((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(X!50)) | (segmentP(nil, X!50) <=> (nil = X!50)))) <=> ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(X!50)) | (segmentP(nil, X!50) <=> (nil = X!50)))),
% 1.82/1.38 inference(rewrite,[status(thm)],[])).
% 1.82/1.38 tff(71,plain,
% 1.82/1.38 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(X!50)) | (segmentP(nil, X!50) <=> (nil = X!50)))),
% 1.82/1.38 inference(quant_inst,[status(thm)],[])).
% 1.82/1.38 tff(72,plain,
% 1.82/1.38 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(X!50)) | (segmentP(nil, X!50) <=> (nil = X!50))),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.82/1.38 tff(73,plain,
% 1.82/1.38 (segmentP(nil, X!50) <=> (nil = X!50)),
% 1.82/1.38 inference(unit_resolution,[status(thm)],[72, 69, 59])).
% 1.82/1.38 tff(74,plain,
% 1.82/1.38 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V)))))),
% 1.82/1.38 inference(rewrite,[status(thm)],[])).
% 1.82/1.38 tff(75,plain,
% 1.82/1.38 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V)))))),
% 1.82/1.38 inference(quant_inst,[status(thm)],[])).
% 1.82/1.38 tff(76,plain,
% 1.82/1.38 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[75, 74])).
% 1.82/1.38 tff(77,plain,
% 1.82/1.38 (![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))),
% 1.82/1.38 inference(unit_resolution,[status(thm)],[76, 38, 59])).
% 1.82/1.38 tff(78,plain,
% 1.82/1.38 (((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | ((~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | (~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil))))),
% 1.82/1.38 inference(rewrite,[status(thm)],[])).
% 1.82/1.38 tff(79,plain,
% 1.82/1.38 ((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | ((~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil))))),
% 1.82/1.38 inference(quant_inst,[status(thm)],[])).
% 1.82/1.38 tff(80,plain,
% 1.82/1.38 ((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | (~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil)))),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[79, 78])).
% 1.82/1.38 tff(81,plain,
% 1.82/1.38 (neq(X!50, nil) <=> (~(X!50 = nil))),
% 1.82/1.38 inference(unit_resolution,[status(thm)],[80, 45, 77])).
% 1.82/1.38 tff(82,plain,
% 1.82/1.38 (V!48 = X!50),
% 1.82/1.38 inference(and_elim,[status(thm)],[24])).
% 1.82/1.38 tff(83,plain,
% 1.82/1.38 (X!50 = V!48),
% 1.82/1.38 inference(symmetry,[status(thm)],[82])).
% 1.82/1.38 tff(84,plain,
% 1.82/1.38 (neq(X!50, nil) <=> neq(V!48, nil)),
% 1.82/1.38 inference(monotonicity,[status(thm)],[83])).
% 1.82/1.38 tff(85,plain,
% 1.82/1.38 (neq(V!48, nil) <=> neq(X!50, nil)),
% 1.82/1.38 inference(symmetry,[status(thm)],[84])).
% 1.82/1.38 tff(86,plain,
% 1.82/1.38 (neq(V!48, nil)),
% 1.82/1.38 inference(and_elim,[status(thm)],[24])).
% 1.82/1.38 tff(87,plain,
% 1.82/1.38 (neq(X!50, nil)),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[86, 85])).
% 1.82/1.38 tff(88,plain,
% 1.82/1.38 ((~(neq(X!50, nil) <=> (~(X!50 = nil)))) | (~neq(X!50, nil)) | (~(X!50 = nil))),
% 1.82/1.38 inference(tautology,[status(thm)],[])).
% 1.82/1.38 tff(89,plain,
% 1.82/1.38 (~(X!50 = nil)),
% 1.82/1.38 inference(unit_resolution,[status(thm)],[88, 87, 81])).
% 1.82/1.38 tff(90,plain,
% 1.82/1.38 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 1.82/1.38 inference(bind,[status(th)],[])).
% 1.82/1.38 tff(91,plain,
% 1.82/1.38 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 1.82/1.38 inference(quant_intro,[status(thm)],[90])).
% 1.82/1.38 tff(92,plain,
% 1.82/1.38 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 1.82/1.38 inference(bind,[status(th)],[])).
% 1.82/1.38 tff(93,plain,
% 1.82/1.38 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 1.82/1.38 inference(quant_intro,[status(thm)],[92])).
% 1.82/1.38 tff(94,plain,
% 1.82/1.38 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 1.82/1.38 inference(transitivity,[status(thm)],[93, 91])).
% 1.82/1.38 tff(95,plain,
% 1.82/1.38 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 1.82/1.38 inference(bind,[status(th)],[])).
% 1.82/1.38 tff(96,plain,
% 1.82/1.38 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 1.82/1.38 inference(quant_intro,[status(thm)],[95])).
% 1.82/1.38 tff(97,plain,
% 1.82/1.38 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 1.82/1.38 inference(rewrite,[status(thm)],[])).
% 1.82/1.38 tff(98,plain,
% 1.82/1.38 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite(((segmentP(U, V) & segmentP(V, U)) => (U = V)) <=> ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))), ((ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> (ssList(V) => ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))))), rewrite((ssList(V) => ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))) <=> ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))), ((ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))))), (![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> (ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))))), rewrite((ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))))),
% 1.82/1.38 inference(bind,[status(th)],[])).
% 1.82/1.38 tff(99,plain,
% 1.82/1.38 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 1.82/1.38 inference(quant_intro,[status(thm)],[98])).
% 1.82/1.38 tff(100,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax54')).
% 1.82/1.38 tff(101,plain,
% 1.82/1.38 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[100, 99])).
% 1.82/1.38 tff(102,plain,
% 1.82/1.38 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[101, 97])).
% 1.82/1.38 tff(103,plain,(
% 1.82/1.38 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 1.82/1.38 inference(skolemize,[status(sab)],[102])).
% 1.82/1.38 tff(104,plain,
% 1.82/1.38 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[103, 96])).
% 1.82/1.38 tff(105,plain,
% 1.82/1.38 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[104, 94])).
% 1.82/1.38 tff(106,plain,
% 1.82/1.38 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))),
% 1.82/1.38 inference(rewrite,[status(thm)],[])).
% 1.82/1.38 tff(107,plain,
% 1.82/1.38 (((~ssList(X!50)) | ![V: $i] : ((X!50 = V) | (~ssList(V)) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) <=> ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))),
% 1.82/1.38 inference(rewrite,[status(thm)],[])).
% 1.82/1.38 tff(108,plain,
% 1.82/1.38 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(X!50)) | ![V: $i] : ((X!50 = V) | (~ssList(V)) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))))),
% 1.82/1.38 inference(monotonicity,[status(thm)],[107])).
% 1.82/1.38 tff(109,plain,
% 1.82/1.38 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(X!50)) | ![V: $i] : ((X!50 = V) | (~ssList(V)) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))),
% 1.82/1.38 inference(transitivity,[status(thm)],[108, 106])).
% 1.82/1.38 tff(110,plain,
% 1.82/1.38 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(X!50)) | ![V: $i] : ((X!50 = V) | (~ssList(V)) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))),
% 1.82/1.38 inference(quant_inst,[status(thm)],[])).
% 1.82/1.38 tff(111,plain,
% 1.82/1.38 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))),
% 1.82/1.38 inference(modus_ponens,[status(thm)],[110, 109])).
% 1.82/1.38 tff(112,plain,
% 1.82/1.38 (![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))),
% 1.82/1.38 inference(unit_resolution,[status(thm)],[111, 105, 59])).
% 1.82/1.38 tff(113,plain,
% 1.82/1.38 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 1.82/1.38 inference(bind,[status(th)],[])).
% 1.82/1.38 tff(114,plain,
% 1.82/1.38 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 1.82/1.38 inference(quant_intro,[status(thm)],[113])).
% 1.82/1.38 tff(115,plain,
% 1.82/1.38 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 1.82/1.38 inference(rewrite,[status(thm)],[])).
% 1.82/1.38 tff(116,plain,
% 1.82/1.38 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 1.82/1.39 inference(bind,[status(th)],[])).
% 1.82/1.39 tff(117,plain,
% 1.82/1.39 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 1.82/1.39 inference(quant_intro,[status(thm)],[116])).
% 1.82/1.39 tff(118,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax57')).
% 1.82/1.39 tff(119,plain,
% 1.82/1.39 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 1.82/1.39 inference(modus_ponens,[status(thm)],[118, 117])).
% 1.82/1.39 tff(120,plain,
% 1.82/1.39 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 1.82/1.39 inference(modus_ponens,[status(thm)],[119, 115])).
% 1.82/1.39 tff(121,plain,(
% 1.82/1.39 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 1.82/1.39 inference(skolemize,[status(sab)],[120])).
% 1.82/1.39 tff(122,plain,
% 1.82/1.39 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 1.82/1.39 inference(modus_ponens,[status(thm)],[121, 114])).
% 1.82/1.39 tff(123,plain,
% 1.82/1.39 (((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(X!50)) | segmentP(X!50, nil))) <=> ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(X!50)) | segmentP(X!50, nil))),
% 1.82/1.39 inference(rewrite,[status(thm)],[])).
% 1.82/1.39 tff(124,plain,
% 1.82/1.39 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(X!50)) | segmentP(X!50, nil))),
% 1.82/1.39 inference(quant_inst,[status(thm)],[])).
% 1.82/1.39 tff(125,plain,
% 1.82/1.39 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(X!50)) | segmentP(X!50, nil)),
% 1.82/1.39 inference(modus_ponens,[status(thm)],[124, 123])).
% 1.82/1.39 tff(126,plain,
% 1.82/1.39 (segmentP(X!50, nil)),
% 1.82/1.39 inference(unit_resolution,[status(thm)],[125, 122, 59])).
% 1.82/1.39 tff(127,plain,
% 1.82/1.39 (((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | ((~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil)))) <=> ((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | (~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil)))),
% 1.82/1.39 inference(rewrite,[status(thm)],[])).
% 1.82/1.39 tff(128,plain,
% 1.82/1.39 (((~ssList(nil)) | (X!50 = nil) | (~segmentP(X!50, nil)) | (~segmentP(nil, X!50))) <=> ((~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil)))),
% 1.82/1.39 inference(rewrite,[status(thm)],[])).
% 1.82/1.39 tff(129,plain,
% 1.82/1.39 (((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | ((~ssList(nil)) | (X!50 = nil) | (~segmentP(X!50, nil)) | (~segmentP(nil, X!50)))) <=> ((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | ((~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil))))),
% 1.82/1.39 inference(monotonicity,[status(thm)],[128])).
% 1.82/1.39 tff(130,plain,
% 1.82/1.39 (((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | ((~ssList(nil)) | (X!50 = nil) | (~segmentP(X!50, nil)) | (~segmentP(nil, X!50)))) <=> ((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | (~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil)))),
% 1.82/1.39 inference(transitivity,[status(thm)],[129, 127])).
% 1.82/1.39 tff(131,plain,
% 1.82/1.39 ((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | ((~ssList(nil)) | (X!50 = nil) | (~segmentP(X!50, nil)) | (~segmentP(nil, X!50)))),
% 1.82/1.39 inference(quant_inst,[status(thm)],[])).
% 1.82/1.39 tff(132,plain,
% 1.82/1.39 ((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | (~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil))),
% 1.82/1.39 inference(modus_ponens,[status(thm)],[131, 130])).
% 1.82/1.39 tff(133,plain,
% 1.82/1.39 ((~segmentP(nil, X!50)) | (X!50 = nil)),
% 1.82/1.39 inference(unit_resolution,[status(thm)],[132, 45, 126, 112])).
% 1.82/1.39 tff(134,plain,
% 1.82/1.39 (~segmentP(nil, X!50)),
% 1.82/1.39 inference(unit_resolution,[status(thm)],[133, 89])).
% 1.82/1.39 tff(135,plain,
% 1.82/1.39 ((~(segmentP(nil, X!50) <=> (nil = X!50))) | segmentP(nil, X!50) | (~(nil = X!50))),
% 1.82/1.39 inference(tautology,[status(thm)],[])).
% 1.82/1.39 tff(136,plain,
% 1.82/1.39 (~(nil = X!50)),
% 1.82/1.39 inference(unit_resolution,[status(thm)],[135, 134, 73])).
% 1.82/1.39 tff(137,plain,
% 1.82/1.39 (((~(nil = W!49)) | (~(nil = X!50))) | (nil = X!50)),
% 1.82/1.39 inference(tautology,[status(thm)],[])).
% 1.82/1.39 tff(138,plain,
% 1.82/1.39 ((~(nil = W!49)) | (~(nil = X!50))),
% 1.82/1.39 inference(unit_resolution,[status(thm)],[137, 136])).
% 1.82/1.39 tff(139,plain,
% 1.82/1.39 (((~((~(nil = W!49)) | (~(nil = X!50)))) | (~((~(cons(Y!51, nil) = W!49)) | (~ssItem(Y!51)) | (~memberP(X!50, Y!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (Y!51 = Z) | (~leq(Y!51, Z))))))) <=> ((~((~(nil = W!49)) | (~(nil = X!50)))) | (~((~(cons(Y!51, nil) = W!49)) | (~ssItem(Y!51)) | (~memberP(X!50, Y!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (Y!51 = Z) | (~leq(Y!51, Z)))))))),
% 1.82/1.39 inference(rewrite,[status(thm)],[])).
% 1.82/1.39 tff(140,plain,
% 1.82/1.39 (((~((~(cons(Y!51, nil) = W!49)) | (~ssItem(Y!51)) | (~memberP(X!50, Y!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (Y!51 = Z) | (~leq(Y!51, Z)))))) | (~((~(nil = W!49)) | (~(nil = X!50))))) <=> ((~((~(nil = W!49)) | (~(nil = X!50)))) | (~((~(cons(Y!51, nil) = W!49)) | (~ssItem(Y!51)) | (~memberP(X!50, Y!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (Y!51 = Z) | (~leq(Y!51, Z)))))))),
% 1.82/1.39 inference(rewrite,[status(thm)],[])).
% 1.82/1.39 tff(141,plain,
% 1.82/1.39 (((cons(Y!51, nil) = W!49) & ssItem(Y!51) & memberP(X!50, Y!51) & ![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (Y!51 = Z) | (~leq(Y!51, Z)))) <=> (~((~(cons(Y!51, nil) = W!49)) | (~ssItem(Y!51)) | (~memberP(X!50, Y!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (Y!51 = Z) | (~leq(Y!51, Z))))))),
% 1.82/1.39 inference(rewrite,[status(thm)],[])).
% 1.82/1.39 tff(142,plain,
% 1.82/1.39 (^[Z: $i] : trans(monotonicity(rewrite((ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)) <=> (~((~ssItem(Z)) | (~memberP(X!50, Z)) | (Y!51 = Z) | (~leq(Y!51, Z))))), ((~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z))) <=> (~(~((~ssItem(Z)) | (~memberP(X!50, Z)) | (Y!51 = Z) | (~leq(Y!51, Z))))))), rewrite((~(~((~ssItem(Z)) | (~memberP(X!50, Z)) | (Y!51 = Z) | (~leq(Y!51, Z))))) <=> ((~ssItem(Z)) | (~memberP(X!50, Z)) | (Y!51 = Z) | (~leq(Y!51, Z)))), ((~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z))) <=> ((~ssItem(Z)) | (~memberP(X!50, Z)) | (Y!51 = Z) | (~leq(Y!51, Z)))))),
% 1.82/1.39 inference(bind,[status(th)],[])).
% 1.82/1.39 tff(143,plain,
% 1.82/1.39 (![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z))) <=> ![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (Y!51 = Z) | (~leq(Y!51, Z)))),
% 1.82/1.39 inference(quant_intro,[status(thm)],[142])).
% 1.82/1.39 tff(144,plain,
% 1.82/1.39 (((cons(Y!51, nil) = W!49) & ssItem(Y!51) & memberP(X!50, Y!51) & ![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)))) <=> ((cons(Y!51, nil) = W!49) & ssItem(Y!51) & memberP(X!50, Y!51) & ![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (Y!51 = Z) | (~leq(Y!51, Z))))),
% 1.82/1.39 inference(monotonicity,[status(thm)],[143])).
% 1.82/1.39 tff(145,plain,
% 1.82/1.39 (((cons(Y!51, nil) = W!49) & ssItem(Y!51) & memberP(X!50, Y!51) & ![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)))) <=> (~((~(cons(Y!51, nil) = W!49)) | (~ssItem(Y!51)) | (~memberP(X!50, Y!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (Y!51 = Z) | (~leq(Y!51, Z))))))),
% 1.82/1.39 inference(transitivity,[status(thm)],[144, 141])).
% 1.82/1.39 tff(146,plain,
% 1.82/1.39 ((((cons(Y!51, nil) = W!49) & ssItem(Y!51) & memberP(X!50, Y!51) & ![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)))) | (~((~(nil = W!49)) | (~(nil = X!50))))) <=> ((~((~(cons(Y!51, nil) = W!49)) | (~ssItem(Y!51)) | (~memberP(X!50, Y!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (Y!51 = Z) | (~leq(Y!51, Z)))))) | (~((~(nil = W!49)) | (~(nil = X!50)))))),
% 1.82/1.39 inference(monotonicity,[status(thm)],[145])).
% 1.82/1.39 tff(147,plain,
% 1.82/1.39 ((((cons(Y!51, nil) = W!49) & ssItem(Y!51) & memberP(X!50, Y!51) & ![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)))) | (~((~(nil = W!49)) | (~(nil = X!50))))) <=> ((~((~(nil = W!49)) | (~(nil = X!50)))) | (~((~(cons(Y!51, nil) = W!49)) | (~ssItem(Y!51)) | (~memberP(X!50, Y!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (Y!51 = Z) | (~leq(Y!51, Z)))))))),
% 1.82/1.39 inference(transitivity,[status(thm)],[146, 140])).
% 1.82/1.39 tff(148,plain,
% 1.82/1.39 (((cons(Y!51, nil) = W!49) & ssItem(Y!51) & memberP(X!50, Y!51) & ![Z: $i] : (~(ssItem(Z) & (~(Y!51 = Z)) & memberP(X!50, Z) & leq(Y!51, Z)))) | (~((~(nil = W!49)) | (~(nil = X!50))))),
% 1.82/1.39 inference(and_elim,[status(thm)],[24])).
% 1.82/1.39 tff(149,plain,
% 1.82/1.39 ((~((~(nil = W!49)) | (~(nil = X!50)))) | (~((~(cons(Y!51, nil) = W!49)) | (~ssItem(Y!51)) | (~memberP(X!50, Y!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (Y!51 = Z) | (~leq(Y!51, Z))))))),
% 1.82/1.39 inference(modus_ponens,[status(thm)],[148, 147])).
% 1.82/1.39 tff(150,plain,
% 1.82/1.39 ((~((~(nil = W!49)) | (~(nil = X!50)))) | (~((~(cons(Y!51, nil) = W!49)) | (~ssItem(Y!51)) | (~memberP(X!50, Y!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (Y!51 = Z) | (~leq(Y!51, Z))))))),
% 1.82/1.39 inference(modus_ponens,[status(thm)],[149, 139])).
% 1.82/1.39 tff(151,plain,
% 1.82/1.39 (~((~(cons(Y!51, nil) = W!49)) | (~ssItem(Y!51)) | (~memberP(X!50, Y!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (Y!51 = Z) | (~leq(Y!51, Z)))))),
% 1.82/1.39 inference(unit_resolution,[status(thm)],[150, 138])).
% 1.82/1.39 tff(152,plain,
% 1.82/1.39 (((~(cons(Y!51, nil) = W!49)) | (~ssItem(Y!51)) | (~memberP(X!50, Y!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (Y!51 = Z) | (~leq(Y!51, Z))))) | (cons(Y!51, nil) = W!49)),
% 1.82/1.39 inference(tautology,[status(thm)],[])).
% 1.82/1.39 tff(153,plain,
% 1.82/1.39 (cons(Y!51, nil) = W!49),
% 1.82/1.39 inference(unit_resolution,[status(thm)],[152, 151])).
% 1.82/1.39 tff(154,plain,
% 1.82/1.39 (cons(Y!51, nil) = nil),
% 1.82/1.39 inference(transitivity,[status(thm)],[153, 58])).
% 1.82/1.39 tff(155,plain,
% 1.82/1.39 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))),
% 1.82/1.39 inference(bind,[status(th)],[])).
% 1.82/1.39 tff(156,plain,
% 1.82/1.39 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 1.82/1.39 inference(quant_intro,[status(thm)],[155])).
% 1.82/1.39 tff(157,plain,
% 1.82/1.39 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))),
% 1.82/1.39 inference(bind,[status(th)],[])).
% 1.82/1.39 tff(158,plain,
% 1.82/1.39 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 1.82/1.39 inference(quant_intro,[status(thm)],[157])).
% 1.82/1.39 tff(159,plain,
% 1.82/1.39 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 1.82/1.39 inference(transitivity,[status(thm)],[158, 156])).
% 1.82/1.39 tff(160,plain,
% 1.82/1.39 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 1.82/1.39 inference(rewrite,[status(thm)],[])).
% 1.82/1.39 tff(161,plain,
% 1.82/1.39 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (~(cons(V, U) = U))) <=> ((~ssItem(V)) | (~(cons(V, U) = U))))), (![V: $i] : (ssItem(V) => (~(cons(V, U) = U))) <=> ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))))),
% 1.82/1.39 inference(bind,[status(th)],[])).
% 1.82/1.39 tff(162,plain,
% 1.82/1.39 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 1.82/1.39 inference(quant_intro,[status(thm)],[161])).
% 1.82/1.39 tff(163,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax18')).
% 1.82/1.39 tff(164,plain,
% 1.82/1.39 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 1.82/1.39 inference(modus_ponens,[status(thm)],[163, 162])).
% 1.82/1.39 tff(165,plain,
% 1.82/1.39 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 1.82/1.39 inference(modus_ponens,[status(thm)],[164, 160])).
% 1.82/1.40 tff(166,plain,(
% 1.82/1.40 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 1.82/1.40 inference(skolemize,[status(sab)],[165])).
% 1.82/1.40 tff(167,plain,
% 1.82/1.40 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 1.82/1.40 inference(modus_ponens,[status(thm)],[166, 159])).
% 1.82/1.40 tff(168,plain,
% 1.82/1.40 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil))))),
% 1.82/1.40 inference(rewrite,[status(thm)],[])).
% 1.82/1.40 tff(169,plain,
% 1.82/1.40 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil))))),
% 1.82/1.40 inference(quant_inst,[status(thm)],[])).
% 1.82/1.40 tff(170,plain,
% 1.82/1.40 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))),
% 1.82/1.40 inference(modus_ponens,[status(thm)],[169, 168])).
% 1.82/1.40 tff(171,plain,
% 1.82/1.40 (![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))),
% 1.82/1.40 inference(unit_resolution,[status(thm)],[170, 45, 167])).
% 1.82/1.40 tff(172,plain,
% 1.82/1.40 (((~(cons(Y!51, nil) = W!49)) | (~ssItem(Y!51)) | (~memberP(X!50, Y!51)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(X!50, Z)) | (Y!51 = Z) | (~leq(Y!51, Z))))) | ssItem(Y!51)),
% 1.82/1.40 inference(tautology,[status(thm)],[])).
% 1.82/1.40 tff(173,plain,
% 1.82/1.40 (ssItem(Y!51)),
% 1.82/1.40 inference(unit_resolution,[status(thm)],[172, 151])).
% 1.82/1.40 tff(174,plain,
% 1.82/1.40 (((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | ((~ssItem(Y!51)) | (~(cons(Y!51, nil) = nil)))) <=> ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | (~ssItem(Y!51)) | (~(cons(Y!51, nil) = nil)))),
% 1.82/1.40 inference(rewrite,[status(thm)],[])).
% 1.82/1.40 tff(175,plain,
% 1.82/1.40 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | ((~ssItem(Y!51)) | (~(cons(Y!51, nil) = nil)))),
% 1.82/1.40 inference(quant_inst,[status(thm)],[])).
% 1.82/1.40 tff(176,plain,
% 1.82/1.40 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | (~ssItem(Y!51)) | (~(cons(Y!51, nil) = nil))),
% 1.82/1.40 inference(modus_ponens,[status(thm)],[175, 174])).
% 1.82/1.40 tff(177,plain,
% 1.82/1.40 ($false),
% 1.82/1.40 inference(unit_resolution,[status(thm)],[176, 173, 171, 154])).
% 1.82/1.40 % SZS output end Proof
%------------------------------------------------------------------------------