TSTP Solution File: SWC040+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC040+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 11:54:50 EDT 2022
% Result : Theorem 0.17s 0.44s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWC040+1 : TPTP v8.1.0. Released v2.4.0.
% 0.10/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n012.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat Sep 3 20:53:48 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 0.17/0.44 % SZS status Theorem
% 0.17/0.44 % SZS output start Proof
% 0.17/0.44 tff(tptp_fun_X_50_type, type, (
% 0.17/0.44 tptp_fun_X_50: $i)).
% 0.17/0.44 tff(nil_type, type, (
% 0.17/0.44 nil: $i)).
% 0.17/0.44 tff(tptp_fun_V_48_type, type, (
% 0.17/0.44 tptp_fun_V_48: $i)).
% 0.17/0.44 tff(ssList_type, type, (
% 0.17/0.44 ssList: $i > $o)).
% 0.17/0.44 tff(tptp_fun_Z_52_type, type, (
% 0.17/0.44 tptp_fun_Z_52: $i)).
% 0.17/0.44 tff(app_type, type, (
% 0.17/0.44 app: ( $i * $i ) > $i)).
% 0.17/0.44 tff(cons_type, type, (
% 0.17/0.44 cons: ( $i * $i ) > $i)).
% 0.17/0.44 tff(tptp_fun_Y_51_type, type, (
% 0.17/0.44 tptp_fun_Y_51: $i)).
% 0.17/0.44 tff(tptp_fun_W_49_type, type, (
% 0.17/0.44 tptp_fun_W_49: $i)).
% 0.17/0.44 tff(ssItem_type, type, (
% 0.17/0.44 ssItem: $i > $o)).
% 0.17/0.44 tff(neq_type, type, (
% 0.17/0.44 neq: ( $i * $i ) > $o)).
% 0.17/0.44 tff(tptp_fun_U_47_type, type, (
% 0.17/0.44 tptp_fun_U_47: $i)).
% 0.17/0.44 tff(1,plain,
% 0.17/0.44 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (~((~(nil = W!49)) & (nil = X!50))) & (nil = V!48) & ssList(X!50) & ((~neq(X!50, nil)) | (ssItem(Y!51) & (~((~(app(cons(Y!51, nil), Z!52) = W!49)) | (~(app(Z!52, cons(Y!51, nil)) = X!50)) | (~ssList(Z!52)))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (~((~(nil = W!49)) & (nil = X!50))) & (nil = V!48) & ssList(X!50) & ((~neq(X!50, nil)) | (ssItem(Y!51) & (~((~(app(cons(Y!51, nil), Z!52) = W!49)) | (~(app(Z!52, cons(Y!51, nil)) = X!50)) | (~ssList(Z!52)))))))),
% 0.17/0.44 inference(rewrite,[status(thm)],[])).
% 0.17/0.44 tff(2,plain,
% 0.17/0.44 ((ssList(V!48) & (ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (~((~(nil = W!49)) & (nil = X!50))) & (nil = V!48) & ssList(X!50) & ((~neq(X!50, nil)) | (ssItem(Y!51) & (~((~(app(cons(Y!51, nil), Z!52) = W!49)) | (~(app(Z!52, cons(Y!51, nil)) = X!50)) | (~ssList(Z!52)))))))) <=> (ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (~((~(nil = W!49)) & (nil = X!50))) & (nil = V!48) & ssList(X!50) & ((~neq(X!50, nil)) | (ssItem(Y!51) & (~((~(app(cons(Y!51, nil), Z!52) = W!49)) | (~(app(Z!52, cons(Y!51, nil)) = X!50)) | (~ssList(Z!52)))))))),
% 0.17/0.44 inference(rewrite,[status(thm)],[])).
% 0.17/0.44 tff(3,plain,
% 0.17/0.44 ((ssList(W!49) & ((~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (~((~(nil = W!49)) & (nil = X!50))) & (nil = V!48) & ssList(X!50) & ((~neq(X!50, nil)) | (ssItem(Y!51) & (~((~(app(cons(Y!51, nil), Z!52) = W!49)) | (~(app(Z!52, cons(Y!51, nil)) = X!50)) | (~ssList(Z!52)))))))) <=> (ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (~((~(nil = W!49)) & (nil = X!50))) & (nil = V!48) & ssList(X!50) & ((~neq(X!50, nil)) | (ssItem(Y!51) & (~((~(app(cons(Y!51, nil), Z!52) = W!49)) | (~(app(Z!52, cons(Y!51, nil)) = X!50)) | (~ssList(Z!52)))))))),
% 0.17/0.44 inference(rewrite,[status(thm)],[])).
% 0.17/0.44 tff(4,plain,
% 0.17/0.44 (((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & (((~(~ssItem(Y!51))) & (~((~(app(cons(Y!51, nil), Z!52) = W!49)) | (~(app(Z!52, cons(Y!51, nil)) = X!50)) | (~ssList(Z!52))))) | (~neq(X!50, nil)))) <=> ((~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (~((~(nil = W!49)) & (nil = X!50))) & (nil = V!48) & ssList(X!50) & ((~neq(X!50, nil)) | (ssItem(Y!51) & (~((~(app(cons(Y!51, nil), Z!52) = W!49)) | (~(app(Z!52, cons(Y!51, nil)) = X!50)) | (~ssList(Z!52)))))))),
% 0.17/0.44 inference(rewrite,[status(thm)],[])).
% 0.17/0.44 tff(5,plain,
% 0.17/0.44 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 0.17/0.44 inference(rewrite,[status(thm)],[])).
% 0.17/0.44 tff(6,plain,
% 0.17/0.44 (((~(~ssList(W!49))) & ((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & (((~(~ssItem(Y!51))) & (~((~(app(cons(Y!51, nil), Z!52) = W!49)) | (~(app(Z!52, cons(Y!51, nil)) = X!50)) | (~ssList(Z!52))))) | (~neq(X!50, nil))))) <=> (ssList(W!49) & ((~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (~((~(nil = W!49)) & (nil = X!50))) & (nil = V!48) & ssList(X!50) & ((~neq(X!50, nil)) | (ssItem(Y!51) & (~((~(app(cons(Y!51, nil), Z!52) = W!49)) | (~(app(Z!52, cons(Y!51, nil)) = X!50)) | (~ssList(Z!52))))))))),
% 0.17/0.44 inference(monotonicity,[status(thm)],[5, 4])).
% 0.17/0.44 tff(7,plain,
% 0.17/0.44 (((~(~ssList(W!49))) & ((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & (((~(~ssItem(Y!51))) & (~((~(app(cons(Y!51, nil), Z!52) = W!49)) | (~(app(Z!52, cons(Y!51, nil)) = X!50)) | (~ssList(Z!52))))) | (~neq(X!50, nil))))) <=> (ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (~((~(nil = W!49)) & (nil = X!50))) & (nil = V!48) & ssList(X!50) & ((~neq(X!50, nil)) | (ssItem(Y!51) & (~((~(app(cons(Y!51, nil), Z!52) = W!49)) | (~(app(Z!52, cons(Y!51, nil)) = X!50)) | (~ssList(Z!52)))))))),
% 0.17/0.45 inference(transitivity,[status(thm)],[6, 3])).
% 0.17/0.45 tff(8,plain,
% 0.17/0.45 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 0.17/0.45 inference(rewrite,[status(thm)],[])).
% 0.17/0.45 tff(9,plain,
% 0.17/0.45 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & (((~(~ssItem(Y!51))) & (~((~(app(cons(Y!51, nil), Z!52) = W!49)) | (~(app(Z!52, cons(Y!51, nil)) = X!50)) | (~ssList(Z!52))))) | (~neq(X!50, nil)))))) <=> (ssList(V!48) & (ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (~((~(nil = W!49)) & (nil = X!50))) & (nil = V!48) & ssList(X!50) & ((~neq(X!50, nil)) | (ssItem(Y!51) & (~((~(app(cons(Y!51, nil), Z!52) = W!49)) | (~(app(Z!52, cons(Y!51, nil)) = X!50)) | (~ssList(Z!52))))))))),
% 0.17/0.45 inference(monotonicity,[status(thm)],[8, 7])).
% 0.17/0.45 tff(10,plain,
% 0.17/0.45 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & (((~(~ssItem(Y!51))) & (~((~(app(cons(Y!51, nil), Z!52) = W!49)) | (~(app(Z!52, cons(Y!51, nil)) = X!50)) | (~ssList(Z!52))))) | (~neq(X!50, nil)))))) <=> (ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (~((~(nil = W!49)) & (nil = X!50))) & (nil = V!48) & ssList(X!50) & ((~neq(X!50, nil)) | (ssItem(Y!51) & (~((~(app(cons(Y!51, nil), Z!52) = W!49)) | (~(app(Z!52, cons(Y!51, nil)) = X!50)) | (~ssList(Z!52)))))))),
% 0.17/0.45 inference(transitivity,[status(thm)],[9, 2])).
% 0.17/0.45 tff(11,plain,
% 0.17/0.45 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 0.17/0.45 inference(rewrite,[status(thm)],[])).
% 0.17/0.45 tff(12,plain,
% 0.17/0.45 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & (((~(~ssItem(Y!51))) & (~((~(app(cons(Y!51, nil), Z!52) = W!49)) | (~(app(Z!52, cons(Y!51, nil)) = X!50)) | (~ssList(Z!52))))) | (~neq(X!50, nil))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (~((~(nil = W!49)) & (nil = X!50))) & (nil = V!48) & ssList(X!50) & ((~neq(X!50, nil)) | (ssItem(Y!51) & (~((~(app(cons(Y!51, nil), Z!52) = W!49)) | (~(app(Z!52, cons(Y!51, nil)) = X!50)) | (~ssList(Z!52))))))))),
% 0.17/0.45 inference(monotonicity,[status(thm)],[11, 10])).
% 0.17/0.45 tff(13,plain,
% 0.17/0.45 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & (((~(~ssItem(Y!51))) & (~((~(app(cons(Y!51, nil), Z!52) = W!49)) | (~(app(Z!52, cons(Y!51, nil)) = X!50)) | (~ssList(Z!52))))) | (~neq(X!50, nil))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (~((~(nil = W!49)) & (nil = X!50))) & (nil = V!48) & ssList(X!50) & ((~neq(X!50, nil)) | (ssItem(Y!51) & (~((~(app(cons(Y!51, nil), Z!52) = W!49)) | (~(app(Z!52, cons(Y!51, nil)) = X!50)) | (~ssList(Z!52)))))))),
% 0.17/0.45 inference(transitivity,[status(thm)],[12, 1])).
% 0.17/0.45 tff(14,plain,
% 0.17/0.45 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | ((~(nil = W)) & (nil = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~(app(cons(Y, nil), Z) = W)) | (~(app(Z, cons(Y, nil)) = X)) | (~ssList(Z)))) & neq(X, nil))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | ((~(nil = W)) & (nil = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~(app(cons(Y, nil), Z) = W)) | (~(app(Z, cons(Y, nil)) = X)) | (~ssList(Z)))) & neq(X, nil)))))))),
% 0.17/0.45 inference(rewrite,[status(thm)],[])).
% 0.17/0.45 tff(15,plain,
% 0.17/0.45 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(nil = V)) | (~(V = X))) | (~(U = W))) | (nil = U)) | ((~(nil = W)) & (nil = X))) | (![Y: $i] : (ssItem(Y) => ![Z: $i] : (ssList(Z) => ((~(app(cons(Y, nil), Z) = W)) | (~(app(Z, cons(Y, nil)) = X))))) & neq(X, nil)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | ((~(nil = W)) & (nil = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~(app(cons(Y, nil), Z) = W)) | (~(app(Z, cons(Y, nil)) = X)) | (~ssList(Z)))) & neq(X, nil)))))))),
% 0.17/0.45 inference(rewrite,[status(thm)],[])).
% 0.17/0.45 tff(16,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(nil = V)) | (~(V = X))) | (~(U = W))) | (nil = U)) | ((~(nil = W)) & (nil = X))) | (![Y: $i] : (ssItem(Y) => ![Z: $i] : (ssList(Z) => ((~(app(cons(Y, nil), Z) = W)) | (~(app(Z, cons(Y, nil)) = X))))) & neq(X, nil)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.17/0.45 tff(17,plain,
% 0.17/0.45 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | ((~(nil = W)) & (nil = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~(app(cons(Y, nil), Z) = W)) | (~(app(Z, cons(Y, nil)) = X)) | (~ssList(Z)))) & neq(X, nil))))))),
% 0.17/0.45 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.17/0.45 tff(18,plain,
% 0.17/0.45 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | ((~(nil = W)) & (nil = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~(app(cons(Y, nil), Z) = W)) | (~(app(Z, cons(Y, nil)) = X)) | (~ssList(Z)))) & neq(X, nil))))))),
% 0.17/0.45 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.17/0.45 tff(19,plain,
% 0.17/0.45 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | ((~(nil = W)) & (nil = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~(app(cons(Y, nil), Z) = W)) | (~(app(Z, cons(Y, nil)) = X)) | (~ssList(Z)))) & neq(X, nil))))))),
% 0.17/0.45 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.17/0.45 tff(20,plain,
% 0.17/0.45 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | ((~(nil = W)) & (nil = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~(app(cons(Y, nil), Z) = W)) | (~(app(Z, cons(Y, nil)) = X)) | (~ssList(Z)))) & neq(X, nil))))))),
% 0.17/0.45 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.17/0.45 tff(21,plain,
% 0.17/0.45 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | ((~(nil = W)) & (nil = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~(app(cons(Y, nil), Z) = W)) | (~(app(Z, cons(Y, nil)) = X)) | (~ssList(Z)))) & neq(X, nil))))))),
% 0.17/0.45 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.17/0.45 tff(22,plain,
% 0.17/0.45 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | ((~(nil = W)) & (nil = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~(app(cons(Y, nil), Z) = W)) | (~(app(Z, cons(Y, nil)) = X)) | (~ssList(Z)))) & neq(X, nil))))))),
% 0.17/0.45 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.17/0.45 tff(23,plain,
% 0.17/0.45 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | ((~(nil = W)) & (nil = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~(app(cons(Y, nil), Z) = W)) | (~(app(Z, cons(Y, nil)) = X)) | (~ssList(Z)))) & neq(X, nil))))))),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[22, 14])).
% 0.17/0.46 tff(24,plain,
% 0.17/0.46 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (~((~(nil = W!49)) & (nil = X!50))) & (nil = V!48) & ssList(X!50) & ((~neq(X!50, nil)) | (ssItem(Y!51) & (~((~(app(cons(Y!51, nil), Z!52) = W!49)) | (~(app(Z!52, cons(Y!51, nil)) = X!50)) | (~ssList(Z!52))))))),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.17/0.46 tff(25,plain,
% 0.17/0.46 (V!48 = X!50),
% 0.17/0.46 inference(and_elim,[status(thm)],[24])).
% 0.17/0.46 tff(26,plain,
% 0.17/0.46 (nil = V!48),
% 0.17/0.46 inference(and_elim,[status(thm)],[24])).
% 0.17/0.46 tff(27,plain,
% 0.17/0.46 (nil = X!50),
% 0.17/0.46 inference(transitivity,[status(thm)],[26, 25])).
% 0.17/0.46 tff(28,plain,
% 0.17/0.46 (U!47 = W!49),
% 0.17/0.46 inference(and_elim,[status(thm)],[24])).
% 0.17/0.46 tff(29,plain,
% 0.17/0.46 ((nil = U!47) <=> (nil = W!49)),
% 0.17/0.46 inference(monotonicity,[status(thm)],[28])).
% 0.17/0.46 tff(30,plain,
% 0.17/0.46 ((~(nil = U!47)) <=> (~(nil = W!49))),
% 0.17/0.46 inference(monotonicity,[status(thm)],[29])).
% 0.17/0.46 tff(31,plain,
% 0.17/0.46 (~(nil = U!47)),
% 0.17/0.46 inference(and_elim,[status(thm)],[24])).
% 0.17/0.46 tff(32,plain,
% 0.17/0.46 (~(nil = W!49)),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.17/0.46 tff(33,plain,
% 0.17/0.46 ((~(~((nil = W!49) | (~(nil = X!50))))) <=> ((nil = W!49) | (~(nil = X!50)))),
% 0.17/0.46 inference(rewrite,[status(thm)],[])).
% 0.17/0.46 tff(34,plain,
% 0.17/0.46 (((~(nil = W!49)) & (nil = X!50)) <=> (~((nil = W!49) | (~(nil = X!50))))),
% 0.17/0.46 inference(rewrite,[status(thm)],[])).
% 0.17/0.46 tff(35,plain,
% 0.17/0.46 ((~((~(nil = W!49)) & (nil = X!50))) <=> (~(~((nil = W!49) | (~(nil = X!50)))))),
% 0.17/0.46 inference(monotonicity,[status(thm)],[34])).
% 0.17/0.46 tff(36,plain,
% 0.17/0.46 ((~((~(nil = W!49)) & (nil = X!50))) <=> ((nil = W!49) | (~(nil = X!50)))),
% 0.17/0.46 inference(transitivity,[status(thm)],[35, 33])).
% 0.17/0.46 tff(37,plain,
% 0.17/0.46 (~((~(nil = W!49)) & (nil = X!50))),
% 0.17/0.46 inference(and_elim,[status(thm)],[24])).
% 0.17/0.46 tff(38,plain,
% 0.17/0.46 ((nil = W!49) | (~(nil = X!50))),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.17/0.46 tff(39,plain,
% 0.17/0.46 ($false),
% 0.17/0.46 inference(unit_resolution,[status(thm)],[38, 32, 27])).
% 0.17/0.46 % SZS output end Proof
%------------------------------------------------------------------------------