TSTP Solution File: SWC385+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC385+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 11:57:35 EDT 2022
% Result : Theorem 0.22s 0.49s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC385+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.35 % Computer : n019.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun Sep 4 00:37:20 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.36 Usage: tptp [options] [-file:]file
% 0.15/0.36 -h, -? prints this message.
% 0.15/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.36 -m, -model generate model.
% 0.15/0.36 -p, -proof generate proof.
% 0.15/0.36 -c, -core generate unsat core of named formulas.
% 0.15/0.36 -st, -statistics display statistics.
% 0.15/0.36 -t:timeout set timeout (in second).
% 0.15/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.36 -<param>:<value> configuration parameter and value.
% 0.15/0.36 -o:<output-file> file to place output in.
% 0.22/0.49 % SZS status Theorem
% 0.22/0.49 % SZS output start Proof
% 0.22/0.49 tff(singletonP_type, type, (
% 0.22/0.49 singletonP: $i > $o)).
% 0.22/0.49 tff(tptp_fun_U_47_type, type, (
% 0.22/0.49 tptp_fun_U_47: $i)).
% 0.22/0.49 tff(tptp_fun_W_49_type, type, (
% 0.22/0.49 tptp_fun_W_49: $i)).
% 0.22/0.49 tff(ssList_type, type, (
% 0.22/0.49 ssList: $i > $o)).
% 0.22/0.49 tff(tptp_fun_X_50_type, type, (
% 0.22/0.49 tptp_fun_X_50: $i)).
% 0.22/0.49 tff(tptp_fun_V_48_type, type, (
% 0.22/0.49 tptp_fun_V_48: $i)).
% 0.22/0.49 tff(segmentP_type, type, (
% 0.22/0.49 segmentP: ( $i * $i ) > $o)).
% 0.22/0.49 tff(neq_type, type, (
% 0.22/0.49 neq: ( $i * $i ) > $o)).
% 0.22/0.49 tff(nil_type, type, (
% 0.22/0.49 nil: $i)).
% 0.22/0.49 tff(1,plain,
% 0.22/0.49 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~((singletonP(U!47) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | ((~singletonP(W!49)) & neq(X!50, nil)) | (~segmentP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((singletonP(U!47) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | ((~singletonP(W!49)) & neq(X!50, nil)) | (~segmentP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(2,plain,
% 0.22/0.49 ((ssList(V!48) & (ssList(W!49) & (~((singletonP(U!47) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | ((~singletonP(W!49)) & neq(X!50, nil)) | (~segmentP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))) <=> (ssList(V!48) & ssList(W!49) & (~((singletonP(U!47) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | ((~singletonP(W!49)) & neq(X!50, nil)) | (~segmentP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(3,plain,
% 0.22/0.49 (((~(~ssList(W!49))) & (~(((~singletonP(W!49)) & neq(X!50, nil)) | (~segmentP(X!50, W!49)) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (singletonP(U!47) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~ssList(X!50))))) <=> (ssList(W!49) & (~((singletonP(U!47) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | ((~singletonP(W!49)) & neq(X!50, nil)) | (~segmentP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(4,plain,
% 0.22/0.49 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(5,plain,
% 0.22/0.49 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~(((~singletonP(W!49)) & neq(X!50, nil)) | (~segmentP(X!50, W!49)) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (singletonP(U!47) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~ssList(X!50)))))) <=> (ssList(V!48) & (ssList(W!49) & (~((singletonP(U!47) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | ((~singletonP(W!49)) & neq(X!50, nil)) | (~segmentP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50))))))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[4, 3])).
% 0.22/0.49 tff(6,plain,
% 0.22/0.49 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~(((~singletonP(W!49)) & neq(X!50, nil)) | (~segmentP(X!50, W!49)) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (singletonP(U!47) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~ssList(X!50)))))) <=> (ssList(V!48) & ssList(W!49) & (~((singletonP(U!47) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | ((~singletonP(W!49)) & neq(X!50, nil)) | (~segmentP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))),
% 0.22/0.49 inference(transitivity,[status(thm)],[5, 2])).
% 0.22/0.49 tff(7,plain,
% 0.22/0.49 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(8,plain,
% 0.22/0.49 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~(((~singletonP(W!49)) & neq(X!50, nil)) | (~segmentP(X!50, W!49)) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (singletonP(U!47) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~ssList(X!50))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~((singletonP(U!47) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | ((~singletonP(W!49)) & neq(X!50, nil)) | (~segmentP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50))))))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[7, 6])).
% 0.22/0.49 tff(9,plain,
% 0.22/0.49 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~(((~singletonP(W!49)) & neq(X!50, nil)) | (~segmentP(X!50, W!49)) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (singletonP(U!47) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~ssList(X!50))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((singletonP(U!47) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | ((~singletonP(W!49)) & neq(X!50, nil)) | (~segmentP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))),
% 0.22/0.49 inference(transitivity,[status(thm)],[8, 1])).
% 0.22/0.49 tff(10,plain,
% 0.22/0.49 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~singletonP(W)) & neq(X, nil)) | (~segmentP(X, W)) | (~(U = W)) | (~(V = X)) | (singletonP(U) & segmentP(V, U)) | (~neq(V, nil)) | (~ssList(X))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~singletonP(W)) & neq(X, nil)) | (~segmentP(X, W)) | (~(U = W)) | (~(V = X)) | (singletonP(U) & segmentP(V, U)) | (~neq(V, nil)) | (~ssList(X)))))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(11,plain,
% 0.22/0.49 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | (~segmentP(X, W))) | ((~singletonP(W)) & neq(X, nil))) | (singletonP(U) & segmentP(V, U)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~singletonP(W)) & neq(X, nil)) | (~segmentP(X, W)) | (~(U = W)) | (~(V = X)) | (singletonP(U) & segmentP(V, U)) | (~neq(V, nil)) | (~ssList(X)))))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(12,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | (~segmentP(X, W))) | ((~singletonP(W)) & neq(X, nil))) | (singletonP(U) & segmentP(V, U)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.22/0.49 tff(13,plain,
% 0.22/0.49 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~singletonP(W)) & neq(X, nil)) | (~segmentP(X, W)) | (~(U = W)) | (~(V = X)) | (singletonP(U) & segmentP(V, U)) | (~neq(V, nil)) | (~ssList(X))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.22/0.49 tff(14,plain,
% 0.22/0.49 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~singletonP(W)) & neq(X, nil)) | (~segmentP(X, W)) | (~(U = W)) | (~(V = X)) | (singletonP(U) & segmentP(V, U)) | (~neq(V, nil)) | (~ssList(X))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.22/0.49 tff(15,plain,
% 0.22/0.49 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~singletonP(W)) & neq(X, nil)) | (~segmentP(X, W)) | (~(U = W)) | (~(V = X)) | (singletonP(U) & segmentP(V, U)) | (~neq(V, nil)) | (~ssList(X))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.22/0.49 tff(16,plain,
% 0.22/0.49 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~singletonP(W)) & neq(X, nil)) | (~segmentP(X, W)) | (~(U = W)) | (~(V = X)) | (singletonP(U) & segmentP(V, U)) | (~neq(V, nil)) | (~ssList(X))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.22/0.49 tff(17,plain,
% 0.22/0.49 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~singletonP(W)) & neq(X, nil)) | (~segmentP(X, W)) | (~(U = W)) | (~(V = X)) | (singletonP(U) & segmentP(V, U)) | (~neq(V, nil)) | (~ssList(X))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.22/0.49 tff(18,plain,
% 0.22/0.49 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~singletonP(W)) & neq(X, nil)) | (~segmentP(X, W)) | (~(U = W)) | (~(V = X)) | (singletonP(U) & segmentP(V, U)) | (~neq(V, nil)) | (~ssList(X))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.22/0.49 tff(19,plain,
% 0.22/0.49 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~singletonP(W)) & neq(X, nil)) | (~segmentP(X, W)) | (~(U = W)) | (~(V = X)) | (singletonP(U) & segmentP(V, U)) | (~neq(V, nil)) | (~ssList(X))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.22/0.49 tff(20,plain,
% 0.22/0.49 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((singletonP(U!47) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | ((~singletonP(W!49)) & neq(X!50, nil)) | (~segmentP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50))))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[19, 9])).
% 0.22/0.50 tff(21,plain,
% 0.22/0.50 (~((singletonP(U!47) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | ((~singletonP(W!49)) & neq(X!50, nil)) | (~segmentP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))),
% 0.22/0.50 inference(and_elim,[status(thm)],[20])).
% 0.22/0.50 tff(22,plain,
% 0.22/0.50 (U!47 = W!49),
% 0.22/0.50 inference(or_elim,[status(thm)],[21])).
% 0.22/0.50 tff(23,plain,
% 0.22/0.50 (singletonP(U!47) <=> singletonP(W!49)),
% 0.22/0.50 inference(monotonicity,[status(thm)],[22])).
% 0.22/0.50 tff(24,plain,
% 0.22/0.50 (singletonP(W!49) <=> singletonP(U!47)),
% 0.22/0.50 inference(symmetry,[status(thm)],[23])).
% 0.22/0.50 tff(25,plain,
% 0.22/0.50 (V!48 = X!50),
% 0.22/0.50 inference(or_elim,[status(thm)],[21])).
% 0.22/0.50 tff(26,plain,
% 0.22/0.50 (neq(V!48, nil) <=> neq(X!50, nil)),
% 0.22/0.50 inference(monotonicity,[status(thm)],[25])).
% 0.22/0.50 tff(27,plain,
% 0.22/0.50 (neq(V!48, nil)),
% 0.22/0.50 inference(or_elim,[status(thm)],[21])).
% 0.22/0.50 tff(28,plain,
% 0.22/0.50 (neq(X!50, nil)),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.22/0.50 tff(29,plain,
% 0.22/0.50 ((~(~(singletonP(W!49) | (~neq(X!50, nil))))) <=> (singletonP(W!49) | (~neq(X!50, nil)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(30,plain,
% 0.22/0.50 (((~singletonP(W!49)) & neq(X!50, nil)) <=> (~(singletonP(W!49) | (~neq(X!50, nil))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(31,plain,
% 0.22/0.50 ((~((~singletonP(W!49)) & neq(X!50, nil))) <=> (~(~(singletonP(W!49) | (~neq(X!50, nil)))))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[30])).
% 0.22/0.50 tff(32,plain,
% 0.22/0.50 ((~((~singletonP(W!49)) & neq(X!50, nil))) <=> (singletonP(W!49) | (~neq(X!50, nil)))),
% 0.22/0.50 inference(transitivity,[status(thm)],[31, 29])).
% 0.22/0.50 tff(33,plain,
% 0.22/0.50 (~((~singletonP(W!49)) & neq(X!50, nil))),
% 0.22/0.50 inference(or_elim,[status(thm)],[21])).
% 0.22/0.50 tff(34,plain,
% 0.22/0.50 (singletonP(W!49) | (~neq(X!50, nil))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.22/0.50 tff(35,plain,
% 0.22/0.50 (singletonP(W!49)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[34, 28])).
% 0.22/0.50 tff(36,plain,
% 0.22/0.50 (singletonP(U!47)),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[35, 24])).
% 0.22/0.50 tff(37,plain,
% 0.22/0.50 (segmentP(V!48, U!47) <=> segmentP(X!50, W!49)),
% 0.22/0.50 inference(monotonicity,[status(thm)],[25, 22])).
% 0.22/0.50 tff(38,plain,
% 0.22/0.50 (segmentP(X!50, W!49) <=> segmentP(V!48, U!47)),
% 0.22/0.50 inference(symmetry,[status(thm)],[37])).
% 0.22/0.50 tff(39,plain,
% 0.22/0.50 (segmentP(X!50, W!49)),
% 0.22/0.50 inference(or_elim,[status(thm)],[21])).
% 0.22/0.50 tff(40,plain,
% 0.22/0.50 (segmentP(V!48, U!47)),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.22/0.50 tff(41,plain,
% 0.22/0.50 ((~(~((~singletonP(U!47)) | (~segmentP(V!48, U!47))))) <=> ((~singletonP(U!47)) | (~segmentP(V!48, U!47)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(42,plain,
% 0.22/0.50 ((singletonP(U!47) & segmentP(V!48, U!47)) <=> (~((~singletonP(U!47)) | (~segmentP(V!48, U!47))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(43,plain,
% 0.22/0.50 ((~(singletonP(U!47) & segmentP(V!48, U!47))) <=> (~(~((~singletonP(U!47)) | (~segmentP(V!48, U!47)))))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[42])).
% 0.22/0.50 tff(44,plain,
% 0.22/0.50 ((~(singletonP(U!47) & segmentP(V!48, U!47))) <=> ((~singletonP(U!47)) | (~segmentP(V!48, U!47)))),
% 0.22/0.50 inference(transitivity,[status(thm)],[43, 41])).
% 0.22/0.50 tff(45,plain,
% 0.22/0.50 (~(singletonP(U!47) & segmentP(V!48, U!47))),
% 0.22/0.50 inference(or_elim,[status(thm)],[21])).
% 0.22/0.50 tff(46,plain,
% 0.22/0.50 ((~singletonP(U!47)) | (~segmentP(V!48, U!47))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.22/0.50 tff(47,plain,
% 0.22/0.50 (~singletonP(U!47)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[46, 40])).
% 0.22/0.50 tff(48,plain,
% 0.22/0.50 ($false),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[47, 36])).
% 0.22/0.50 % SZS output end Proof
%------------------------------------------------------------------------------