TSTP Solution File: SWC146+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC146+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 11:55:37 EDT 2022
% Result : Theorem 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC146+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 21:56:25 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.
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 % SZS output start Proof
% 0.19/0.45 tff(neq_type, type, (
% 0.19/0.45 neq: ( $i * $i ) > $o)).
% 0.19/0.45 tff(nil_type, type, (
% 0.19/0.45 nil: $i)).
% 0.19/0.45 tff(tptp_fun_V_48_type, type, (
% 0.19/0.45 tptp_fun_V_48: $i)).
% 0.19/0.45 tff(tptp_fun_X_50_type, type, (
% 0.19/0.45 tptp_fun_X_50: $i)).
% 0.19/0.45 tff(ssList_type, type, (
% 0.19/0.45 ssList: $i > $o)).
% 0.19/0.45 tff(tptp_fun_W_49_type, type, (
% 0.19/0.45 tptp_fun_W_49: $i)).
% 0.19/0.45 tff(tptp_fun_U_47_type, type, (
% 0.19/0.45 tptp_fun_U_47: $i)).
% 0.19/0.45 tff(singletonP_type, type, (
% 0.19/0.45 singletonP: $i > $o)).
% 0.19/0.45 tff(1,plain,
% 0.19/0.45 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~(singletonP(V!48) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | neq(X!50, nil) | (~(V!48 = X!50)) | (~ssList(X!50)))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(singletonP(V!48) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | neq(X!50, nil) | (~(V!48 = X!50)) | (~ssList(X!50)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(2,plain,
% 0.19/0.45 ((ssList(V!48) & (ssList(W!49) & (~(singletonP(V!48) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | neq(X!50, nil) | (~(V!48 = X!50)) | (~ssList(X!50)))))) <=> (ssList(V!48) & ssList(W!49) & (~(singletonP(V!48) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | neq(X!50, nil) | (~(V!48 = X!50)) | (~ssList(X!50)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(3,plain,
% 0.19/0.45 (((~(~ssList(W!49))) & (~(singletonP(V!48) | (~neq(V!48, nil)) | neq(X!50, nil) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (~ssList(X!50))))) <=> (ssList(W!49) & (~(singletonP(V!48) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | neq(X!50, nil) | (~(V!48 = X!50)) | (~ssList(X!50)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(4,plain,
% 0.19/0.45 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(5,plain,
% 0.19/0.45 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~(singletonP(V!48) | (~neq(V!48, nil)) | neq(X!50, nil) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))) <=> (ssList(V!48) & (ssList(W!49) & (~(singletonP(V!48) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | neq(X!50, nil) | (~(V!48 = X!50)) | (~ssList(X!50))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[4, 3])).
% 0.19/0.45 tff(6,plain,
% 0.19/0.45 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~(singletonP(V!48) | (~neq(V!48, nil)) | neq(X!50, nil) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))) <=> (ssList(V!48) & ssList(W!49) & (~(singletonP(V!48) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | neq(X!50, nil) | (~(V!48 = X!50)) | (~ssList(X!50)))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[5, 2])).
% 0.19/0.45 tff(7,plain,
% 0.19/0.45 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(8,plain,
% 0.19/0.45 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~(singletonP(V!48) | (~neq(V!48, nil)) | neq(X!50, nil) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (~ssList(X!50))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~(singletonP(V!48) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | neq(X!50, nil) | (~(V!48 = X!50)) | (~ssList(X!50))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[7, 6])).
% 0.19/0.45 tff(9,plain,
% 0.19/0.45 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~(singletonP(V!48) | (~neq(V!48, nil)) | neq(X!50, nil) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (~ssList(X!50))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(singletonP(V!48) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | neq(X!50, nil) | (~(V!48 = X!50)) | (~ssList(X!50)))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[8, 1])).
% 0.19/0.45 tff(10,plain,
% 0.19/0.45 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (singletonP(V) | (~neq(V, nil)) | neq(X, nil) | (~(U = W)) | (~(V = X)) | (~ssList(X))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (singletonP(V) | (~neq(V, nil)) | neq(X, nil) | (~(U = W)) | (~(V = X)) | (~ssList(X)))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(11,plain,
% 0.19/0.45 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | neq(X, nil)) | singletonP(V))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (singletonP(V) | (~neq(V, nil)) | neq(X, nil) | (~(U = W)) | (~(V = X)) | (~ssList(X)))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 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))) | neq(X, nil)) | singletonP(V))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.19/0.46 tff(13,plain,
% 0.19/0.46 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (singletonP(V) | (~neq(V, nil)) | neq(X, nil) | (~(U = W)) | (~(V = X)) | (~ssList(X))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.19/0.46 tff(14,plain,
% 0.19/0.46 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (singletonP(V) | (~neq(V, nil)) | neq(X, nil) | (~(U = W)) | (~(V = X)) | (~ssList(X))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.19/0.46 tff(15,plain,
% 0.19/0.46 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (singletonP(V) | (~neq(V, nil)) | neq(X, nil) | (~(U = W)) | (~(V = X)) | (~ssList(X))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.19/0.46 tff(16,plain,
% 0.19/0.46 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (singletonP(V) | (~neq(V, nil)) | neq(X, nil) | (~(U = W)) | (~(V = X)) | (~ssList(X))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.19/0.46 tff(17,plain,
% 0.19/0.46 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (singletonP(V) | (~neq(V, nil)) | neq(X, nil) | (~(U = W)) | (~(V = X)) | (~ssList(X))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.19/0.46 tff(18,plain,
% 0.19/0.46 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (singletonP(V) | (~neq(V, nil)) | neq(X, nil) | (~(U = W)) | (~(V = X)) | (~ssList(X))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.19/0.46 tff(19,plain,
% 0.19/0.46 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (singletonP(V) | (~neq(V, nil)) | neq(X, nil) | (~(U = W)) | (~(V = X)) | (~ssList(X))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.19/0.46 tff(20,plain,
% 0.19/0.46 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(singletonP(V!48) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | neq(X!50, nil) | (~(V!48 = X!50)) | (~ssList(X!50))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[19, 9])).
% 0.19/0.46 tff(21,plain,
% 0.19/0.46 (~(singletonP(V!48) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | neq(X!50, nil) | (~(V!48 = X!50)) | (~ssList(X!50)))),
% 0.19/0.46 inference(and_elim,[status(thm)],[20])).
% 0.19/0.46 tff(22,plain,
% 0.19/0.46 (V!48 = X!50),
% 0.19/0.46 inference(or_elim,[status(thm)],[21])).
% 0.19/0.46 tff(23,plain,
% 0.19/0.46 (neq(V!48, nil) <=> neq(X!50, nil)),
% 0.19/0.46 inference(monotonicity,[status(thm)],[22])).
% 0.19/0.46 tff(24,plain,
% 0.19/0.46 (neq(X!50, nil) <=> neq(V!48, nil)),
% 0.19/0.46 inference(symmetry,[status(thm)],[23])).
% 0.19/0.46 tff(25,plain,
% 0.19/0.46 ((~neq(X!50, nil)) <=> (~neq(V!48, nil))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[24])).
% 0.19/0.46 tff(26,plain,
% 0.19/0.46 (~neq(X!50, nil)),
% 0.19/0.46 inference(or_elim,[status(thm)],[21])).
% 0.19/0.46 tff(27,plain,
% 0.19/0.46 (~neq(V!48, nil)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.46 tff(28,plain,
% 0.19/0.46 (neq(V!48, nil)),
% 0.19/0.46 inference(or_elim,[status(thm)],[21])).
% 0.19/0.46 tff(29,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.19/0.46 % SZS output end Proof
%------------------------------------------------------------------------------