TSTP Solution File: SWC044+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC044+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 11:54:52 EDT 2022
% Result : Theorem 0.19s 0.52s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC044+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 21:10:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.19/0.52 % SZS status Theorem
% 0.19/0.52 % SZS output start Proof
% 0.19/0.52 tff(tptp_fun_W_49_type, type, (
% 0.19/0.52 tptp_fun_W_49: $i)).
% 0.19/0.52 tff(nil_type, type, (
% 0.19/0.52 nil: $i)).
% 0.19/0.52 tff(rearsegP_type, type, (
% 0.19/0.52 rearsegP: ( $i * $i ) > $o)).
% 0.19/0.52 tff(ssList_type, type, (
% 0.19/0.52 ssList: $i > $o)).
% 0.19/0.52 tff(tptp_fun_X_50_type, type, (
% 0.19/0.52 tptp_fun_X_50: $i)).
% 0.19/0.52 tff(tptp_fun_V_48_type, type, (
% 0.19/0.52 tptp_fun_V_48: $i)).
% 0.19/0.52 tff(tptp_fun_U_47_type, type, (
% 0.19/0.52 tptp_fun_U_47: $i)).
% 0.19/0.52 tff(1,plain,
% 0.19/0.52 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~((nil = U!47) | (~(nil = V!48)) | (~(U!47 = W!49)) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((nil = U!47) | (~(nil = V!48)) | (~(U!47 = W!49)) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(2,plain,
% 0.19/0.52 ((ssList(V!48) & (ssList(W!49) & (~((nil = U!47) | (~(nil = V!48)) | (~(U!47 = W!49)) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))) <=> (ssList(V!48) & ssList(W!49) & (~((nil = U!47) | (~(nil = V!48)) | (~(U!47 = W!49)) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(3,plain,
% 0.19/0.52 (((~(~ssList(W!49))) & (~((nil = U!47) | (~rearsegP(X!50, W!49)) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (~(nil = V!48)) | (~ssList(X!50))))) <=> (ssList(W!49) & (~((nil = U!47) | (~(nil = V!48)) | (~(U!47 = W!49)) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(4,plain,
% 0.19/0.52 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(5,plain,
% 0.19/0.52 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~((nil = U!47) | (~rearsegP(X!50, W!49)) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (~(nil = V!48)) | (~ssList(X!50)))))) <=> (ssList(V!48) & (ssList(W!49) & (~((nil = U!47) | (~(nil = V!48)) | (~(U!47 = W!49)) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50))))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[4, 3])).
% 0.19/0.52 tff(6,plain,
% 0.19/0.52 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~((nil = U!47) | (~rearsegP(X!50, W!49)) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (~(nil = V!48)) | (~ssList(X!50)))))) <=> (ssList(V!48) & ssList(W!49) & (~((nil = U!47) | (~(nil = V!48)) | (~(U!47 = W!49)) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[5, 2])).
% 0.19/0.52 tff(7,plain,
% 0.19/0.52 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(8,plain,
% 0.19/0.52 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~((nil = U!47) | (~rearsegP(X!50, W!49)) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (~(nil = V!48)) | (~ssList(X!50))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~((nil = U!47) | (~(nil = V!48)) | (~(U!47 = W!49)) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50))))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[7, 6])).
% 0.19/0.52 tff(9,plain,
% 0.19/0.52 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~((nil = U!47) | (~rearsegP(X!50, W!49)) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (~(nil = V!48)) | (~ssList(X!50))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((nil = U!47) | (~(nil = V!48)) | (~(U!47 = W!49)) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[8, 1])).
% 0.19/0.52 tff(10,plain,
% 0.19/0.52 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~rearsegP(X, W)) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~rearsegP(X, W)) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(11,plain,
% 0.19/0.52 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(nil = V)) | (~(V = X))) | (~(U = W))) | (~rearsegP(X, W))) | (nil = U))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~rearsegP(X, W)) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(12,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(nil = V)) | (~(V = X))) | (~(U = W))) | (~rearsegP(X, W))) | (nil = U))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.19/0.52 tff(13,plain,
% 0.19/0.52 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~rearsegP(X, W)) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.19/0.52 tff(14,plain,
% 0.19/0.52 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~rearsegP(X, W)) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.19/0.52 tff(15,plain,
% 0.19/0.52 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~rearsegP(X, W)) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.19/0.52 tff(16,plain,
% 0.19/0.52 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~rearsegP(X, W)) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.19/0.52 tff(17,plain,
% 0.19/0.52 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~rearsegP(X, W)) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.19/0.52 tff(18,plain,
% 0.19/0.52 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~rearsegP(X, W)) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.19/0.52 tff(19,plain,
% 0.19/0.52 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~rearsegP(X, W)) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.19/0.52 tff(20,plain,
% 0.19/0.52 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((nil = U!47) | (~(nil = V!48)) | (~(U!47 = W!49)) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[19, 9])).
% 0.19/0.52 tff(21,plain,
% 0.19/0.52 (ssList(W!49)),
% 0.19/0.52 inference(and_elim,[status(thm)],[20])).
% 0.19/0.52 tff(22,plain,
% 0.19/0.52 (^[U: $i] : refl(((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(23,plain,
% 0.19/0.52 (![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.52 tff(24,plain,
% 0.19/0.52 (![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(25,plain,
% 0.19/0.52 (^[U: $i] : rewrite((ssList(U) => (rearsegP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(26,plain,
% 0.19/0.52 (![U: $i] : (ssList(U) => (rearsegP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.52 tff(27,axiom,(![U: $i] : (ssList(U) => (rearsegP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax52')).
% 0.19/0.52 tff(28,plain,
% 0.19/0.52 (![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.52 tff(29,plain,
% 0.19/0.52 (![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.19/0.52 tff(30,plain,(
% 0.19/0.52 ![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 0.19/0.52 inference(skolemize,[status(sab)],[29])).
% 0.19/0.52 tff(31,plain,
% 0.19/0.52 (![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.19/0.53 tff(32,plain,
% 0.19/0.53 (((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | ((~ssList(W!49)) | (rearsegP(nil, W!49) <=> (nil = W!49)))) <=> ((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | (~ssList(W!49)) | (rearsegP(nil, W!49) <=> (nil = W!49)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(33,plain,
% 0.19/0.53 ((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | ((~ssList(W!49)) | (rearsegP(nil, W!49) <=> (nil = W!49)))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(34,plain,
% 0.19/0.53 ((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | (~ssList(W!49)) | (rearsegP(nil, W!49) <=> (nil = W!49))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.53 tff(35,plain,
% 0.19/0.53 (rearsegP(nil, W!49) <=> (nil = W!49)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[34, 31, 21])).
% 0.19/0.53 tff(36,plain,
% 0.19/0.53 (~((nil = U!47) | (~(nil = V!48)) | (~(U!47 = W!49)) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))),
% 0.19/0.53 inference(and_elim,[status(thm)],[20])).
% 0.19/0.53 tff(37,plain,
% 0.19/0.53 (V!48 = X!50),
% 0.19/0.53 inference(or_elim,[status(thm)],[36])).
% 0.19/0.53 tff(38,plain,
% 0.19/0.53 (nil = V!48),
% 0.19/0.53 inference(or_elim,[status(thm)],[36])).
% 0.19/0.53 tff(39,plain,
% 0.19/0.53 (nil = X!50),
% 0.19/0.53 inference(transitivity,[status(thm)],[38, 37])).
% 0.19/0.53 tff(40,plain,
% 0.19/0.53 (rearsegP(nil, W!49) <=> rearsegP(X!50, W!49)),
% 0.19/0.53 inference(monotonicity,[status(thm)],[39])).
% 0.19/0.53 tff(41,plain,
% 0.19/0.53 (rearsegP(X!50, W!49) <=> rearsegP(nil, W!49)),
% 0.19/0.53 inference(symmetry,[status(thm)],[40])).
% 0.19/0.53 tff(42,plain,
% 0.19/0.53 (rearsegP(X!50, W!49)),
% 0.19/0.53 inference(or_elim,[status(thm)],[36])).
% 0.19/0.53 tff(43,plain,
% 0.19/0.53 (rearsegP(nil, W!49)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.53 tff(44,plain,
% 0.19/0.53 (U!47 = W!49),
% 0.19/0.53 inference(or_elim,[status(thm)],[36])).
% 0.19/0.53 tff(45,plain,
% 0.19/0.53 (W!49 = U!47),
% 0.19/0.53 inference(symmetry,[status(thm)],[44])).
% 0.19/0.53 tff(46,plain,
% 0.19/0.53 ((nil = W!49) <=> (nil = U!47)),
% 0.19/0.53 inference(monotonicity,[status(thm)],[45])).
% 0.19/0.53 tff(47,plain,
% 0.19/0.53 ((nil = U!47) <=> (nil = W!49)),
% 0.19/0.53 inference(symmetry,[status(thm)],[46])).
% 0.19/0.53 tff(48,plain,
% 0.19/0.53 ((~(nil = U!47)) <=> (~(nil = W!49))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[47])).
% 0.19/0.53 tff(49,plain,
% 0.19/0.53 (~(nil = U!47)),
% 0.19/0.53 inference(or_elim,[status(thm)],[36])).
% 0.19/0.53 tff(50,plain,
% 0.19/0.53 (~(nil = W!49)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.53 tff(51,plain,
% 0.19/0.53 ((~(rearsegP(nil, W!49) <=> (nil = W!49))) | (~rearsegP(nil, W!49)) | (nil = W!49)),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(52,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[51, 50, 43, 35])).
% 0.19/0.53 % SZS output end Proof
%------------------------------------------------------------------------------