TSTP Solution File: SYN937+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN937+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 : Fri Sep 30 00:01:19 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN937+1 : TPTP v8.1.0. Released v3.1.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n028.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Sep 5 09:44:41 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.19/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34 Usage: tptp [options] [-file:]file
% 0.19/0.34 -h, -? prints this message.
% 0.19/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.34 -m, -model generate model.
% 0.19/0.34 -p, -proof generate proof.
% 0.19/0.34 -c, -core generate unsat core of named formulas.
% 0.19/0.34 -st, -statistics display statistics.
% 0.19/0.34 -t:timeout set timeout (in second).
% 0.19/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34 -<param>:<value> configuration parameter and value.
% 0.19/0.34 -o:<output-file> file to place output in.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(p_type, type, (
% 0.19/0.40 p: $i > $o)).
% 0.19/0.40 tff(tptp_fun_X_0_type, type, (
% 0.19/0.40 tptp_fun_X_0: $i)).
% 0.19/0.40 tff(c_type, type, (
% 0.19/0.40 c: $o)).
% 0.19/0.40 tff(tptp_fun_X_1_type, type, (
% 0.19/0.40 tptp_fun_X_1: $i)).
% 0.19/0.40 tff(1,assumption,(~(c | (~p(X!1)))), introduced(assumption)).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 ((c | (~p(X!1))) | p(X!1)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 (p(X!1)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 ((c | (~p(X!1))) | (~c)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 (~c),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.19/0.40 tff(6,assumption,(p(X!1)), introduced(assumption)).
% 0.19/0.40 tff(7,assumption,(![X: $i] : (c | (~p(X)))), introduced(assumption)).
% 0.19/0.40 tff(8,assumption,(~c), introduced(assumption)).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (((~![X: $i] : (c | (~p(X)))) | (c | (~p(X!1)))) <=> ((~![X: $i] : (c | (~p(X)))) | c | (~p(X!1)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 ((~![X: $i] : (c | (~p(X)))) | (c | (~p(X!1)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 ((~![X: $i] : (c | (~p(X)))) | c | (~p(X!1))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[11, 8, 7, 6])).
% 0.19/0.40 tff(13,plain,((~![X: $i] : (c | (~p(X)))) | c | (~p(X!1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (~![X: $i] : (c | (~p(X)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[13, 5, 3])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 ((c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))) <=> (c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (((![X: $i] : (c | (~p(X))) | (c | ![X: $i] : (~p(X)))) & ((~(c | (~p(X!0)))) | ((~c) & p(X!1)))) <=> ((c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))) & ((~(c | (~p(X!0)))) | ((~c) & p(X!1))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 ((~?[X: $i] : p(X)) <=> (~?[X: $i] : p(X))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 ((c | (~?[X: $i] : p(X))) <=> (c | (~?[X: $i] : p(X)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[17])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 ((~![X: $i] : (c | (~p(X)))) <=> (~![X: $i] : (c | (~p(X))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (((~![X: $i] : (c | (~p(X)))) <=> (c | (~?[X: $i] : p(X)))) <=> ((~![X: $i] : (c | (~p(X)))) <=> (c | (~?[X: $i] : p(X))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[19, 18])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (((~![X: $i] : (c | (~p(X)))) <=> (c | (~?[X: $i] : p(X)))) <=> ((~![X: $i] : (c | (~p(X)))) <=> (c | (~?[X: $i] : p(X))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 ((~(![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X))))) <=> ((~![X: $i] : (c | (~p(X)))) <=> (c | (~?[X: $i] : p(X))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 ((![X: $i] : (p(X) => c) <=> (?[X: $i] : p(X) => c)) <=> (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 ((~(![X: $i] : (p(X) => c) <=> (?[X: $i] : p(X) => c))) <=> (~(![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[23])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 ((~(![X: $i] : (p(X) => c) <=> (?[X: $i] : p(X) => c))) <=> ((~![X: $i] : (c | (~p(X)))) <=> (c | (~?[X: $i] : p(X))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[24, 22])).
% 0.19/0.40 tff(26,axiom,(~(![X: $i] : (p(X) => c) <=> (?[X: $i] : p(X) => c))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 ((~![X: $i] : (c | (~p(X)))) <=> (c | (~?[X: $i] : p(X)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 ((~![X: $i] : (c | (~p(X)))) <=> (c | (~?[X: $i] : p(X)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 ((~![X: $i] : (c | (~p(X)))) <=> (c | (~?[X: $i] : p(X)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 ((~![X: $i] : (c | (~p(X)))) <=> (c | (~?[X: $i] : p(X)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[29, 20])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 ((~![X: $i] : (c | (~p(X)))) <=> (c | (~?[X: $i] : p(X)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[30, 20])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 ((~![X: $i] : (c | (~p(X)))) <=> (c | (~?[X: $i] : p(X)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[31, 20])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 ((~![X: $i] : (c | (~p(X)))) <=> (c | (~?[X: $i] : p(X)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[32, 20])).
% 0.19/0.40 tff(34,plain,(
% 0.19/0.40 (![X: $i] : (c | (~p(X))) | (c | ![X: $i] : (~p(X)))) & ((~(c | (~p(X!0)))) | ((~c) & p(X!1)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[33])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 ((c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))) & ((~(c | (~p(X!0)))) | ((~c) & p(X!1)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[34, 16])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 (c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))),
% 0.19/0.40 inference(and_elim,[status(thm)],[35])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[36, 15])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (![X: $i] : (~p(X))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[37, 14, 5])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 ((~![X: $i] : (~p(X))) | (~p(X!1))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[39, 38, 3])).
% 0.19/0.40 tff(41,plain,(c | (~p(X!1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (((~(c | (~p(X!0)))) | ((~c) & p(X!1))) <=> ((~(c | (~p(X!0)))) | (~(c | (~p(X!1)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 ((~(c | (~p(X!0)))) | ((~c) & p(X!1))),
% 0.19/0.40 inference(and_elim,[status(thm)],[35])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 ((~(c | (~p(X!0)))) | (~(c | (~p(X!1))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (~(c | (~p(X!0)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[44, 41])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 ((c | (~p(X!0))) | p(X!0)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (p(X!0)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.19/0.40 tff(48,assumption,(![X: $i] : (~p(X))), introduced(assumption)).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 ((~![X: $i] : (~p(X))) | (~p(X!0))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[49, 48, 47])).
% 0.19/0.40 tff(51,plain,(~![X: $i] : (~p(X))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 ((c | (~p(X!0))) | (~c)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (~c),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[52, 45])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[37, 53])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (![X: $i] : (c | (~p(X)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[54, 51])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (((~![X: $i] : (c | (~p(X)))) | (c | (~p(X!0)))) <=> ((~![X: $i] : (c | (~p(X)))) | c | (~p(X!0)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 ((~![X: $i] : (c | (~p(X)))) | (c | (~p(X!0)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 ((~![X: $i] : (c | (~p(X)))) | c | (~p(X!0))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[58, 53, 55, 47])).
% 0.19/0.40 % SZS output end Proof
%------------------------------------------------------------------------------