TSTP Solution File: SYN315+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN315+1 : TPTP v8.1.0. Released v2.0.0.
% 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 : Thu Sep 29 23:54:39 EDT 2022
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYN315+1 : TPTP v8.1.0. Released v2.0.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 02:31:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(big_f_type, type, (
% 0.12/0.38 big_f: $i > $o)).
% 0.12/0.38 tff(tptp_fun_Y_0_type, type, (
% 0.12/0.38 tptp_fun_Y_0: $i > $i)).
% 0.12/0.38 tff(elem_1_type, type, (
% 0.12/0.38 elem_1: $i)).
% 0.12/0.38 tff(p_type, type, (
% 0.12/0.38 p: $o)).
% 0.12/0.38 tff(1,assumption,(~big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))))), introduced(assumption)).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (^[X: $i] : refl((~((big_f(tptp_fun_Y_0(X)) <=> p) | ((~big_f(X)) <=> p))) <=> (~((big_f(tptp_fun_Y_0(X)) <=> p) | ((~big_f(X)) <=> p))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![X: $i] : (~((big_f(tptp_fun_Y_0(X)) <=> p) | ((~big_f(X)) <=> p))) <=> ![X: $i] : (~((big_f(tptp_fun_Y_0(X)) <=> p) | ((~big_f(X)) <=> p)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 ((~?[X: $i] : ![Y: $i] : ((big_f(Y) <=> p) | ((~big_f(X)) <=> p))) <=> (~?[X: $i] : ![Y: $i] : ((big_f(Y) <=> p) | ((~big_f(X)) <=> p)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 ((~?[X: $i] : ![Y: $i] : ((big_f(X) <=> p) => (big_f(Y) <=> p))) <=> (~?[X: $i] : ![Y: $i] : ((big_f(Y) <=> p) | ((~big_f(X)) <=> p)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(6,axiom,(~?[X: $i] : ![Y: $i] : ((big_f(X) <=> p) => (big_f(Y) <=> p))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','church_46_2_1')).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (~?[X: $i] : ![Y: $i] : ((big_f(Y) <=> p) | ((~big_f(X)) <=> p))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (~?[X: $i] : ![Y: $i] : ((big_f(Y) <=> p) | ((~big_f(X)) <=> p))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (~?[X: $i] : ![Y: $i] : ((big_f(Y) <=> p) | ((~big_f(X)) <=> p))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (~?[X: $i] : ![Y: $i] : ((big_f(Y) <=> p) | ((~big_f(X)) <=> p))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (~?[X: $i] : ![Y: $i] : ((big_f(Y) <=> p) | ((~big_f(X)) <=> p))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (~?[X: $i] : ![Y: $i] : ((big_f(Y) <=> p) | ((~big_f(X)) <=> p))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (~?[X: $i] : ![Y: $i] : ((big_f(Y) <=> p) | ((~big_f(X)) <=> p))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[12, 4])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (^[X: $i] : sk($oeq((~![Y: $i] : ((big_f(Y) <=> p) | ((~big_f(X)) <=> p))), (~((big_f(tptp_fun_Y_0(X)) <=> p) | ((~big_f(X)) <=> p)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(15,plain,(
% 0.12/0.38 ![X: $i] : (~((big_f(tptp_fun_Y_0(X)) <=> p) | ((~big_f(X)) <=> p)))),
% 0.12/0.38 inference(nnf-neg,[status(sab)],[13, 14])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![X: $i] : (~((big_f(tptp_fun_Y_0(X)) <=> p) | ((~big_f(X)) <=> p)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[15, 3])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 ((~![X: $i] : (~((big_f(tptp_fun_Y_0(X)) <=> p) | ((~big_f(X)) <=> p)))) | (~((big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))))) <=> p) | ((~big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))))) <=> p)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (~((big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))))) <=> p) | ((~big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))))) <=> p))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (((big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))))) <=> p) | ((~big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))))) <=> p)) | (~(big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))))) <=> p))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (~(big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))))) <=> p)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 ((big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))))) <=> p) | big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))))) | p),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))))) | p),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (p),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[22, 1])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 ((~![X: $i] : (~((big_f(tptp_fun_Y_0(X)) <=> p) | ((~big_f(X)) <=> p)))) | (~((big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))))) <=> p) | ((~big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))))) <=> p)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (~((big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))))) <=> p) | ((~big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))))) <=> p))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[24, 16])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (((big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))))) <=> p) | ((~big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))))) <=> p)) | (~((~big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))))) <=> p))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (~((~big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))))) <=> p)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (((~big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))))) <=> p) | big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))))) | (~p)),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))))) | (~p)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[29, 23, 1])).
% 0.12/0.38 tff(31,plain,(big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 ((big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))))) <=> p) | (~big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))))) | (~p)),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 ((~big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))))) | (~p)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[32, 20])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (~p),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[33, 31])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (((~big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))))) <=> p) | (~big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))))) | p),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 ((~big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))))) | p),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[35, 27])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[36, 34, 31])).
% 0.12/0.38 % SZS output end Proof
%------------------------------------------------------------------------------