TSTP Solution File: SEU139+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU139+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 07:27:42 EDT 2022
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU139+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Sep 3 09:39:59 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 tff(subset_type, type, (
% 0.14/0.40 subset: ( $i * $i ) > $o)).
% 0.14/0.40 tff(tptp_fun_B_0_type, type, (
% 0.14/0.40 tptp_fun_B_0: $i)).
% 0.14/0.40 tff(tptp_fun_A_1_type, type, (
% 0.14/0.40 tptp_fun_A_1: $i)).
% 0.14/0.40 tff(proper_subset_type, type, (
% 0.14/0.40 proper_subset: ( $i * $i ) > $o)).
% 0.14/0.40 tff(1,plain,
% 0.14/0.40 (^[A: $i, B: $i] : refl(((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(2,plain,
% 0.14/0.40 (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.40 tff(3,plain,
% 0.14/0.40 (^[A: $i, B: $i] : rewrite(((A = B) <=> (subset(A, B) & subset(B, A))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(4,plain,
% 0.14/0.40 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.14/0.40 tff(5,plain,
% 0.14/0.40 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(6,axiom,(![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d10_xboole_0')).
% 0.14/0.40 tff(7,plain,
% 0.14/0.40 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.14/0.40 tff(8,plain,(
% 0.14/0.40 ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.14/0.40 inference(skolemize,[status(sab)],[7])).
% 0.14/0.40 tff(9,plain,
% 0.14/0.40 (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.14/0.40 tff(10,plain,
% 0.14/0.40 (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.14/0.40 tff(11,plain,
% 0.14/0.40 ((~![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | ((B!0 = A!1) <=> (~((~subset(B!0, A!1)) | (~subset(A!1, B!0)))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(12,plain,
% 0.14/0.40 ((B!0 = A!1) <=> (~((~subset(B!0, A!1)) | (~subset(A!1, B!0))))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.14/0.40 tff(13,plain,
% 0.14/0.40 (^[A: $i, B: $i] : refl((proper_subset(A, B) <=> (~((~subset(A, B)) | (A = B)))) <=> (proper_subset(A, B) <=> (~((~subset(A, B)) | (A = B)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(14,plain,
% 0.14/0.40 (![A: $i, B: $i] : (proper_subset(A, B) <=> (~((~subset(A, B)) | (A = B)))) <=> ![A: $i, B: $i] : (proper_subset(A, B) <=> (~((~subset(A, B)) | (A = B))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.14/0.40 tff(15,plain,
% 0.14/0.40 (^[A: $i, B: $i] : rewrite((proper_subset(A, B) <=> (subset(A, B) & (~(A = B)))) <=> (proper_subset(A, B) <=> (~((~subset(A, B)) | (A = B)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(16,plain,
% 0.14/0.40 (![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B)))) <=> ![A: $i, B: $i] : (proper_subset(A, B) <=> (~((~subset(A, B)) | (A = B))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.14/0.40 tff(17,plain,
% 0.14/0.40 (![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B)))) <=> ![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(18,axiom,(![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d8_xboole_0')).
% 0.14/0.40 tff(19,plain,
% 0.14/0.40 (![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.14/0.40 tff(20,plain,(
% 0.14/0.40 ![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B))))),
% 0.14/0.40 inference(skolemize,[status(sab)],[19])).
% 0.14/0.40 tff(21,plain,
% 0.14/0.40 (![A: $i, B: $i] : (proper_subset(A, B) <=> (~((~subset(A, B)) | (A = B))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.14/0.40 tff(22,plain,
% 0.14/0.40 (![A: $i, B: $i] : (proper_subset(A, B) <=> (~((~subset(A, B)) | (A = B))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.14/0.40 tff(23,plain,
% 0.14/0.40 ((~![A: $i, B: $i] : (proper_subset(A, B) <=> (~((~subset(A, B)) | (A = B))))) | (proper_subset(B!0, A!1) <=> (~((~subset(B!0, A!1)) | (B!0 = A!1))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(24,plain,
% 0.14/0.40 (proper_subset(B!0, A!1) <=> (~((~subset(B!0, A!1)) | (B!0 = A!1)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.14/0.40 tff(25,plain,
% 0.14/0.40 ((~(~(subset(A!1, B!0) & proper_subset(B!0, A!1)))) <=> (subset(A!1, B!0) & proper_subset(B!0, A!1))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(26,plain,
% 0.14/0.40 ((~![A: $i, B: $i] : (~(subset(A, B) & proper_subset(B, A)))) <=> (~![A: $i, B: $i] : (~(subset(A, B) & proper_subset(B, A))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(27,axiom,(~![A: $i, B: $i] : (~(subset(A, B) & proper_subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t60_xboole_1')).
% 0.14/0.40 tff(28,plain,
% 0.14/0.40 (~![A: $i, B: $i] : (~(subset(A, B) & proper_subset(B, A)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.14/0.40 tff(29,plain,
% 0.14/0.40 (~![A: $i, B: $i] : (~(subset(A, B) & proper_subset(B, A)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[28, 26])).
% 0.14/0.40 tff(30,plain,
% 0.14/0.40 (~![A: $i, B: $i] : (~(subset(A, B) & proper_subset(B, A)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.14/0.40 tff(31,plain,
% 0.14/0.40 (~![A: $i, B: $i] : (~(subset(A, B) & proper_subset(B, A)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.14/0.40 tff(32,plain,
% 0.14/0.40 (~![A: $i, B: $i] : (~(subset(A, B) & proper_subset(B, A)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.14/0.40 tff(33,plain,
% 0.14/0.40 (~![A: $i, B: $i] : (~(subset(A, B) & proper_subset(B, A)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[32, 26])).
% 0.14/0.40 tff(34,plain,
% 0.14/0.40 (~![A: $i, B: $i] : (~(subset(A, B) & proper_subset(B, A)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.14/0.40 tff(35,plain,(
% 0.14/0.40 ~(~(subset(A!1, B!0) & proper_subset(B!0, A!1)))),
% 0.14/0.40 inference(skolemize,[status(sab)],[34])).
% 0.14/0.40 tff(36,plain,
% 0.14/0.40 (subset(A!1, B!0) & proper_subset(B!0, A!1)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.14/0.40 tff(37,plain,
% 0.14/0.40 (proper_subset(B!0, A!1)),
% 0.14/0.40 inference(and_elim,[status(thm)],[36])).
% 0.14/0.40 tff(38,plain,
% 0.14/0.40 ((~(proper_subset(B!0, A!1) <=> (~((~subset(B!0, A!1)) | (B!0 = A!1))))) | (~proper_subset(B!0, A!1)) | (~((~subset(B!0, A!1)) | (B!0 = A!1)))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(39,plain,
% 0.14/0.40 ((~(proper_subset(B!0, A!1) <=> (~((~subset(B!0, A!1)) | (B!0 = A!1))))) | (~((~subset(B!0, A!1)) | (B!0 = A!1)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.14/0.40 tff(40,plain,
% 0.14/0.40 (~((~subset(B!0, A!1)) | (B!0 = A!1))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[39, 24])).
% 0.14/0.40 tff(41,plain,
% 0.14/0.40 (((~subset(B!0, A!1)) | (B!0 = A!1)) | (~(B!0 = A!1))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(42,plain,
% 0.14/0.40 (~(B!0 = A!1)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.14/0.40 tff(43,plain,
% 0.14/0.40 (((~subset(B!0, A!1)) | (B!0 = A!1)) | subset(B!0, A!1)),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(44,plain,
% 0.14/0.40 (subset(B!0, A!1)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[43, 40])).
% 0.14/0.40 tff(45,plain,
% 0.14/0.40 (subset(A!1, B!0)),
% 0.14/0.40 inference(and_elim,[status(thm)],[36])).
% 0.14/0.40 tff(46,plain,
% 0.14/0.40 ((~((~subset(B!0, A!1)) | (~subset(A!1, B!0)))) | (~subset(B!0, A!1)) | (~subset(A!1, B!0))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(47,plain,
% 0.14/0.40 ((~((~subset(B!0, A!1)) | (~subset(A!1, B!0)))) | (~subset(B!0, A!1))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.14/0.40 tff(48,plain,
% 0.14/0.40 (~((~subset(B!0, A!1)) | (~subset(A!1, B!0)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[47, 44])).
% 0.14/0.40 tff(49,plain,
% 0.14/0.40 ((~((B!0 = A!1) <=> (~((~subset(B!0, A!1)) | (~subset(A!1, B!0)))))) | (B!0 = A!1) | ((~subset(B!0, A!1)) | (~subset(A!1, B!0)))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(50,plain,
% 0.14/0.40 ($false),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[49, 48, 42, 12])).
% 0.14/0.40 % SZS output end Proof
%------------------------------------------------------------------------------