TSTP Solution File: SET604+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET604+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 05:07:15 EDT 2022
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET604+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n001.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 07:14:10 EDT 2022
% 0.13/0.33 % 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.
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(subset_type, type, (
% 0.19/0.38 subset: ( $i * $i ) > $o)).
% 0.19/0.38 tff(tptp_fun_B_2_type, type, (
% 0.19/0.38 tptp_fun_B_2: $i)).
% 0.19/0.38 tff(empty_set_type, type, (
% 0.19/0.38 empty_set: $i)).
% 0.19/0.38 tff(difference_type, type, (
% 0.19/0.38 difference: ( $i * $i ) > $i)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 (^[B: $i, C: $i] : refl(((difference(B, C) = empty_set) <=> subset(B, C)) <=> ((difference(B, C) = empty_set) <=> subset(B, C)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C)) <=> ![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C)) <=> ![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(4,axiom,(![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','difference_empty_set')).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.38 tff(6,plain,(
% 0.19/0.38 ![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C))),
% 0.19/0.38 inference(skolemize,[status(sab)],[5])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 ((~![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C))) | ((difference(empty_set, B!2) = empty_set) <=> subset(empty_set, B!2))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 ((difference(empty_set, B!2) = empty_set) <=> subset(empty_set, B!2)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 ((~![B: $i] : (difference(empty_set, B) = empty_set)) <=> (~![B: $i] : (difference(empty_set, B) = empty_set))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(11,axiom,(~![B: $i] : (difference(empty_set, B) = empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_no_difference_with_empty_set')).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (~![B: $i] : (difference(empty_set, B) = empty_set)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (~![B: $i] : (difference(empty_set, B) = empty_set)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[12, 10])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (~![B: $i] : (difference(empty_set, B) = empty_set)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (~![B: $i] : (difference(empty_set, B) = empty_set)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (~![B: $i] : (difference(empty_set, B) = empty_set)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 (~![B: $i] : (difference(empty_set, B) = empty_set)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (~![B: $i] : (difference(empty_set, B) = empty_set)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.19/0.38 tff(19,plain,(
% 0.19/0.38 ~(difference(empty_set, B!2) = empty_set)),
% 0.19/0.38 inference(skolemize,[status(sab)],[18])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 ((~((difference(empty_set, B!2) = empty_set) <=> subset(empty_set, B!2))) | (difference(empty_set, B!2) = empty_set) | (~subset(empty_set, B!2))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 ((~((difference(empty_set, B!2) = empty_set) <=> subset(empty_set, B!2))) | (~subset(empty_set, B!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 (~subset(empty_set, B!2)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[21, 9])).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 (^[B: $i] : refl(subset(empty_set, B) <=> subset(empty_set, B))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 (![B: $i] : subset(empty_set, B) <=> ![B: $i] : subset(empty_set, B)),
% 0.19/0.38 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 (![B: $i] : subset(empty_set, B) <=> ![B: $i] : subset(empty_set, B)),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(26,axiom,(![B: $i] : subset(empty_set, B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','empty_set_subset')).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 (![B: $i] : subset(empty_set, B)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.38 tff(28,plain,(
% 0.19/0.38 ![B: $i] : subset(empty_set, B)),
% 0.19/0.38 inference(skolemize,[status(sab)],[27])).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 (![B: $i] : subset(empty_set, B)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 ((~![B: $i] : subset(empty_set, B)) | subset(empty_set, B!2)),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[30, 29, 22])).
% 0.19/0.38 % SZS output end Proof
%------------------------------------------------------------------------------