TSTP Solution File: SEU382+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU382+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 07:29:15 EDT 2022
% Result : Theorem 22.19s 14.59s
% Output : Proof 22.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU382+2 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n015.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
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Sep 3 13:08:10 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.
% 22.19/14.59 % SZS status Theorem
% 22.19/14.59 % SZS output start Proof
% 22.19/14.59 tff(powerset_type, type, (
% 22.19/14.59 powerset: $i > $i)).
% 22.19/14.59 tff(tptp_fun_A_486_type, type, (
% 22.19/14.59 tptp_fun_A_486: $i)).
% 22.19/14.59 tff(the_carrier_type, type, (
% 22.19/14.59 the_carrier: $i > $i)).
% 22.19/14.59 tff(boole_POSet_type, type, (
% 22.19/14.59 boole_POSet: $i > $i)).
% 22.19/14.59 tff(incl_POSet_type, type, (
% 22.19/14.59 incl_POSet: $i > $i)).
% 22.19/14.59 tff(inclusion_order_type, type, (
% 22.19/14.59 inclusion_order: $i > $i)).
% 22.19/14.59 tff(the_InternalRel_type, type, (
% 22.19/14.59 the_InternalRel: $i > $i)).
% 22.19/14.59 tff(1,plain,
% 22.19/14.59 (^[A: $i] : refl((~((~(the_carrier(incl_POSet(A)) = A)) | (~(the_InternalRel(incl_POSet(A)) = inclusion_order(A))))) <=> (~((~(the_carrier(incl_POSet(A)) = A)) | (~(the_InternalRel(incl_POSet(A)) = inclusion_order(A))))))),
% 22.19/14.59 inference(bind,[status(th)],[])).
% 22.19/14.59 tff(2,plain,
% 22.19/14.59 (![A: $i] : (~((~(the_carrier(incl_POSet(A)) = A)) | (~(the_InternalRel(incl_POSet(A)) = inclusion_order(A))))) <=> ![A: $i] : (~((~(the_carrier(incl_POSet(A)) = A)) | (~(the_InternalRel(incl_POSet(A)) = inclusion_order(A)))))),
% 22.19/14.59 inference(quant_intro,[status(thm)],[1])).
% 22.19/14.59 tff(3,plain,
% 22.19/14.59 (^[A: $i] : rewrite(((the_carrier(incl_POSet(A)) = A) & (the_InternalRel(incl_POSet(A)) = inclusion_order(A))) <=> (~((~(the_carrier(incl_POSet(A)) = A)) | (~(the_InternalRel(incl_POSet(A)) = inclusion_order(A))))))),
% 22.19/14.59 inference(bind,[status(th)],[])).
% 22.19/14.59 tff(4,plain,
% 22.19/14.59 (![A: $i] : ((the_carrier(incl_POSet(A)) = A) & (the_InternalRel(incl_POSet(A)) = inclusion_order(A))) <=> ![A: $i] : (~((~(the_carrier(incl_POSet(A)) = A)) | (~(the_InternalRel(incl_POSet(A)) = inclusion_order(A)))))),
% 22.19/14.59 inference(quant_intro,[status(thm)],[3])).
% 22.19/14.59 tff(5,plain,
% 22.19/14.59 (![A: $i] : ((the_carrier(incl_POSet(A)) = A) & (the_InternalRel(incl_POSet(A)) = inclusion_order(A))) <=> ![A: $i] : ((the_carrier(incl_POSet(A)) = A) & (the_InternalRel(incl_POSet(A)) = inclusion_order(A)))),
% 22.19/14.59 inference(rewrite,[status(thm)],[])).
% 22.19/14.59 tff(6,axiom,(![A: $i] : ((the_carrier(incl_POSet(A)) = A) & (the_InternalRel(incl_POSet(A)) = inclusion_order(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_yellow_1')).
% 22.19/14.59 tff(7,plain,
% 22.19/14.59 (![A: $i] : ((the_carrier(incl_POSet(A)) = A) & (the_InternalRel(incl_POSet(A)) = inclusion_order(A)))),
% 22.19/14.59 inference(modus_ponens,[status(thm)],[6, 5])).
% 22.19/14.59 tff(8,plain,(
% 22.19/14.59 ![A: $i] : ((the_carrier(incl_POSet(A)) = A) & (the_InternalRel(incl_POSet(A)) = inclusion_order(A)))),
% 22.19/14.59 inference(skolemize,[status(sab)],[7])).
% 22.19/14.59 tff(9,plain,
% 22.19/14.59 (![A: $i] : (~((~(the_carrier(incl_POSet(A)) = A)) | (~(the_InternalRel(incl_POSet(A)) = inclusion_order(A)))))),
% 22.19/14.59 inference(modus_ponens,[status(thm)],[8, 4])).
% 22.19/14.59 tff(10,plain,
% 22.19/14.59 (![A: $i] : (~((~(the_carrier(incl_POSet(A)) = A)) | (~(the_InternalRel(incl_POSet(A)) = inclusion_order(A)))))),
% 22.19/14.59 inference(modus_ponens,[status(thm)],[9, 2])).
% 22.19/14.59 tff(11,plain,
% 22.19/14.59 ((~![A: $i] : (~((~(the_carrier(incl_POSet(A)) = A)) | (~(the_InternalRel(incl_POSet(A)) = inclusion_order(A)))))) | (~((~(the_carrier(incl_POSet(powerset(A!486))) = powerset(A!486))) | (~(the_InternalRel(incl_POSet(powerset(A!486))) = inclusion_order(powerset(A!486))))))),
% 22.19/14.59 inference(quant_inst,[status(thm)],[])).
% 22.19/14.59 tff(12,plain,
% 22.19/14.59 (~((~(the_carrier(incl_POSet(powerset(A!486))) = powerset(A!486))) | (~(the_InternalRel(incl_POSet(powerset(A!486))) = inclusion_order(powerset(A!486)))))),
% 22.19/14.59 inference(unit_resolution,[status(thm)],[11, 10])).
% 22.19/14.59 tff(13,plain,
% 22.19/14.59 (((~(the_carrier(incl_POSet(powerset(A!486))) = powerset(A!486))) | (~(the_InternalRel(incl_POSet(powerset(A!486))) = inclusion_order(powerset(A!486))))) | (the_carrier(incl_POSet(powerset(A!486))) = powerset(A!486))),
% 22.19/14.59 inference(tautology,[status(thm)],[])).
% 22.19/14.59 tff(14,plain,
% 22.19/14.59 (the_carrier(incl_POSet(powerset(A!486))) = powerset(A!486)),
% 22.19/14.59 inference(unit_resolution,[status(thm)],[13, 12])).
% 22.19/14.59 tff(15,plain,
% 22.19/14.59 (^[A: $i] : refl((boole_POSet(A) = incl_POSet(powerset(A))) <=> (boole_POSet(A) = incl_POSet(powerset(A))))),
% 22.19/14.59 inference(bind,[status(th)],[])).
% 22.19/14.59 tff(16,plain,
% 22.19/14.59 (![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A))) <=> ![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A)))),
% 22.19/14.59 inference(quant_intro,[status(thm)],[15])).
% 22.19/14.59 tff(17,plain,
% 22.19/14.65 (![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A))) <=> ![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A)))),
% 22.19/14.65 inference(rewrite,[status(thm)],[])).
% 22.19/14.65 tff(18,axiom,(![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t4_yellow_1')).
% 22.19/14.65 tff(19,plain,
% 22.19/14.65 (![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A)))),
% 22.19/14.65 inference(modus_ponens,[status(thm)],[18, 17])).
% 22.19/14.65 tff(20,plain,(
% 22.19/14.65 ![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A)))),
% 22.19/14.65 inference(skolemize,[status(sab)],[19])).
% 22.19/14.65 tff(21,plain,
% 22.19/14.65 (![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A)))),
% 22.19/14.65 inference(modus_ponens,[status(thm)],[20, 16])).
% 22.19/14.65 tff(22,plain,
% 22.19/14.65 ((~![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A)))) | (boole_POSet(A!486) = incl_POSet(powerset(A!486)))),
% 22.19/14.65 inference(quant_inst,[status(thm)],[])).
% 22.19/14.65 tff(23,plain,
% 22.19/14.65 (boole_POSet(A!486) = incl_POSet(powerset(A!486))),
% 22.19/14.65 inference(unit_resolution,[status(thm)],[22, 21])).
% 22.19/14.65 tff(24,plain,
% 22.19/14.65 (the_carrier(boole_POSet(A!486)) = the_carrier(incl_POSet(powerset(A!486)))),
% 22.19/14.65 inference(monotonicity,[status(thm)],[23])).
% 22.19/14.65 tff(25,plain,
% 22.19/14.65 (the_carrier(boole_POSet(A!486)) = powerset(A!486)),
% 22.19/14.65 inference(transitivity,[status(thm)],[24, 14])).
% 22.19/14.65 tff(26,plain,
% 22.19/14.65 ((~![A: $i] : (the_carrier(boole_POSet(A)) = powerset(A))) <=> (~![A: $i] : (the_carrier(boole_POSet(A)) = powerset(A)))),
% 22.19/14.65 inference(rewrite,[status(thm)],[])).
% 22.19/14.65 tff(27,axiom,(~![A: $i] : (the_carrier(boole_POSet(A)) = powerset(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t4_waybel_7')).
% 22.19/14.65 tff(28,plain,
% 22.19/14.65 (~![A: $i] : (the_carrier(boole_POSet(A)) = powerset(A))),
% 22.19/14.65 inference(modus_ponens,[status(thm)],[27, 26])).
% 22.19/14.65 tff(29,plain,
% 22.19/14.65 (~![A: $i] : (the_carrier(boole_POSet(A)) = powerset(A))),
% 22.19/14.65 inference(modus_ponens,[status(thm)],[28, 26])).
% 22.19/14.65 tff(30,plain,
% 22.19/14.65 (~![A: $i] : (the_carrier(boole_POSet(A)) = powerset(A))),
% 22.19/14.65 inference(modus_ponens,[status(thm)],[29, 26])).
% 22.19/14.65 tff(31,plain,
% 22.19/14.65 (~![A: $i] : (the_carrier(boole_POSet(A)) = powerset(A))),
% 22.19/14.65 inference(modus_ponens,[status(thm)],[30, 26])).
% 22.19/14.65 tff(32,plain,
% 22.19/14.65 (~![A: $i] : (the_carrier(boole_POSet(A)) = powerset(A))),
% 22.19/14.65 inference(modus_ponens,[status(thm)],[31, 26])).
% 22.19/14.65 tff(33,plain,
% 22.19/14.65 (~![A: $i] : (the_carrier(boole_POSet(A)) = powerset(A))),
% 22.19/14.65 inference(modus_ponens,[status(thm)],[32, 26])).
% 22.19/14.65 tff(34,plain,
% 22.19/14.65 (~![A: $i] : (the_carrier(boole_POSet(A)) = powerset(A))),
% 22.19/14.65 inference(modus_ponens,[status(thm)],[33, 26])).
% 22.19/14.65 tff(35,plain,(
% 22.19/14.65 ~(the_carrier(boole_POSet(A!486)) = powerset(A!486))),
% 22.19/14.65 inference(skolemize,[status(sab)],[34])).
% 22.19/14.65 tff(36,plain,
% 22.19/14.65 ($false),
% 22.19/14.65 inference(unit_resolution,[status(thm)],[35, 25])).
% 22.19/14.65 % SZS output end Proof
%------------------------------------------------------------------------------