%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU382+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 : Sat Jun 21 05:27:46 AM UTC 2025
% Result : Theorem 14.54s 14.74s
% Output : Proof 14.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU382+2 : TPTP v9.0.0. Released v3.3.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 06:57:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 14.54/14.74 % SZS status Theorem
% 14.54/14.74 % SZS output start Proof
% 14.54/14.74 tff(powerset_type, type, (
% 14.54/14.74 powerset: $i > $i)).
% 14.54/14.74 tff(tptp_fun_A_369_type, type, (
% 14.54/14.74 tptp_fun_A_369: $i)).
% 14.54/14.74 tff(the_carrier_type, type, (
% 14.54/14.74 the_carrier: $i > $i)).
% 14.54/14.74 tff(boole_POSet_type, type, (
% 14.54/14.74 boole_POSet: $i > $i)).
% 14.54/14.74 tff(incl_POSet_type, type, (
% 14.54/14.74 incl_POSet: $i > $i)).
% 14.54/14.74 tff(inclusion_order_type, type, (
% 14.54/14.74 inclusion_order: $i > $i)).
% 14.54/14.74 tff(the_InternalRel_type, type, (
% 14.54/14.74 the_InternalRel: $i > $i)).
% 14.54/14.74 tff(1,plain,
% 14.54/14.74 (^[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))))))),
% 14.54/14.74 inference(bind,[status(th)],[])).
% 14.54/14.74 tff(2,plain,
% 14.54/14.74 (![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)))))),
% 14.54/14.74 inference(quant_intro,[status(thm)],[1])).
% 14.54/14.74 tff(3,plain,
% 14.54/14.74 (^[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))))))),
% 14.54/14.74 inference(bind,[status(th)],[])).
% 14.54/14.74 tff(4,plain,
% 14.54/14.74 (![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)))))),
% 14.54/14.74 inference(quant_intro,[status(thm)],[3])).
% 14.54/14.74 tff(5,plain,
% 14.54/14.74 (![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)))),
% 14.54/14.74 inference(rewrite,[status(thm)],[])).
% 14.54/14.74 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')).
% 14.54/14.74 tff(7,plain,
% 14.54/14.74 (![A: $i] : ((the_carrier(incl_POSet(A)) = A) & (the_InternalRel(incl_POSet(A)) = inclusion_order(A)))),
% 14.54/14.74 inference(modus_ponens,[status(thm)],[6, 5])).
% 14.54/14.74 tff(8,plain,(
% 14.54/14.74 ![A: $i] : ((the_carrier(incl_POSet(A)) = A) & (the_InternalRel(incl_POSet(A)) = inclusion_order(A)))),
% 14.54/14.74 inference(skolemize,[status(sab)],[7])).
% 14.54/14.74 tff(9,plain,
% 14.54/14.74 (![A: $i] : (~((~(the_carrier(incl_POSet(A)) = A)) | (~(the_InternalRel(incl_POSet(A)) = inclusion_order(A)))))),
% 14.54/14.74 inference(modus_ponens,[status(thm)],[8, 4])).
% 14.54/14.74 tff(10,plain,
% 14.54/14.74 (![A: $i] : (~((~(the_carrier(incl_POSet(A)) = A)) | (~(the_InternalRel(incl_POSet(A)) = inclusion_order(A)))))),
% 14.54/14.74 inference(modus_ponens,[status(thm)],[9, 2])).
% 14.54/14.74 tff(11,plain,
% 14.54/14.74 ((~![A: $i] : (~((~(the_carrier(incl_POSet(A)) = A)) | (~(the_InternalRel(incl_POSet(A)) = inclusion_order(A)))))) | (~((~(the_carrier(incl_POSet(powerset(A!369))) = powerset(A!369))) | (~(the_InternalRel(incl_POSet(powerset(A!369))) = inclusion_order(powerset(A!369))))))),
% 14.54/14.74 inference(quant_inst,[status(thm)],[])).
% 14.54/14.74 tff(12,plain,
% 14.54/14.74 (~((~(the_carrier(incl_POSet(powerset(A!369))) = powerset(A!369))) | (~(the_InternalRel(incl_POSet(powerset(A!369))) = inclusion_order(powerset(A!369)))))),
% 14.54/14.74 inference(unit_resolution,[status(thm)],[11, 10])).
% 14.54/14.74 tff(13,plain,
% 14.54/14.74 (((~(the_carrier(incl_POSet(powerset(A!369))) = powerset(A!369))) | (~(the_InternalRel(incl_POSet(powerset(A!369))) = inclusion_order(powerset(A!369))))) | (the_carrier(incl_POSet(powerset(A!369))) = powerset(A!369))),
% 14.54/14.74 inference(tautology,[status(thm)],[])).
% 14.54/14.74 tff(14,plain,
% 14.54/14.74 (the_carrier(incl_POSet(powerset(A!369))) = powerset(A!369)),
% 14.54/14.74 inference(unit_resolution,[status(thm)],[13, 12])).
% 14.54/14.74 tff(15,plain,
% 14.54/14.74 (^[A: $i] : refl((boole_POSet(A) = incl_POSet(powerset(A))) <=> (boole_POSet(A) = incl_POSet(powerset(A))))),
% 14.54/14.74 inference(bind,[status(th)],[])).
% 14.54/14.74 tff(16,plain,
% 14.54/14.74 (![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A))) <=> ![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A)))),
% 14.54/14.74 inference(quant_intro,[status(thm)],[15])).
% 14.54/14.74 tff(17,plain,
% 14.63/14.79 (![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A))) <=> ![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A)))),
% 14.63/14.79 inference(rewrite,[status(thm)],[])).
% 14.63/14.79 tff(18,axiom,(![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t4_yellow_1')).
% 14.63/14.79 tff(19,plain,
% 14.63/14.79 (![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A)))),
% 14.63/14.79 inference(modus_ponens,[status(thm)],[18, 17])).
% 14.63/14.79 tff(20,plain,(
% 14.63/14.79 ![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A)))),
% 14.63/14.79 inference(skolemize,[status(sab)],[19])).
% 14.63/14.79 tff(21,plain,
% 14.63/14.79 (![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A)))),
% 14.63/14.79 inference(modus_ponens,[status(thm)],[20, 16])).
% 14.63/14.79 tff(22,plain,
% 14.63/14.79 ((~![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A)))) | (boole_POSet(A!369) = incl_POSet(powerset(A!369)))),
% 14.63/14.79 inference(quant_inst,[status(thm)],[])).
% 14.63/14.79 tff(23,plain,
% 14.63/14.79 (boole_POSet(A!369) = incl_POSet(powerset(A!369))),
% 14.63/14.79 inference(unit_resolution,[status(thm)],[22, 21])).
% 14.63/14.79 tff(24,plain,
% 14.63/14.79 (the_carrier(boole_POSet(A!369)) = the_carrier(incl_POSet(powerset(A!369)))),
% 14.63/14.79 inference(monotonicity,[status(thm)],[23])).
% 14.63/14.79 tff(25,plain,
% 14.63/14.79 (the_carrier(boole_POSet(A!369)) = powerset(A!369)),
% 14.63/14.79 inference(transitivity,[status(thm)],[24, 14])).
% 14.63/14.79 tff(26,plain,
% 14.63/14.79 ((~![A: $i] : (the_carrier(boole_POSet(A)) = powerset(A))) <=> (~![A: $i] : (the_carrier(boole_POSet(A)) = powerset(A)))),
% 14.63/14.79 inference(rewrite,[status(thm)],[])).
% 14.63/14.79 tff(27,axiom,(~![A: $i] : (the_carrier(boole_POSet(A)) = powerset(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t4_waybel_7')).
% 14.63/14.79 tff(28,plain,
% 14.63/14.79 (~![A: $i] : (the_carrier(boole_POSet(A)) = powerset(A))),
% 14.63/14.79 inference(modus_ponens,[status(thm)],[27, 26])).
% 14.63/14.79 tff(29,plain,
% 14.63/14.79 (~![A: $i] : (the_carrier(boole_POSet(A)) = powerset(A))),
% 14.63/14.79 inference(modus_ponens,[status(thm)],[28, 26])).
% 14.63/14.79 tff(30,plain,
% 14.63/14.79 (~![A: $i] : (the_carrier(boole_POSet(A)) = powerset(A))),
% 14.63/14.79 inference(modus_ponens,[status(thm)],[29, 26])).
% 14.63/14.79 tff(31,plain,
% 14.63/14.79 (~![A: $i] : (the_carrier(boole_POSet(A)) = powerset(A))),
% 14.63/14.79 inference(modus_ponens,[status(thm)],[30, 26])).
% 14.63/14.79 tff(32,plain,(
% 14.63/14.79 ~(the_carrier(boole_POSet(A!369)) = powerset(A!369))),
% 14.63/14.79 inference(skolemize,[status(sab)],[31])).
% 14.63/14.79 tff(33,plain,
% 14.63/14.79 ($false),
% 14.63/14.79 inference(unit_resolution,[status(thm)],[32, 25])).
% 14.63/14.79 % SZS output end Proof
% 14.63/14.83 % E exiting
%------------------------------------------------------------------------------