%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP399_1 : TPTP v9.0.0. Released v8.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:12:48 AM UTC 2025
% Result : Theorem 0.19s 0.57s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ITP399_1 : TPTP v9.0.0. Released v8.0.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 18:49:09 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.57 % SZS status Theorem
% 0.19/0.57 % SZS output start Proof
% 0.19/0.57 tff(tptp_fun__complements___type, type, (
% 0.19/0.57 tptp_fun__complements__: ( |'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| * |'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| ) > $o)).
% 0.19/0.57 tff(tptp_fun__register_pair___type, type, (
% 0.19/0.57 tptp_fun__register_pair__: ( |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| * |'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| ) > |'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|)).
% 0.19/0.57 tff(tptp_fun__complement___type, type, (
% 0.19/0.57 tptp_fun__complement__: |'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| > |'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|)).
% 0.19/0.57 tff(tptp_fun__register_pair_a__type, type, (
% 0.19/0.57 tptp_fun__register_pair_a_: ( |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| * |'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| ) > |'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|)).
% 0.19/0.57 tff(tptp_fun__compatible___type, type, (
% 0.19/0.57 tptp_fun__compatible__: ( |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| * |'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| ) > $o)).
% 0.19/0.57 tff(tptp_fun__g___type, type, (
% 0.19/0.57 tptp_fun__g__: |'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|)).
% 0.19/0.57 tff(tptp_fun__f___type, type, (
% 0.19/0.57 tptp_fun__f__: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|)).
% 0.19/0.57 tff(1,plain,
% 0.19/0.57 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : refl(((~tptp_fun__compatible__(A__questionmark_v0, A__questionmark_v1)) | tptp_fun__complements__(A__questionmark_v1, tptp_fun__register_pair__(A__questionmark_v0, tptp_fun__complement__(tptp_fun__register_pair_a_(A__questionmark_v0, A__questionmark_v1))))) <=> ((~tptp_fun__compatible__(A__questionmark_v0, A__questionmark_v1)) | tptp_fun__complements__(A__questionmark_v1, tptp_fun__register_pair__(A__questionmark_v0, tptp_fun__complement__(tptp_fun__register_pair_a_(A__questionmark_v0, A__questionmark_v1))))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(2,plain,
% 0.19/0.57 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__compatible__(A__questionmark_v0, A__questionmark_v1)) | tptp_fun__complements__(A__questionmark_v1, tptp_fun__register_pair__(A__questionmark_v0, tptp_fun__complement__(tptp_fun__register_pair_a_(A__questionmark_v0, A__questionmark_v1))))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__compatible__(A__questionmark_v0, A__questionmark_v1)) | tptp_fun__complements__(A__questionmark_v1, tptp_fun__register_pair__(A__questionmark_v0, tptp_fun__complement__(tptp_fun__register_pair_a_(A__questionmark_v0, A__questionmark_v1)))))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.57 tff(3,plain,
% 0.19/0.57 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__compatible__(A__questionmark_v0, A__questionmark_v1)) | tptp_fun__complements__(A__questionmark_v1, tptp_fun__register_pair__(A__questionmark_v0, tptp_fun__complement__(tptp_fun__register_pair_a_(A__questionmark_v0, A__questionmark_v1))))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__compatible__(A__questionmark_v0, A__questionmark_v1)) | tptp_fun__complements__(A__questionmark_v1, tptp_fun__register_pair__(A__questionmark_v0, tptp_fun__complement__(tptp_fun__register_pair_a_(A__questionmark_v0, A__questionmark_v1)))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(4,plain,
% 0.19/0.57 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : rewrite((tptp_fun__compatible__(A__questionmark_v0, A__questionmark_v1) => tptp_fun__complements__(A__questionmark_v1, tptp_fun__register_pair__(A__questionmark_v0, tptp_fun__complement__(tptp_fun__register_pair_a_(A__questionmark_v0, A__questionmark_v1))))) <=> ((~tptp_fun__compatible__(A__questionmark_v0, A__questionmark_v1)) | tptp_fun__complements__(A__questionmark_v1, tptp_fun__register_pair__(A__questionmark_v0, tptp_fun__complement__(tptp_fun__register_pair_a_(A__questionmark_v0, A__questionmark_v1))))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(5,plain,
% 0.19/0.57 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__compatible__(A__questionmark_v0, A__questionmark_v1) => tptp_fun__complements__(A__questionmark_v1, tptp_fun__register_pair__(A__questionmark_v0, tptp_fun__complement__(tptp_fun__register_pair_a_(A__questionmark_v0, A__questionmark_v1))))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__compatible__(A__questionmark_v0, A__questionmark_v1)) | tptp_fun__complements__(A__questionmark_v1, tptp_fun__register_pair__(A__questionmark_v0, tptp_fun__complement__(tptp_fun__register_pair_a_(A__questionmark_v0, A__questionmark_v1)))))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.57 tff(6,axiom,(![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__compatible__(A__questionmark_v0, A__questionmark_v1) => tptp_fun__complements__(A__questionmark_v1, tptp_fun__register_pair__(A__questionmark_v0, tptp_fun__complement__(tptp_fun__register_pair_a_(A__questionmark_v0, A__questionmark_v1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom18')).
% 0.19/0.57 tff(7,plain,
% 0.19/0.57 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__compatible__(A__questionmark_v0, A__questionmark_v1)) | tptp_fun__complements__(A__questionmark_v1, tptp_fun__register_pair__(A__questionmark_v0, tptp_fun__complement__(tptp_fun__register_pair_a_(A__questionmark_v0, A__questionmark_v1)))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.57 tff(8,plain,
% 0.19/0.57 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__compatible__(A__questionmark_v0, A__questionmark_v1)) | tptp_fun__complements__(A__questionmark_v1, tptp_fun__register_pair__(A__questionmark_v0, tptp_fun__complement__(tptp_fun__register_pair_a_(A__questionmark_v0, A__questionmark_v1)))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.57 tff(9,plain,(
% 0.19/0.57 ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__compatible__(A__questionmark_v0, A__questionmark_v1)) | tptp_fun__complements__(A__questionmark_v1, tptp_fun__register_pair__(A__questionmark_v0, tptp_fun__complement__(tptp_fun__register_pair_a_(A__questionmark_v0, A__questionmark_v1)))))),
% 0.19/0.57 inference(skolemize,[status(sab)],[8])).
% 0.19/0.57 tff(10,plain,
% 0.19/0.57 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__compatible__(A__questionmark_v0, A__questionmark_v1)) | tptp_fun__complements__(A__questionmark_v1, tptp_fun__register_pair__(A__questionmark_v0, tptp_fun__complement__(tptp_fun__register_pair_a_(A__questionmark_v0, A__questionmark_v1)))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.57 tff(11,plain,
% 0.19/0.57 (tptp_fun__compatible__(|'f$'|, |'g$'|) <=> tptp_fun__compatible__(|'f$'|, |'g$'|)),
% 0.47/0.62 inference(rewrite,[status(thm)],[])).
% 0.47/0.62 tff(12,axiom,(tptp_fun__compatible__(|'f$'|, |'g$'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom3')).
% 0.47/0.62 tff(13,plain,
% 0.47/0.62 (tptp_fun__compatible__(|'f$'|, |'g$'|)),
% 0.47/0.62 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.47/0.62 tff(14,plain,
% 0.47/0.62 ((~tptp_fun__complements__(|'g$'|, tptp_fun__register_pair__(|'f$'|, tptp_fun__complement__(tptp_fun__register_pair_a_(|'f$'|, |'g$'|))))) <=> (~tptp_fun__complements__(|'g$'|, tptp_fun__register_pair__(|'f$'|, tptp_fun__complement__(tptp_fun__register_pair_a_(|'f$'|, |'g$'|)))))),
% 0.47/0.62 inference(rewrite,[status(thm)],[])).
% 0.47/0.62 tff(15,axiom,(~tptp_fun__complements__(|'g$'|, tptp_fun__register_pair__(|'f$'|, tptp_fun__complement__(tptp_fun__register_pair_a_(|'f$'|, |'g$'|))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conjecture0')).
% 0.47/0.62 tff(16,plain,
% 0.47/0.62 (~tptp_fun__complements__(|'g$'|, tptp_fun__register_pair__(|'f$'|, tptp_fun__complement__(tptp_fun__register_pair_a_(|'f$'|, |'g$'|))))),
% 0.47/0.62 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.47/0.62 tff(17,plain,
% 0.47/0.62 (((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__compatible__(A__questionmark_v0, A__questionmark_v1)) | tptp_fun__complements__(A__questionmark_v1, tptp_fun__register_pair__(A__questionmark_v0, tptp_fun__complement__(tptp_fun__register_pair_a_(A__questionmark_v0, A__questionmark_v1)))))) | ((~tptp_fun__compatible__(|'f$'|, |'g$'|)) | tptp_fun__complements__(|'g$'|, tptp_fun__register_pair__(|'f$'|, tptp_fun__complement__(tptp_fun__register_pair_a_(|'f$'|, |'g$'|)))))) <=> ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__compatible__(A__questionmark_v0, A__questionmark_v1)) | tptp_fun__complements__(A__questionmark_v1, tptp_fun__register_pair__(A__questionmark_v0, tptp_fun__complement__(tptp_fun__register_pair_a_(A__questionmark_v0, A__questionmark_v1)))))) | (~tptp_fun__compatible__(|'f$'|, |'g$'|)) | tptp_fun__complements__(|'g$'|, tptp_fun__register_pair__(|'f$'|, tptp_fun__complement__(tptp_fun__register_pair_a_(|'f$'|, |'g$'|)))))),
% 0.47/0.62 inference(rewrite,[status(thm)],[])).
% 0.47/0.62 tff(18,plain,
% 0.47/0.62 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__compatible__(A__questionmark_v0, A__questionmark_v1)) | tptp_fun__complements__(A__questionmark_v1, tptp_fun__register_pair__(A__questionmark_v0, tptp_fun__complement__(tptp_fun__register_pair_a_(A__questionmark_v0, A__questionmark_v1)))))) | ((~tptp_fun__compatible__(|'f$'|, |'g$'|)) | tptp_fun__complements__(|'g$'|, tptp_fun__register_pair__(|'f$'|, tptp_fun__complement__(tptp_fun__register_pair_a_(|'f$'|, |'g$'|)))))),
% 0.47/0.62 inference(quant_inst,[status(thm)],[])).
% 0.47/0.62 tff(19,plain,
% 0.47/0.62 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__compatible__(A__questionmark_v0, A__questionmark_v1)) | tptp_fun__complements__(A__questionmark_v1, tptp_fun__register_pair__(A__questionmark_v0, tptp_fun__complement__(tptp_fun__register_pair_a_(A__questionmark_v0, A__questionmark_v1)))))) | (~tptp_fun__compatible__(|'f$'|, |'g$'|)) | tptp_fun__complements__(|'g$'|, tptp_fun__register_pair__(|'f$'|, tptp_fun__complement__(tptp_fun__register_pair_a_(|'f$'|, |'g$'|))))),
% 0.47/0.62 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.47/0.62 tff(20,plain,
% 0.47/0.62 ($false),
% 0.47/0.62 inference(unit_resolution,[status(thm)],[19, 16, 13, 10])).
% 0.47/0.62 % SZS output end Proof
% 0.47/0.63 % E exiting
%------------------------------------------------------------------------------