%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP327_1 : TPTP v9.0.0. Released v8.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:12:43 AM UTC 2025
% Result : Theorem 0.39s 0.58s
% Output : Proof 0.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ITP327_1 : TPTP v9.0.0. Released v8.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.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 18:47:41 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.39/0.58 % SZS status Theorem
% 0.39/0.58 % SZS output start Proof
% 0.39/0.58 tff(tptp_fun__zero___type, type, (
% 0.39/0.58 tptp_fun__zero__: |'A$'|)).
% 0.39/0.58 tff(tptp_fun__fun_app_m__type, type, (
% 0.39/0.58 tptp_fun__fun_app_m_: ( |'A_a_fun$'| * |'A$'| ) > |'A$'|)).
% 0.39/0.58 tff(tptp_fun__fun_app_d__type, type, (
% 0.39/0.58 tptp_fun__fun_app_d_: ( |'N_a_fun$'| * |'N$'| ) > |'A$'|)).
% 0.39/0.58 tff(tptp_fun__i___type, type, (
% 0.39/0.58 tptp_fun__i__: |'N$'|)).
% 0.39/0.58 tff(tptp_fun__vec_nth_b__type, type, (
% 0.39/0.58 tptp_fun__vec_nth_b_: |'A_n_vec$'| > |'N_a_fun$'|)).
% 0.39/0.58 tff(tptp_fun__xa___type, type, (
% 0.39/0.58 tptp_fun__xa__: |'A_n_vec$'|)).
% 0.39/0.58 tff(tptp_fun__fun_app_n__type, type, (
% 0.39/0.58 tptp_fun__fun_app_n_: ( |'A_a_a_fun_fun$'| * |'A$'| ) > |'A_a_fun$'|)).
% 0.39/0.58 tff(tptp_fun__the___type, type, (
% 0.39/0.58 tptp_fun__the__: |'N_bool_fun$'| > |'N$'|)).
% 0.39/0.58 tff(tptp_fun__uu___type, type, (
% 0.39/0.58 tptp_fun__uu__: |'N_bool_fun$'|)).
% 0.39/0.58 tff(tptp_fun__x___type, type, (
% 0.39/0.58 tptp_fun__x__: |'A_n_vec$'|)).
% 0.39/0.58 tff(tptp_fun__times_e__type, type, (
% 0.39/0.58 tptp_fun__times_e_: |'A_a_a_fun_fun$'|)).
% 0.39/0.58 tff(tptp_fun__one___type, type, (
% 0.39/0.58 tptp_fun__one__: |'A$'|)).
% 0.39/0.58 tff(1,plain,
% 0.39/0.58 (^[A__questionmark_v0: |'A$'|, A__questionmark_v1: |'A$'|] : refl(((tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, A__questionmark_v0), A__questionmark_v1) = A__questionmark_v1) <=> ((A__questionmark_v1 = |'zero$'|) | (A__questionmark_v0 = |'one$'|))) <=> ((tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, A__questionmark_v0), A__questionmark_v1) = A__questionmark_v1) <=> ((A__questionmark_v1 = |'zero$'|) | (A__questionmark_v0 = |'one$'|))))),
% 0.39/0.58 inference(bind,[status(th)],[])).
% 0.39/0.58 tff(2,plain,
% 0.39/0.58 (![A__questionmark_v0: |'A$'|, A__questionmark_v1: |'A$'|] : ((tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, A__questionmark_v0), A__questionmark_v1) = A__questionmark_v1) <=> ((A__questionmark_v1 = |'zero$'|) | (A__questionmark_v0 = |'one$'|))) <=> ![A__questionmark_v0: |'A$'|, A__questionmark_v1: |'A$'|] : ((tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, A__questionmark_v0), A__questionmark_v1) = A__questionmark_v1) <=> ((A__questionmark_v1 = |'zero$'|) | (A__questionmark_v0 = |'one$'|)))),
% 0.39/0.58 inference(quant_intro,[status(thm)],[1])).
% 0.39/0.58 tff(3,plain,
% 0.39/0.58 (![A__questionmark_v0: |'A$'|, A__questionmark_v1: |'A$'|] : ((tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, A__questionmark_v0), A__questionmark_v1) = A__questionmark_v1) <=> ((A__questionmark_v1 = |'zero$'|) | (A__questionmark_v0 = |'one$'|))) <=> ![A__questionmark_v0: |'A$'|, A__questionmark_v1: |'A$'|] : ((tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, A__questionmark_v0), A__questionmark_v1) = A__questionmark_v1) <=> ((A__questionmark_v1 = |'zero$'|) | (A__questionmark_v0 = |'one$'|)))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(4,axiom,(![A__questionmark_v0: |'A$'|, A__questionmark_v1: |'A$'|] : ((tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, A__questionmark_v0), A__questionmark_v1) = A__questionmark_v1) <=> ((A__questionmark_v1 = |'zero$'|) | (A__questionmark_v0 = |'one$'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom252')).
% 0.39/0.58 tff(5,plain,
% 0.39/0.58 (![A__questionmark_v0: |'A$'|, A__questionmark_v1: |'A$'|] : ((tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, A__questionmark_v0), A__questionmark_v1) = A__questionmark_v1) <=> ((A__questionmark_v1 = |'zero$'|) | (A__questionmark_v0 = |'one$'|)))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.39/0.58 tff(6,plain,(
% 0.39/0.58 ![A__questionmark_v0: |'A$'|, A__questionmark_v1: |'A$'|] : ((tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, A__questionmark_v0), A__questionmark_v1) = A__questionmark_v1) <=> ((A__questionmark_v1 = |'zero$'|) | (A__questionmark_v0 = |'one$'|)))),
% 0.39/0.58 inference(skolemize,[status(sab)],[5])).
% 0.39/0.58 tff(7,plain,
% 0.39/0.58 (![A__questionmark_v0: |'A$'|, A__questionmark_v1: |'A$'|] : ((tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, A__questionmark_v0), A__questionmark_v1) = A__questionmark_v1) <=> ((A__questionmark_v1 = |'zero$'|) | (A__questionmark_v0 = |'one$'|)))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.39/0.58 tff(8,plain,
% 0.39/0.58 (((~![A__questionmark_v0: |'A$'|, A__questionmark_v1: |'A$'|] : ((tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, A__questionmark_v0), A__questionmark_v1) = A__questionmark_v1) <=> ((A__questionmark_v1 = |'zero$'|) | (A__questionmark_v0 = |'one$'|)))) | (tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|))), |'zero$'|) = |'zero$'|)) <=> ((~![A__questionmark_v0: |'A$'|, A__questionmark_v1: |'A$'|] : ((tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, A__questionmark_v0), A__questionmark_v1) = A__questionmark_v1) <=> ((A__questionmark_v1 = |'zero$'|) | (A__questionmark_v0 = |'one$'|)))) | (tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|))), |'zero$'|) = |'zero$'|))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(9,plain,
% 0.39/0.58 (((tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|))), |'zero$'|) = |'zero$'|) <=> $true) <=> (tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|))), |'zero$'|) = |'zero$'|)),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(10,plain,
% 0.39/0.58 (($true | (tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|)) = |'one$'|)) <=> $true),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(11,plain,
% 0.39/0.58 ((|'zero$'| = |'zero$'|) <=> $true),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(12,plain,
% 0.39/0.58 (((|'zero$'| = |'zero$'|) | (tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|)) = |'one$'|)) <=> ($true | (tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|)) = |'one$'|))),
% 0.39/0.58 inference(monotonicity,[status(thm)],[11])).
% 0.39/0.58 tff(13,plain,
% 0.39/0.58 (((|'zero$'| = |'zero$'|) | (tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|)) = |'one$'|)) <=> $true),
% 0.39/0.58 inference(transitivity,[status(thm)],[12, 10])).
% 0.39/0.58 tff(14,plain,
% 0.39/0.58 (((tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|))), |'zero$'|) = |'zero$'|) <=> ((|'zero$'| = |'zero$'|) | (tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|)) = |'one$'|))) <=> ((tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|))), |'zero$'|) = |'zero$'|) <=> $true)),
% 0.39/0.58 inference(monotonicity,[status(thm)],[13])).
% 0.39/0.58 tff(15,plain,
% 0.39/0.58 (((tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|))), |'zero$'|) = |'zero$'|) <=> ((|'zero$'| = |'zero$'|) | (tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|)) = |'one$'|))) <=> (tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|))), |'zero$'|) = |'zero$'|)),
% 0.39/0.58 inference(transitivity,[status(thm)],[14, 9])).
% 0.39/0.58 tff(16,plain,
% 0.39/0.58 (((~![A__questionmark_v0: |'A$'|, A__questionmark_v1: |'A$'|] : ((tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, A__questionmark_v0), A__questionmark_v1) = A__questionmark_v1) <=> ((A__questionmark_v1 = |'zero$'|) | (A__questionmark_v0 = |'one$'|)))) | ((tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|))), |'zero$'|) = |'zero$'|) <=> ((|'zero$'| = |'zero$'|) | (tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|)) = |'one$'|)))) <=> ((~![A__questionmark_v0: |'A$'|, A__questionmark_v1: |'A$'|] : ((tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, A__questionmark_v0), A__questionmark_v1) = A__questionmark_v1) <=> ((A__questionmark_v1 = |'zero$'|) | (A__questionmark_v0 = |'one$'|)))) | (tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|))), |'zero$'|) = |'zero$'|))),
% 0.39/0.58 inference(monotonicity,[status(thm)],[15])).
% 0.39/0.58 tff(17,plain,
% 0.39/0.58 (((~![A__questionmark_v0: |'A$'|, A__questionmark_v1: |'A$'|] : ((tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, A__questionmark_v0), A__questionmark_v1) = A__questionmark_v1) <=> ((A__questionmark_v1 = |'zero$'|) | (A__questionmark_v0 = |'one$'|)))) | ((tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|))), |'zero$'|) = |'zero$'|) <=> ((|'zero$'| = |'zero$'|) | (tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|)) = |'one$'|)))) <=> ((~![A__questionmark_v0: |'A$'|, A__questionmark_v1: |'A$'|] : ((tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, A__questionmark_v0), A__questionmark_v1) = A__questionmark_v1) <=> ((A__questionmark_v1 = |'zero$'|) | (A__questionmark_v0 = |'one$'|)))) | (tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|))), |'zero$'|) = |'zero$'|))),
% 0.39/0.58 inference(transitivity,[status(thm)],[16, 8])).
% 0.39/0.58 tff(18,plain,
% 0.39/0.58 ((~![A__questionmark_v0: |'A$'|, A__questionmark_v1: |'A$'|] : ((tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, A__questionmark_v0), A__questionmark_v1) = A__questionmark_v1) <=> ((A__questionmark_v1 = |'zero$'|) | (A__questionmark_v0 = |'one$'|)))) | ((tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|))), |'zero$'|) = |'zero$'|) <=> ((|'zero$'| = |'zero$'|) | (tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|)) = |'one$'|)))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(19,plain,
% 0.39/0.58 ((~![A__questionmark_v0: |'A$'|, A__questionmark_v1: |'A$'|] : ((tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, A__questionmark_v0), A__questionmark_v1) = A__questionmark_v1) <=> ((A__questionmark_v1 = |'zero$'|) | (A__questionmark_v0 = |'one$'|)))) | (tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|))), |'zero$'|) = |'zero$'|)),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.39/0.58 tff(20,plain,
% 0.39/0.58 (tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|))), |'zero$'|) = |'zero$'|),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[19, 7])).
% 0.39/0.58 tff(21,plain,
% 0.39/0.58 ((tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'xa$'|), |'i$'|) = |'zero$'|) <=> (tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'xa$'|), |'i$'|) = |'zero$'|)),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(22,axiom,(tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'xa$'|), |'i$'|) = |'zero$'|), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom119')).
% 0.39/0.58 tff(23,plain,
% 0.39/0.58 (tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'xa$'|), |'i$'|) = |'zero$'|),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.39/0.58 tff(24,plain,
% 0.39/0.58 (tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|))), tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'xa$'|), |'i$'|)) = tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|))), |'zero$'|)),
% 0.39/0.58 inference(monotonicity,[status(thm)],[23])).
% 0.39/0.58 tff(25,plain,
% 0.39/0.58 (tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|))), tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'xa$'|), |'i$'|)) = |'zero$'|),
% 0.39/0.58 inference(transitivity,[status(thm)],[24, 20])).
% 0.39/0.58 tff(26,plain,
% 0.39/0.58 ((~(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|))), tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'xa$'|), |'i$'|)) = |'zero$'|)) <=> (~(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|))), tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'xa$'|), |'i$'|)) = |'zero$'|))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(27,axiom,(~(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|))), tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'xa$'|), |'i$'|)) = |'zero$'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conjecture118')).
% 0.39/0.62 tff(28,plain,
% 0.39/0.62 (~(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'times$e'|, tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'x$'|), tptp_fun__the__(|'uu$'|))), tptp_fun__fun_app_d_(tptp_fun__vec_nth_b_(|'xa$'|), |'i$'|)) = |'zero$'|)),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.39/0.62 tff(29,plain,
% 0.39/0.62 ($false),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[28, 25])).
% 0.39/0.62 % SZS output end Proof
% 0.47/0.63 % E exiting
%------------------------------------------------------------------------------