TSTP Solution File: ITP010+2 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : ITP010+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% Computer : n023.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 : Mon Mar 25 14:15:47 EDT 2024
% Result : Theorem 0.46s 0.62s
% Output : Proof 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ITP010+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.10/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Mar 21 01:28:12 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.46/0.62 % SZS status Theorem for theBenchmark
% 0.46/0.62 % SZS output start Proof for theBenchmark
% 0.46/0.62
% 0.46/0.62 % Formula: bool_ne ( axiom ) converted to clauses:
% 0.46/0.62 cnf(bool_ne-1, axiom, ( ne(bool) )).
% 0.46/0.62
% 0.46/0.62 % Formula: ind_ne ( axiom ) converted to clauses:
% 0.46/0.62 cnf(ind_ne-1, axiom, ( ne(ind) )).
% 0.46/0.62
% 0.46/0.62 % Formula: arr_ne ( axiom ) converted to clauses:
% 0.46/0.62 cnf(arr_ne-1, axiom, ( ~ne(_u1) | ~ne(_u0) | ne(arr(_u1, _u0)) )).
% 0.46/0.62
% 0.46/0.62 % Formula: ap_tp ( axiom ) converted to clauses:
% 0.46/0.62 cnf(ap_tp-1, axiom, ( ~mem(_u3, arr(_u5, _u4)) | ~mem(_u2, _u5) | mem(ap(_u3, _u2), _u4) )).
% 0.46/0.62
% 0.46/0.62 % Formula: boolext ( axiom ) converted to clauses:
% 0.46/0.62 cnf(boolext-1, axiom, ( ~mem(_u7, bool) | ~mem(_u6, bool) | ( _u7 = _u6) | p(_u7) | p(_u6) )).
% 0.46/0.62 cnf(boolext-2, axiom, ( ~mem(_u7, bool) | ~mem(_u6, bool) | ( _u7 = _u6) | ~p(_u6) | ~p(_u7) )).
% 0.46/0.62
% 0.46/0.62 % Formula: funcext ( axiom ) converted to clauses:
% 0.46/0.62 cnf(funcext-1, axiom, ( ~mem(_u10, arr(_u12, _u11)) | ~mem(_u9, arr(_u12, _u11)) | ( _u10 = _u9) | mem(skolem1(_u12, _u11, _u10, _u9), _u12) )).
% 0.46/0.62 cnf(funcext-2, axiom, ( ~mem(_u10, arr(_u12, _u11)) | ~mem(_u9, arr(_u12, _u11)) | ( _u10 = _u9) | ( ap(_u10, skolem1(_u12, _u11, _u10, _u9)) != ap(_u9, skolem1(_u12, _u11, _u10, _u9))) )).
% 0.46/0.62
% 0.46/0.62 % Formula: kbeta ( axiom ) converted to clauses:
% 0.46/0.62 cnf(kbeta-1, axiom, ( ~mem(_u13, _u15) | ( ap(k(_u15, _u14), _u13) = _u14) )).
% 0.46/0.62
% 0.46/0.62 % Formula: ibeta ( axiom ) converted to clauses:
% 0.46/0.62 cnf(ibeta-1, axiom, ( ~mem(_u16, _u17) | ( ap(i(_u17), _u16) = _u16) )).
% 0.46/0.62
% 0.46/0.62 % Formula: mem_c_2Ebool_2ET ( axiom ) converted to clauses:
% 0.46/0.62 cnf(mem_c_2Ebool_2ET-1, axiom, ( mem(c_2Ebool_2ET, bool) )).
% 0.46/0.62
% 0.46/0.62 % Formula: ax_true_p ( axiom ) converted to clauses:
% 0.46/0.62 cnf(ax_true_p-1, axiom, ( p(c_2Ebool_2ET) )).
% 0.46/0.62
% 0.46/0.62 % Formula: mem_c_2Ecardinal_2Ecardleq ( axiom ) converted to clauses:
% 0.46/0.62 cnf(mem_c_2Ecardinal_2Ecardleq-1, axiom, ( ~ne(_u19) | ~ne(_u18) | mem(c_2Ecardinal_2Ecardleq(_u19, _u18), arr(arr(_u19, bool), arr(arr(_u18, bool), bool))) )).
% 0.46/0.62
% 0.46/0.62 % Formula: mem_c_2Ebool_2EF ( axiom ) converted to clauses:
% 0.46/0.62 cnf(mem_c_2Ebool_2EF-1, axiom, ( mem(c_2Ebool_2EF, bool) )).
% 0.46/0.62
% 0.46/0.62 % Formula: ax_false_p ( axiom ) converted to clauses:
% 0.46/0.62 cnf(ax_false_p-1, axiom, ( ~p(c_2Ebool_2EF) )).
% 0.46/0.62
% 0.46/0.62 % Formula: mem_c_2Emin_2E_3D_3D_3E ( axiom ) converted to clauses:
% 0.46/0.62 cnf(mem_c_2Emin_2E_3D_3D_3E-1, axiom, ( mem(c_2Emin_2E_3D_3D_3E, arr(bool, arr(bool, bool))) )).
% 0.46/0.62
% 0.46/0.62 % Formula: ax_imp_p ( axiom ) converted to clauses:
% 0.46/0.62 cnf(ax_imp_p-1, axiom, ( ~mem(_u21, bool) | ~mem(_u20, bool) | ~p(ap(ap(c_2Emin_2E_3D_3D_3E, _u21), _u20)) | ~p(_u21) | p(_u20) )).
% 0.46/0.62 cnf(ax_imp_p-2, axiom, ( ~mem(_u21, bool) | ~mem(_u20, bool) | p(ap(ap(c_2Emin_2E_3D_3D_3E, _u21), _u20)) | p(_u21) )).
% 0.46/0.62 cnf(ax_imp_p-3, axiom, ( ~mem(_u21, bool) | ~mem(_u20, bool) | p(ap(ap(c_2Emin_2E_3D_3D_3E, _u21), _u20)) | ~p(_u20) )).
% 0.46/0.62
% 0.46/0.62 % Formula: mem_c_2Ebool_2E_5C_2F ( axiom ) converted to clauses:
% 0.46/0.62 cnf(mem_c_2Ebool_2E_5C_2F-1, axiom, ( mem(c_2Ebool_2E_5C_2F, arr(bool, arr(bool, bool))) )).
% 0.46/0.62
% 0.46/0.62 % Formula: ax_or_p ( axiom ) converted to clauses:
% 0.46/0.62 cnf(ax_or_p-1, axiom, ( ~mem(_u23, bool) | ~mem(_u22, bool) | ~p(ap(ap(c_2Ebool_2E_5C_2F, _u23), _u22)) | p(_u23) | p(_u22) )).
% 0.46/0.62 cnf(ax_or_p-2, axiom, ( ~mem(_u23, bool) | ~mem(_u22, bool) | p(ap(ap(c_2Ebool_2E_5C_2F, _u23), _u22)) | ~p(_u23) )).
% 0.46/0.62 cnf(ax_or_p-3, axiom, ( ~mem(_u23, bool) | ~mem(_u22, bool) | p(ap(ap(c_2Ebool_2E_5C_2F, _u23), _u22)) | ~p(_u22) )).
% 0.46/0.62
% 0.46/0.62 % Formula: mem_c_2Ebool_2E_2F_5C ( axiom ) converted to clauses:
% 0.46/0.62 cnf(mem_c_2Ebool_2E_2F_5C-1, axiom, ( mem(c_2Ebool_2E_2F_5C, arr(bool, arr(bool, bool))) )).
% 0.46/0.62
% 0.46/0.62 % Formula: ax_and_p ( axiom ) converted to clauses:
% 0.46/0.62 cnf(ax_and_p-1, axiom, ( ~mem(_u25, bool) | ~mem(_u24, bool) | ~p(ap(ap(c_2Ebool_2E_2F_5C, _u25), _u24)) | p(_u25) )).
% 0.46/0.62 cnf(ax_and_p-2, axiom, ( ~mem(_u25, bool) | ~mem(_u24, bool) | ~p(ap(ap(c_2Ebool_2E_2F_5C, _u25), _u24)) | p(_u24) )).
% 0.46/0.62 cnf(ax_and_p-3, axiom, ( ~mem(_u25, bool) | ~mem(_u24, bool) | ~p(_u25) | ~p(_u24) | p(ap(ap(c_2Ebool_2E_2F_5C, _u25), _u24)) )).
% 0.46/0.62
% 0.46/0.62 % Formula: mem_c_2Ebool_2E_7E ( axiom ) converted to clauses:
% 0.46/0.62 cnf(mem_c_2Ebool_2E_7E-1, axiom, ( mem(c_2Ebool_2E_7E, arr(bool, bool)) )).
% 0.46/0.62
% 0.46/0.62 % Formula: ax_neg_p ( axiom ) converted to clauses:
% 0.46/0.62 cnf(ax_neg_p-1, axiom, ( ~mem(_u26, bool) | ~p(ap(c_2Ebool_2E_7E, _u26)) | ~p(_u26) )).
% 0.46/0.62 cnf(ax_neg_p-2, axiom, ( ~mem(_u26, bool) | p(_u26) | p(ap(c_2Ebool_2E_7E, _u26)) )).
% 0.46/0.62
% 0.46/0.62 % Formula: mem_c_2Emin_2E_3D ( axiom ) converted to clauses:
% 0.46/0.62 cnf(mem_c_2Emin_2E_3D-1, axiom, ( ~ne(_u27) | mem(c_2Emin_2E_3D(_u27), arr(_u27, arr(_u27, bool))) )).
% 0.46/0.62
% 0.46/0.62 % Formula: ax_eq_p ( axiom ) converted to clauses:
% 0.46/0.62 cnf(ax_eq_p-1, axiom, ( ~ne(_u30) | ~mem(_u29, _u30) | ~mem(_u28, _u30) | ~p(ap(ap(c_2Emin_2E_3D(_u30), _u29), _u28)) | ( _u29 = _u28) )).
% 0.46/0.62 cnf(ax_eq_p-2, axiom, ( ~ne(_u30) | ~mem(_u29, _u30) | ~mem(_u28, _u30) | ( _u29 != _u28) | p(ap(ap(c_2Emin_2E_3D(_u30), _u29), _u28)) )).
% 0.46/0.62
% 0.46/0.62 % Formula: mem_c_2Ebool_2E_21 ( axiom ) converted to clauses:
% 0.46/0.62 cnf(mem_c_2Ebool_2E_21-1, axiom, ( ~ne(_u31) | mem(c_2Ebool_2E_21(_u31), arr(arr(_u31, bool), bool)) )).
% 0.46/0.62
% 0.46/0.62 % Formula: ax_all_p ( axiom ) converted to clauses:
% 0.46/0.62 cnf(ax_all_p-1, axiom, ( ~ne(_u35) | ~mem(_u34, arr(_u35, bool)) | ~p(ap(c_2Ebool_2E_21(_u35), _u34)) | ~mem(_u32, _u35) | p(ap(_u34, _u32)) )).
% 0.46/0.62 cnf(ax_all_p-2, axiom, ( ~ne(_u35) | ~mem(_u34, arr(_u35, bool)) | p(ap(c_2Ebool_2E_21(_u35), _u34)) | mem(skolem2(_u35, _u34), _u35) )).
% 0.46/0.62 cnf(ax_all_p-3, axiom, ( ~ne(_u35) | ~mem(_u34, arr(_u35, bool)) | p(ap(c_2Ebool_2E_21(_u35), _u34)) | ~p(ap(_u34, skolem2(_u35, _u34))) )).
% 0.46/0.62
% 0.46/0.62 % Formula: conj_thm_2Ebool_2ETRUTH ( axiom ) converted to clauses:
% 0.46/0.62 cnf(conj_thm_2Ebool_2ETRUTH, axiom, $true).
% 0.46/0.62
% 0.46/0.62 % Formula: conj_thm_2Ebool_2EFALSITY ( axiom ) converted to clauses:
% 0.46/0.62 cnf(conj_thm_2Ebool_2EFALSITY, axiom, $true).
% 0.46/0.62
% 0.46/0.62 % Formula: conj_thm_2Ebool_2EFORALL__SIMP ( axiom ) converted to clauses:
% 0.46/0.62 cnf(conj_thm_2Ebool_2EFORALL__SIMP-1, axiom, ( ~ne(_u40) | ~mem(_u39, bool) | p(_u39) | mem(skolem3(_u40, _u39), _u40) )).
% 0.46/0.62
% 0.46/0.62 % Formula: conj_thm_2Ebool_2EIMP__CLAUSES ( axiom ) converted to clauses:
% 0.46/0.62 cnf(conj_thm_2Ebool_2EIMP__CLAUSES, axiom, $true).
% 0.46/0.62
% 0.46/0.62 % Formula: conj_thm_2Ebool_2ENOT__CLAUSES ( axiom ) converted to clauses:
% 0.46/0.62 cnf(conj_thm_2Ebool_2ENOT__CLAUSES, axiom, $true).
% 0.46/0.62
% 0.46/0.62 % Formula: conj_thm_2Ebool_2EREFL__CLAUSE ( axiom ) converted to clauses:
% 0.46/0.62 cnf(conj_thm_2Ebool_2EREFL__CLAUSE-1, axiom, ( ~ne(_u44) | ~mem(_u43, _u44) | ( _u43 = _u43) )).
% 0.46/0.62
% 0.46/0.62 % Formula: conj_thm_2Ebool_2EEQ__CLAUSES ( axiom ) converted to clauses:
% 0.46/0.62 cnf(conj_thm_2Ebool_2EEQ__CLAUSES, axiom, $true).
% 0.46/0.62
% 0.46/0.62 % Formula: conj_thm_2Ecardinal_2ECARD__LE__TOTAL ( axiom ) converted to clauses:
% 0.46/0.62 cnf(conj_thm_2Ecardinal_2ECARD__LE__TOTAL-1, axiom, ( ~ne(_u49) | ~ne(_u48) | ~mem(_u47, arr(_u49, bool)) | ~mem(_u46, arr(_u48, bool)) | p(ap(ap(c_2Ecardinal_2Ecardleq(_u49, _u48), _u47), _u46)) | p(ap(ap(c_2Ecardinal_2Ecardleq(_u48, _u49), _u46), _u47)) )).
% 0.46/0.62
% 0.46/0.62 % Formula: conj_thm_2Esat_2ENOT__NOT ( axiom ) converted to clauses:
% 0.46/0.62 cnf(conj_thm_2Esat_2ENOT__NOT, axiom, $true).
% 0.46/0.62
% 0.46/0.62 % Formula: conj_thm_2Esat_2EAND__INV__IMP ( axiom ) converted to clauses:
% 0.46/0.62 cnf(conj_thm_2Esat_2EAND__INV__IMP, axiom, $true).
% 0.46/0.62
% 0.46/0.62 % Formula: conj_thm_2Esat_2EOR__DUAL2 ( axiom ) converted to clauses:
% 0.46/0.62 cnf(conj_thm_2Esat_2EOR__DUAL2, axiom, $true).
% 0.46/0.62
% 0.46/0.62 % Formula: conj_thm_2Esat_2EOR__DUAL3 ( axiom ) converted to clauses:
% 0.46/0.62 cnf(conj_thm_2Esat_2EOR__DUAL3, axiom, $true).
% 0.46/0.62
% 0.46/0.62 % Formula: conj_thm_2Esat_2EAND__INV2 ( axiom ) converted to clauses:
% 0.46/0.62 cnf(conj_thm_2Esat_2EAND__INV2, axiom, $true).
% 0.46/0.62
% 0.46/0.62 % Formula: conj_thm_2Esat_2Edc__eq ( axiom ) converted to clauses:
% 0.46/0.62 cnf(conj_thm_2Esat_2Edc__eq, axiom, $true).
% 0.46/0.62
% 0.46/0.62 % Formula: conj_thm_2Esat_2Edc__neg ( axiom ) converted to clauses:
% 0.46/0.62 cnf(conj_thm_2Esat_2Edc__neg, axiom, $true).
% 0.46/0.62
% 0.46/0.62 % Formula: conj_thm_2Ecardinal_2ECARD__NOT__LE ( conjecture ) (definitionally) converted to clauses:
% 0.46/0.62 cnf(conj_thm_2Ecardinal_2ECARD__NOT__LE-1, negated_conjecture, ( ne(skolem4) )).
% 0.46/0.62 cnf(conj_thm_2Ecardinal_2ECARD__NOT__LE-2, negated_conjecture, ( ne(skolem5) )).
% 0.46/0.62 cnf(conj_thm_2Ecardinal_2ECARD__NOT__LE-3, negated_conjecture, ( mem(skolem6, arr(skolem4, bool)) )).
% 0.46/0.62 cnf(conj_thm_2Ecardinal_2ECARD__NOT__LE-4, negated_conjecture, ( mem(skolem7, arr(skolem5, bool)) )).
% 0.46/0.62 cnf(conj_thm_2Ecardinal_2ECARD__NOT__LE-5, negated_conjecture, ( ~_def0 | ~_def1 )).
% 0.46/0.62 cnf(conj_thm_2Ecardinal_2ECARD__NOT__LE-6, negated_conjecture, ( _def0 | ~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem4, skolem5), skolem6), skolem7)) )).
% 0.46/0.62 cnf(conj_thm_2Ecardinal_2ECARD__NOT__LE-7, negated_conjecture, ( _def0 | p(ap(ap(c_2Ecardinal_2Ecardleq(skolem4, skolem5), skolem6), skolem7)) )).
% 0.46/0.63 cnf(conj_thm_2Ecardinal_2ECARD__NOT__LE-8, negated_conjecture, ( _def1 | ~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem4, skolem5), skolem6), skolem7)) )).
% 0.46/0.63 cnf(conj_thm_2Ecardinal_2ECARD__NOT__LE-9, negated_conjecture, ( _def1 | p(ap(ap(c_2Ecardinal_2Ecardleq(skolem4, skolem5), skolem6), skolem7)) )).
% 0.46/0.63
% 0.46/0.63 % Problem matrix:
% 0.46/0.63 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 0.46/0.63 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 0.46/0.63 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 0.46/0.63 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( arr(__eqx_0, __eqx_1) = arr(__eqy_0, __eqy_1)) )).
% 0.46/0.63 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( ap(__eqx_0, __eqx_1) = ap(__eqy_0, __eqy_1)) )).
% 0.46/0.63 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( k(__eqx_0, __eqx_1) = k(__eqy_0, __eqy_1)) )).
% 0.46/0.63 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( i(__eqx_0) = i(__eqy_0)) )).
% 0.46/0.63 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( c_2Ecardinal_2Ecardleq(__eqx_0, __eqx_1) = c_2Ecardinal_2Ecardleq(__eqy_0, __eqy_1)) )).
% 0.46/0.63 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( c_2Emin_2E_3D(__eqx_0) = c_2Emin_2E_3D(__eqy_0)) )).
% 0.46/0.63 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( c_2Ebool_2E_21(__eqx_0) = c_2Ebool_2E_21(__eqy_0)) )).
% 0.46/0.63 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( skolem1(__eqx_0, __eqx_1, __eqx_2, __eqx_3) = skolem1(__eqy_0, __eqy_1, __eqy_2, __eqy_3)) )).
% 0.46/0.63 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem2(__eqx_0, __eqx_1) = skolem2(__eqy_0, __eqy_1)) )).
% 0.46/0.63 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem3(__eqx_0, __eqx_1) = skolem3(__eqy_0, __eqy_1)) )).
% 0.46/0.63 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ~ne(__eqx_0) | ne(__eqy_0) )).
% 0.46/0.63 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~mem(__eqx_0, __eqx_1) | mem(__eqy_0, __eqy_1) )).
% 0.46/0.63 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ~p(__eqx_0) | p(__eqy_0) )).
% 0.46/0.63 cnf(matrix-16, plain, ( ne(bool) )).
% 0.46/0.63 cnf(matrix-17, plain, ( ne(ind) )).
% 0.46/0.63 cnf(matrix-18, plain, ( ~ne(_u1) | ~ne(_u0) | ne(arr(_u1, _u0)) )).
% 0.46/0.63 cnf(matrix-19, plain, ( ~mem(_u3, arr(_u5, _u4)) | ~mem(_u2, _u5) | mem(ap(_u3, _u2), _u4) )).
% 0.46/0.63 cnf(matrix-20, plain, ( ~mem(_u7, bool) | ~mem(_u6, bool) | ( _u7 = _u6) | p(_u7) | p(_u6) )).
% 0.46/0.63 cnf(matrix-21, plain, ( ~mem(_u7, bool) | ~mem(_u6, bool) | ( _u7 = _u6) | ~p(_u6) | ~p(_u7) )).
% 0.46/0.63 cnf(matrix-22, plain, ( ~mem(_u10, arr(_u12, _u11)) | ~mem(_u9, arr(_u12, _u11)) | ( _u10 = _u9) | mem(skolem1(_u12, _u11, _u10, _u9), _u12) )).
% 0.46/0.63 cnf(matrix-23, plain, ( ~mem(_u10, arr(_u12, _u11)) | ~mem(_u9, arr(_u12, _u11)) | ( _u10 = _u9) | ( ap(_u10, skolem1(_u12, _u11, _u10, _u9)) != ap(_u9, skolem1(_u12, _u11, _u10, _u9))) )).
% 0.46/0.63 cnf(matrix-24, plain, ( ~mem(_u13, _u15) | ( ap(k(_u15, _u14), _u13) = _u14) )).
% 0.46/0.63 cnf(matrix-25, plain, ( ~mem(_u16, _u17) | ( ap(i(_u17), _u16) = _u16) )).
% 0.46/0.63 cnf(matrix-26, plain, ( mem(c_2Ebool_2ET, bool) )).
% 0.46/0.63 cnf(matrix-27, plain, ( p(c_2Ebool_2ET) )).
% 0.46/0.63 cnf(matrix-28, plain, ( ~ne(_u19) | ~ne(_u18) | mem(c_2Ecardinal_2Ecardleq(_u19, _u18), arr(arr(_u19, bool), arr(arr(_u18, bool), bool))) )).
% 0.46/0.63 cnf(matrix-29, plain, ( mem(c_2Ebool_2EF, bool) )).
% 0.46/0.63 cnf(matrix-30, plain, ( ~p(c_2Ebool_2EF) )).
% 0.46/0.63 cnf(matrix-31, plain, ( mem(c_2Emin_2E_3D_3D_3E, arr(bool, arr(bool, bool))) )).
% 0.46/0.63 cnf(matrix-32, plain, ( ~mem(_u21, bool) | ~mem(_u20, bool) | ~p(ap(ap(c_2Emin_2E_3D_3D_3E, _u21), _u20)) | ~p(_u21) | p(_u20) )).
% 0.46/0.63 cnf(matrix-33, plain, ( ~mem(_u21, bool) | ~mem(_u20, bool) | p(ap(ap(c_2Emin_2E_3D_3D_3E, _u21), _u20)) | p(_u21) )).
% 0.46/0.63 cnf(matrix-34, plain, ( ~mem(_u21, bool) | ~mem(_u20, bool) | p(ap(ap(c_2Emin_2E_3D_3D_3E, _u21), _u20)) | ~p(_u20) )).
% 0.46/0.63 cnf(matrix-35, plain, ( mem(c_2Ebool_2E_5C_2F, arr(bool, arr(bool, bool))) )).
% 0.46/0.63 cnf(matrix-36, plain, ( ~mem(_u23, bool) | ~mem(_u22, bool) | ~p(ap(ap(c_2Ebool_2E_5C_2F, _u23), _u22)) | p(_u23) | p(_u22) )).
% 0.46/0.63 cnf(matrix-37, plain, ( ~mem(_u23, bool) | ~mem(_u22, bool) | p(ap(ap(c_2Ebool_2E_5C_2F, _u23), _u22)) | ~p(_u23) )).
% 0.46/0.63 cnf(matrix-38, plain, ( ~mem(_u23, bool) | ~mem(_u22, bool) | p(ap(ap(c_2Ebool_2E_5C_2F, _u23), _u22)) | ~p(_u22) )).
% 0.46/0.63 cnf(matrix-39, plain, ( mem(c_2Ebool_2E_2F_5C, arr(bool, arr(bool, bool))) )).
% 0.46/0.63 cnf(matrix-40, plain, ( ~mem(_u25, bool) | ~mem(_u24, bool) | ~p(ap(ap(c_2Ebool_2E_2F_5C, _u25), _u24)) | p(_u25) )).
% 0.46/0.63 cnf(matrix-41, plain, ( ~mem(_u25, bool) | ~mem(_u24, bool) | ~p(ap(ap(c_2Ebool_2E_2F_5C, _u25), _u24)) | p(_u24) )).
% 0.46/0.63 cnf(matrix-42, plain, ( ~mem(_u25, bool) | ~mem(_u24, bool) | ~p(_u25) | ~p(_u24) | p(ap(ap(c_2Ebool_2E_2F_5C, _u25), _u24)) )).
% 0.46/0.63 cnf(matrix-43, plain, ( mem(c_2Ebool_2E_7E, arr(bool, bool)) )).
% 0.46/0.63 cnf(matrix-44, plain, ( ~mem(_u26, bool) | ~p(ap(c_2Ebool_2E_7E, _u26)) | ~p(_u26) )).
% 0.46/0.63 cnf(matrix-45, plain, ( ~mem(_u26, bool) | p(_u26) | p(ap(c_2Ebool_2E_7E, _u26)) )).
% 0.46/0.63 cnf(matrix-46, plain, ( ~ne(_u27) | mem(c_2Emin_2E_3D(_u27), arr(_u27, arr(_u27, bool))) )).
% 0.46/0.63 cnf(matrix-47, plain, ( ~ne(_u30) | ~mem(_u29, _u30) | ~mem(_u28, _u30) | ~p(ap(ap(c_2Emin_2E_3D(_u30), _u29), _u28)) | ( _u29 = _u28) )).
% 0.46/0.63 cnf(matrix-48, plain, ( ~ne(_u30) | ~mem(_u29, _u30) | ~mem(_u28, _u30) | ( _u29 != _u28) | p(ap(ap(c_2Emin_2E_3D(_u30), _u29), _u28)) )).
% 0.46/0.63 cnf(matrix-49, plain, ( ~ne(_u31) | mem(c_2Ebool_2E_21(_u31), arr(arr(_u31, bool), bool)) )).
% 0.46/0.63 cnf(matrix-50, plain, ( ~ne(_u35) | ~mem(_u34, arr(_u35, bool)) | ~p(ap(c_2Ebool_2E_21(_u35), _u34)) | ~mem(_u32, _u35) | p(ap(_u34, _u32)) )).
% 0.46/0.63 cnf(matrix-51, plain, ( ~ne(_u35) | ~mem(_u34, arr(_u35, bool)) | p(ap(c_2Ebool_2E_21(_u35), _u34)) | mem(skolem2(_u35, _u34), _u35) )).
% 0.46/0.63 cnf(matrix-52, plain, ( ~ne(_u35) | ~mem(_u34, arr(_u35, bool)) | p(ap(c_2Ebool_2E_21(_u35), _u34)) | ~p(ap(_u34, skolem2(_u35, _u34))) )).
% 0.46/0.63 cnf(matrix-53, plain, ( ~ne(_u40) | ~mem(_u39, bool) | p(_u39) | mem(skolem3(_u40, _u39), _u40) )).
% 0.46/0.63 cnf(matrix-54, plain, ( ~ne(_u44) | ~mem(_u43, _u44) | ( _u43 = _u43) )).
% 0.46/0.63 cnf(matrix-55, plain, ( ~ne(_u49) | ~ne(_u48) | ~mem(_u47, arr(_u49, bool)) | ~mem(_u46, arr(_u48, bool)) | p(ap(ap(c_2Ecardinal_2Ecardleq(_u49, _u48), _u47), _u46)) | p(ap(ap(c_2Ecardinal_2Ecardleq(_u48, _u49), _u46), _u47)) )).
% 0.46/0.63 cnf(matrix-56, plain, ( ne(skolem4) )).
% 0.46/0.63 cnf(matrix-57, plain, ( ne(skolem5) )).
% 0.46/0.63 cnf(matrix-58, plain, ( mem(skolem6, arr(skolem4, bool)) )).
% 0.46/0.63 cnf(matrix-59, plain, ( mem(skolem7, arr(skolem5, bool)) )).
% 0.46/0.63 cnf(matrix-60, plain, ( ~_def0 | ~_def1 )).
% 0.46/0.63 cnf(matrix-61, plain, ( _def0 | ~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem4, skolem5), skolem6), skolem7)) )).
% 0.46/0.63 cnf(matrix-62, plain, ( _def0 | p(ap(ap(c_2Ecardinal_2Ecardleq(skolem4, skolem5), skolem6), skolem7)) )).
% 0.46/0.63 cnf(matrix-63, plain, ( _def1 | ~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem4, skolem5), skolem6), skolem7)) )).
% 0.46/0.63 cnf(matrix-64, plain, ( _def1 | p(ap(ap(c_2Ecardinal_2Ecardleq(skolem4, skolem5), skolem6), skolem7)) )).
% 0.46/0.63
% 0.46/0.63 % Proof stack:
% 0.46/0.63 cnf(proof-stack, plain,
% 0.46/0.63 proof_stack(
% 0.46/0.63 start(60),
% 0.46/0.63 left_branch(0, 62, 0, 2),
% 0.46/0.63 left_branch(0, 61, 1, 3),
% 0.46/0.63 reduction(0, 0),
% 0.46/0.63 right_branch(3),
% 0.46/0.63 right_branch(2),
% 0.46/0.63 left_branch(0, 64, 0, 3),
% 0.46/0.63 left_branch(0, 63, 1, 4),
% 0.46/0.63 reduction(0, 0),
% 0.46/0.63 right_branch(4),
% 0.46/0.63 right_branch(3)
% 0.46/0.63 )).
% 0.46/0.63 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------