TSTP Solution File: HAL003+3 by ConnectPP---0.2.2
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%------------------------------------------------------------------------------
% File : ConnectPP---0.2.2
% Problem : HAL003+3 : TPTP v8.1.2. Released v2.6.0.
% 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 : Wed Mar 6 09:05:09 EST 2024
% Result : Theorem 9.31s 9.47s
% Output : Proof 9.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : HAL003+3 : TPTP v8.1.2. Released v2.6.0.
% 0.06/0.12 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Mar 4 03:25:35 EST 2024
% 0.12/0.33 % CPUTime :
% 9.31/9.47 % SZS status Theorem for theBenchmark
% 9.31/9.47 % SZS output start Proof for theBenchmark
% 9.31/9.47
% 9.31/9.47 % Formula: morphism ( axiom ) converted to clauses:
% 9.31/9.47 cnf(morphism-1, axiom, ( ~morphism(_u3, _u2, _u1) | ~element(_u0, _u2) | element(apply(_u3, _u0), _u1) )).
% 9.31/9.47 cnf(morphism-2, axiom, ( ~morphism(_u3, _u2, _u1) | ( apply(_u3, zero(_u2)) = zero(_u1)) )).
% 9.31/9.47
% 9.31/9.47 % Formula: injection_properties ( axiom ) converted to clauses:
% 9.31/9.47 cnf(injection_properties-1, axiom, ( ~element(_u5, _u7) | ~element(_u4, _u7) | ( apply(_u8, _u5) != apply(_u8, _u4)) | ( _u5 = _u4) | ~injection(_u8) | ~morphism(_u8, _u7, _u6) )).
% 9.31/9.47
% 9.31/9.47 % Formula: properties_for_injection ( axiom ) converted to clauses:
% 9.31/9.47 cnf(properties_for_injection-1, axiom, ( injection(_u13) | ~morphism(_u13, _u12, _u11) | element(skolem1(_u13, _u12), _u12) )).
% 9.31/9.47 cnf(properties_for_injection-2, axiom, ( injection(_u13) | ~morphism(_u13, _u12, _u11) | element(skolem2(_u13, _u12), _u12) )).
% 9.31/9.47 cnf(properties_for_injection-3, axiom, ( injection(_u13) | ~morphism(_u13, _u12, _u11) | ( apply(_u13, skolem1(_u13, _u12)) = apply(_u13, skolem2(_u13, _u12))) )).
% 9.31/9.47 cnf(properties_for_injection-4, axiom, ( injection(_u13) | ~morphism(_u13, _u12, _u11) | ( skolem1(_u13, _u12) != skolem2(_u13, _u12)) )).
% 9.31/9.47
% 9.31/9.47 % Formula: surjection_properties ( axiom ) converted to clauses:
% 9.31/9.47 cnf(surjection_properties-1, axiom, ( ~surjection(_u18) | ~morphism(_u18, _u17, _u16) | ~element(_u15, _u16) | element(skolem3(_u18, _u17, _u16, _u15), _u17) )).
% 9.31/9.47 cnf(surjection_properties-2, axiom, ( ~surjection(_u18) | ~morphism(_u18, _u17, _u16) | ~element(_u15, _u16) | ( apply(_u18, skolem3(_u18, _u17, _u16, _u15)) = _u15) )).
% 9.31/9.47
% 9.31/9.47 % Formula: properties_for_surjection ( axiom ) converted to clauses:
% 9.31/9.47 cnf(properties_for_surjection-1, axiom, ( surjection(_u23) | ~morphism(_u23, _u22, _u21) | element(skolem4(_u23, _u22, _u21), _u21) )).
% 9.31/9.47 cnf(properties_for_surjection-2, axiom, ( surjection(_u23) | ~morphism(_u23, _u22, _u21) | ~element(_u19, _u22) | ( apply(_u23, _u19) != skolem4(_u23, _u22, _u21)) )).
% 9.31/9.47
% 9.31/9.47 % Formula: exact_properties ( axiom ) converted to clauses:
% 9.31/9.47 cnf(exact_properties-1, axiom, ( ~exact(_u31, _u30) | ~morphism(_u31, _u29, _u28) | ~morphism(_u30, _u28, _u27) | ~element(_u32, _u28) | ( apply(_u30, _u32) != zero(_u27)) | element(skolem5(_u31, _u30, _u29, _u28, _u27, _u32), _u29) )).
% 9.31/9.47 cnf(exact_properties-2, axiom, ( ~exact(_u31, _u30) | ~morphism(_u31, _u29, _u28) | ~morphism(_u30, _u28, _u27) | ~element(_u32, _u28) | ( apply(_u30, _u32) != zero(_u27)) | ( apply(_u31, skolem5(_u31, _u30, _u29, _u28, _u27, _u32)) = _u32) )).
% 9.31/9.47 cnf(exact_properties-3, axiom, ( ~exact(_u31, _u30) | ~morphism(_u31, _u29, _u28) | ~morphism(_u30, _u28, _u27) | ~element(_u25, _u29) | ( apply(_u31, _u25) != _u33) | element(_u33, _u28) )).
% 9.31/9.47 cnf(exact_properties-4, axiom, ( ~exact(_u31, _u30) | ~morphism(_u31, _u29, _u28) | ~morphism(_u30, _u28, _u27) | ~element(_u25, _u29) | ( apply(_u31, _u25) != _u33) | ( apply(_u30, _u33) = zero(_u27)) )).
% 9.31/9.47
% 9.31/9.47 % Formula: properties_for_exact ( axiom ) converted to clauses:
% 9.31/9.47 cnf(properties_for_exact-1, axiom, ( exact(_u41, _u40) | ~morphism(_u41, _u39, _u38) | ~morphism(_u40, _u38, _u37) | element(skolem6(_u41, _u40, _u39, _u38, _u37), _u38) | element(skolem8(_u41, _u40, _u39, _u38, _u37), _u39) )).
% 9.31/9.47 cnf(properties_for_exact-2, axiom, ( exact(_u41, _u40) | ~morphism(_u41, _u39, _u38) | ~morphism(_u40, _u38, _u37) | element(skolem6(_u41, _u40, _u39, _u38, _u37), _u38) | ( apply(_u41, skolem8(_u41, _u40, _u39, _u38, _u37)) = skolem7(_u41, _u40, _u39, _u38, _u37)) )).
% 9.31/9.47 cnf(properties_for_exact-3, axiom, ( exact(_u41, _u40) | ~morphism(_u41, _u39, _u38) | ~morphism(_u40, _u38, _u37) | ( apply(_u40, skolem6(_u41, _u40, _u39, _u38, _u37)) = zero(_u37)) | element(skolem8(_u41, _u40, _u39, _u38, _u37), _u39) )).
% 9.31/9.47 cnf(properties_for_exact-4, axiom, ( exact(_u41, _u40) | ~morphism(_u41, _u39, _u38) | ~morphism(_u40, _u38, _u37) | ( apply(_u40, skolem6(_u41, _u40, _u39, _u38, _u37)) = zero(_u37)) | ( apply(_u41, skolem8(_u41, _u40, _u39, _u38, _u37)) = skolem7(_u41, _u40, _u39, _u38, _u37)) )).
% 9.31/9.47 cnf(properties_for_exact-5, axiom, ( exact(_u41, _u40) | ~morphism(_u41, _u39, _u38) | ~morphism(_u40, _u38, _u37) | ~element(skolem7(_u41, _u40, _u39, _u38, _u37), _u38) | ( apply(_u40, skolem7(_u41, _u40, _u39, _u38, _u37)) != zero(_u37)) | element(skolem6(_u41, _u40, _u39, _u38, _u37), _u38) )).
% 9.31/9.47 cnf(properties_for_exact-6, axiom, ( exact(_u41, _u40) | ~morphism(_u41, _u39, _u38) | ~morphism(_u40, _u38, _u37) | ~element(skolem7(_u41, _u40, _u39, _u38, _u37), _u38) | ( apply(_u40, skolem7(_u41, _u40, _u39, _u38, _u37)) != zero(_u37)) | ( apply(_u40, skolem6(_u41, _u40, _u39, _u38, _u37)) = zero(_u37)) )).
% 9.31/9.47 cnf(properties_for_exact-7, axiom, ( exact(_u41, _u40) | ~morphism(_u41, _u39, _u38) | ~morphism(_u40, _u38, _u37) | ~element(_u34, _u39) | ( apply(_u41, _u34) != skolem6(_u41, _u40, _u39, _u38, _u37)) | element(skolem8(_u41, _u40, _u39, _u38, _u37), _u39) )).
% 9.31/9.47 cnf(properties_for_exact-8, axiom, ( exact(_u41, _u40) | ~morphism(_u41, _u39, _u38) | ~morphism(_u40, _u38, _u37) | ~element(_u34, _u39) | ( apply(_u41, _u34) != skolem6(_u41, _u40, _u39, _u38, _u37)) | ( apply(_u41, skolem8(_u41, _u40, _u39, _u38, _u37)) = skolem7(_u41, _u40, _u39, _u38, _u37)) )).
% 9.31/9.47 cnf(properties_for_exact-9, axiom, ( exact(_u41, _u40) | ~morphism(_u41, _u39, _u38) | ~morphism(_u40, _u38, _u37) | ~element(_u34, _u39) | ( apply(_u41, _u34) != skolem6(_u41, _u40, _u39, _u38, _u37)) | ~element(skolem7(_u41, _u40, _u39, _u38, _u37), _u38) | ( apply(_u40, skolem7(_u41, _u40, _u39, _u38, _u37)) != zero(_u37)) )).
% 9.31/9.47
% 9.31/9.47 % Formula: commute_properties ( axiom ) converted to clauses:
% 9.31/9.47 cnf(commute_properties-1, axiom, ( ~element(_u44, _u48) | ( apply(_u51, apply(_u52, _u44)) = apply(_u49, apply(_u50, _u44))) | ~commute(_u52, _u51, _u50, _u49) | ~morphism(_u52, _u48, _u47) | ~morphism(_u50, _u48, _u46) | ~morphism(_u51, _u47, _u45) | ~morphism(_u49, _u46, _u45) )).
% 9.31/9.47
% 9.31/9.47 % Formula: properties_for_commute ( axiom ) converted to clauses:
% 9.31/9.47 cnf(properties_for_commute-1, axiom, ( commute(_u61, _u60, _u59, _u58) | ~morphism(_u61, _u57, _u56) | ~morphism(_u59, _u57, _u55) | ~morphism(_u60, _u56, _u54) | ~morphism(_u58, _u55, _u54) | element(skolem9(_u61, _u60, _u59, _u58, _u57), _u57) )).
% 9.31/9.47 cnf(properties_for_commute-2, axiom, ( commute(_u61, _u60, _u59, _u58) | ~morphism(_u61, _u57, _u56) | ~morphism(_u59, _u57, _u55) | ~morphism(_u60, _u56, _u54) | ~morphism(_u58, _u55, _u54) | ( apply(_u60, apply(_u61, skolem9(_u61, _u60, _u59, _u58, _u57))) != apply(_u58, apply(_u59, skolem9(_u61, _u60, _u59, _u58, _u57)))) )).
% 9.31/9.47
% 9.31/9.47 % Formula: subtract_in_domain ( axiom ) converted to clauses:
% 9.31/9.47 cnf(subtract_in_domain-1, axiom, ( ~element(_u63, _u64) | ~element(_u62, _u64) | element(subtract(_u64, _u63, _u62), _u64) )).
% 9.31/9.47
% 9.31/9.47 % Formula: subtract_to_0 ( axiom ) converted to clauses:
% 9.31/9.47 cnf(subtract_to_0-1, axiom, ( ~element(_u65, _u66) | ( subtract(_u66, _u65, _u65) = zero(_u66)) )).
% 9.31/9.47
% 9.31/9.47 % Formula: subtract_cancellation ( axiom ) converted to clauses:
% 9.31/9.47 cnf(subtract_cancellation-1, axiom, ( ~element(_u68, _u69) | ~element(_u67, _u69) | ( subtract(_u69, _u68, subtract(_u69, _u68, _u67)) = _u67) )).
% 9.31/9.47
% 9.31/9.47 % Formula: subtract_distribution ( axiom ) converted to clauses:
% 9.31/9.47 cnf(subtract_distribution-1, axiom, ( ~morphism(_u74, _u73, _u72) | ~element(_u71, _u73) | ~element(_u70, _u73) | ( apply(_u74, subtract(_u73, _u71, _u70)) = subtract(_u72, apply(_u74, _u71), apply(_u74, _u70))) )).
% 9.31/9.47
% 9.31/9.47 % Formula: alpha_morphism ( axiom ) converted to clauses:
% 9.31/9.47 cnf(alpha_morphism-1, axiom, ( morphism(alpha, a, b) )).
% 9.31/9.47
% 9.31/9.47 % Formula: beta_morphism ( axiom ) converted to clauses:
% 9.31/9.47 cnf(beta_morphism-1, axiom, ( morphism(beta, b, c) )).
% 9.31/9.47
% 9.31/9.47 % Formula: gamma_morphism ( axiom ) converted to clauses:
% 9.31/9.47 cnf(gamma_morphism-1, axiom, ( morphism(gamma, d, e) )).
% 9.31/9.47
% 9.31/9.47 % Formula: delta_morphism ( axiom ) converted to clauses:
% 9.31/9.47 cnf(delta_morphism-1, axiom, ( morphism(delta, e, r) )).
% 9.31/9.47
% 9.31/9.47 % Formula: f_morphism ( axiom ) converted to clauses:
% 9.31/9.47 cnf(f_morphism-1, axiom, ( morphism(f, a, d) )).
% 9.31/9.47
% 9.31/9.47 % Formula: g_morphism ( axiom ) converted to clauses:
% 9.31/9.47 cnf(g_morphism-1, axiom, ( morphism(g, b, e) )).
% 9.31/9.47
% 9.31/9.47 % Formula: h_morphism ( axiom ) converted to clauses:
% 9.31/9.47 cnf(h_morphism-1, axiom, ( morphism(h, c, r) )).
% 9.31/9.47
% 9.31/9.47 % Formula: alpha_injection ( axiom ) converted to clauses:
% 9.31/9.47 cnf(alpha_injection-1, axiom, ( injection(alpha) )).
% 9.31/9.47
% 9.31/9.47 % Formula: gamma_injection ( axiom ) converted to clauses:
% 9.31/9.47 cnf(gamma_injection-1, axiom, ( injection(gamma) )).
% 9.31/9.47
% 9.31/9.47 % Formula: beta_surjection ( axiom ) converted to clauses:
% 9.31/9.47 cnf(beta_surjection-1, axiom, ( surjection(beta) )).
% 9.31/9.47
% 9.31/9.47 % Formula: delta_surjection ( axiom ) converted to clauses:
% 9.31/9.47 cnf(delta_surjection-1, axiom, ( surjection(delta) )).
% 9.31/9.47
% 9.31/9.47 % Formula: alpha_beta_exact ( axiom ) converted to clauses:
% 9.31/9.47 cnf(alpha_beta_exact-1, axiom, ( exact(alpha, beta) )).
% 9.31/9.47
% 9.31/9.47 % Formula: gamma_delta_exact ( axiom ) converted to clauses:
% 9.31/9.47 cnf(gamma_delta_exact-1, axiom, ( exact(gammma, delta) )).
% 9.31/9.47
% 9.31/9.47 % Formula: alpha_g_f_gamma_commute ( axiom ) converted to clauses:
% 9.31/9.47 cnf(alpha_g_f_gamma_commute-1, axiom, ( commute(alpha, g, f, gamma) )).
% 9.31/9.47
% 9.31/9.47 % Formula: beta_h_g_delta_commute ( axiom ) converted to clauses:
% 9.31/9.47 cnf(beta_h_g_delta_commute-1, axiom, ( commute(beta, h, g, delta) )).
% 9.31/9.47
% 9.31/9.47 % Formula: f_surjection ( hypothesis ) converted to clauses:
% 9.31/9.47 cnf(f_surjection-1, hypothesis, ( surjection(f) )).
% 9.31/9.47
% 9.31/9.47 % Formula: h_surjection ( hypothesis ) converted to clauses:
% 9.31/9.47 cnf(h_surjection-1, hypothesis, ( surjection(h) )).
% 9.31/9.47
% 9.31/9.47 % Formula: lemma3 ( axiom ) converted to clauses:
% 9.31/9.47 cnf(lemma3-1, axiom, ( ~element(_u77, e) | element(skolem10(_u77), r) )).
% 9.31/9.47 cnf(lemma3-2, axiom, ( ~element(_u77, e) | ( apply(delta, _u77) = skolem10(_u77)) )).
% 9.31/9.47 cnf(lemma3-3, axiom, ( ~element(_u77, e) | element(skolem11(_u77), b) )).
% 9.31/9.47 cnf(lemma3-4, axiom, ( ~element(_u77, e) | ( apply(h, apply(beta, skolem11(_u77))) = skolem10(_u77)) )).
% 9.31/9.47 cnf(lemma3-5, axiom, ( ~element(_u77, e) | ( apply(delta, apply(g, skolem11(_u77))) = skolem10(_u77)) )).
% 9.31/9.47
% 9.31/9.47 % Formula: lemma8 ( axiom ) converted to clauses:
% 9.31/9.47 cnf(lemma8-1, axiom, ( ~element(_u81, e) | element(skolem12(_u81), b) )).
% 9.31/9.47 cnf(lemma8-2, axiom, ( ~element(_u81, e) | element(skolem13(_u81), e) )).
% 9.31/9.47 cnf(lemma8-3, axiom, ( ~element(_u81, e) | ( subtract(e, apply(g, skolem12(_u81)), _u81) = skolem13(_u81)) )).
% 9.31/9.47 cnf(lemma8-4, axiom, ( ~element(_u81, e) | element(skolem14(_u81), a) )).
% 9.31/9.47 cnf(lemma8-5, axiom, ( ~element(_u81, e) | ( apply(gamma, apply(f, skolem14(_u81))) = skolem13(_u81)) )).
% 9.31/9.47 cnf(lemma8-6, axiom, ( ~element(_u81, e) | ( apply(g, apply(alpha, skolem14(_u81))) = skolem13(_u81)) )).
% 9.31/9.47
% 9.31/9.47 % Formula: lemma12 ( axiom ) converted to clauses:
% 9.31/9.47 cnf(lemma12-1, axiom, ( ~element(_u84, e) | element(skolem15(_u84), b) )).
% 9.31/9.47 cnf(lemma12-2, axiom, ( ~element(_u84, e) | element(skolem16(_u84), b) )).
% 9.31/9.47 cnf(lemma12-3, axiom, ( ~element(_u84, e) | ( apply(g, subtract(b, skolem15(_u84), skolem16(_u84))) = _u84) )).
% 9.31/9.47
% 9.31/9.47 % Formula: g_surjection ( conjecture ) converted to clauses:
% 9.31/9.47 cnf(g_surjection-1, negated_conjecture, ( ~surjection(g) )).
% 9.31/9.47
% 9.31/9.47 % Problem matrix:
% 9.31/9.47 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 9.31/9.47 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 9.31/9.47 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 9.31/9.47 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( apply(__eqx_0, __eqx_1) = apply(__eqy_0, __eqy_1)) )).
% 9.31/9.47 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( zero(__eqx_0) = zero(__eqy_0)) )).
% 9.31/9.47 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( subtract(__eqx_0, __eqx_1, __eqx_2) = subtract(__eqy_0, __eqy_1, __eqy_2)) )).
% 9.31/9.47 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 9.31/9.47 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem2(__eqx_0, __eqx_1) = skolem2(__eqy_0, __eqy_1)) )).
% 9.31/9.47 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( skolem3(__eqx_0, __eqx_1, __eqx_2, __eqx_3) = skolem3(__eqy_0, __eqy_1, __eqy_2, __eqy_3)) )).
% 9.31/9.47 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem4(__eqx_0, __eqx_1, __eqx_2) = skolem4(__eqy_0, __eqy_1, __eqy_2)) )).
% 9.31/9.47 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( __eqx_4 != __eqy_4) | ( __eqx_5 != __eqy_5) | ( skolem5(__eqx_0, __eqx_1, __eqx_2, __eqx_3, __eqx_4, __eqx_5) = skolem5(__eqy_0, __eqy_1, __eqy_2, __eqy_3, __eqy_4, __eqy_5)) )).
% 9.31/9.47 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( __eqx_4 != __eqy_4) | ( skolem6(__eqx_0, __eqx_1, __eqx_2, __eqx_3, __eqx_4) = skolem6(__eqy_0, __eqy_1, __eqy_2, __eqy_3, __eqy_4)) )).
% 9.31/9.47 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( __eqx_4 != __eqy_4) | ( skolem7(__eqx_0, __eqx_1, __eqx_2, __eqx_3, __eqx_4) = skolem7(__eqy_0, __eqy_1, __eqy_2, __eqy_3, __eqy_4)) )).
% 9.31/9.47 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( __eqx_4 != __eqy_4) | ( skolem8(__eqx_0, __eqx_1, __eqx_2, __eqx_3, __eqx_4) = skolem8(__eqy_0, __eqy_1, __eqy_2, __eqy_3, __eqy_4)) )).
% 9.31/9.47 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( __eqx_4 != __eqy_4) | ( skolem9(__eqx_0, __eqx_1, __eqx_2, __eqx_3, __eqx_4) = skolem9(__eqy_0, __eqy_1, __eqy_2, __eqy_3, __eqy_4)) )).
% 9.31/9.47 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( skolem10(__eqx_0) = skolem10(__eqy_0)) )).
% 9.31/9.47 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( skolem11(__eqx_0) = skolem11(__eqy_0)) )).
% 9.31/9.47 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( skolem12(__eqx_0) = skolem12(__eqy_0)) )).
% 9.31/9.47 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( skolem13(__eqx_0) = skolem13(__eqy_0)) )).
% 9.31/9.47 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( skolem14(__eqx_0) = skolem14(__eqy_0)) )).
% 9.31/9.47 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( skolem15(__eqx_0) = skolem15(__eqy_0)) )).
% 9.31/9.47 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( skolem16(__eqx_0) = skolem16(__eqy_0)) )).
% 9.31/9.47 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~morphism(__eqx_0, __eqx_1, __eqx_2) | morphism(__eqy_0, __eqy_1, __eqy_2) )).
% 9.31/9.47 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~element(__eqx_0, __eqx_1) | element(__eqy_0, __eqy_1) )).
% 9.31/9.47 cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ~injection(__eqx_0) | injection(__eqy_0) )).
% 9.31/9.47 cnf(matrix-25, plain, ( ( __eqx_0 != __eqy_0) | ~surjection(__eqx_0) | surjection(__eqy_0) )).
% 9.31/9.47 cnf(matrix-26, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~exact(__eqx_0, __eqx_1) | exact(__eqy_0, __eqy_1) )).
% 9.31/9.47 cnf(matrix-27, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ~commute(__eqx_0, __eqx_1, __eqx_2, __eqx_3) | commute(__eqy_0, __eqy_1, __eqy_2, __eqy_3) )).
% 9.31/9.47 cnf(matrix-28, plain, ( ~morphism(_u3, _u2, _u1) | ~element(_u0, _u2) | element(apply(_u3, _u0), _u1) )).
% 9.31/9.47 cnf(matrix-29, plain, ( ~morphism(_u3, _u2, _u1) | ( apply(_u3, zero(_u2)) = zero(_u1)) )).
% 9.31/9.47 cnf(matrix-30, plain, ( ~element(_u5, _u7) | ~element(_u4, _u7) | ( apply(_u8, _u5) != apply(_u8, _u4)) | ( _u5 = _u4) | ~injection(_u8) | ~morphism(_u8, _u7, _u6) )).
% 9.31/9.47 cnf(matrix-31, plain, ( injection(_u13) | ~morphism(_u13, _u12, _u11) | element(skolem1(_u13, _u12), _u12) )).
% 9.31/9.47 cnf(matrix-32, plain, ( injection(_u13) | ~morphism(_u13, _u12, _u11) | element(skolem2(_u13, _u12), _u12) )).
% 9.31/9.47 cnf(matrix-33, plain, ( injection(_u13) | ~morphism(_u13, _u12, _u11) | ( apply(_u13, skolem1(_u13, _u12)) = apply(_u13, skolem2(_u13, _u12))) )).
% 9.31/9.47 cnf(matrix-34, plain, ( injection(_u13) | ~morphism(_u13, _u12, _u11) | ( skolem1(_u13, _u12) != skolem2(_u13, _u12)) )).
% 9.31/9.47 cnf(matrix-35, plain, ( ~surjection(_u18) | ~morphism(_u18, _u17, _u16) | ~element(_u15, _u16) | element(skolem3(_u18, _u17, _u16, _u15), _u17) )).
% 9.31/9.47 cnf(matrix-36, plain, ( ~surjection(_u18) | ~morphism(_u18, _u17, _u16) | ~element(_u15, _u16) | ( apply(_u18, skolem3(_u18, _u17, _u16, _u15)) = _u15) )).
% 9.31/9.47 cnf(matrix-37, plain, ( surjection(_u23) | ~morphism(_u23, _u22, _u21) | element(skolem4(_u23, _u22, _u21), _u21) )).
% 9.31/9.47 cnf(matrix-38, plain, ( surjection(_u23) | ~morphism(_u23, _u22, _u21) | ~element(_u19, _u22) | ( apply(_u23, _u19) != skolem4(_u23, _u22, _u21)) )).
% 9.31/9.47 cnf(matrix-39, plain, ( ~exact(_u31, _u30) | ~morphism(_u31, _u29, _u28) | ~morphism(_u30, _u28, _u27) | ~element(_u32, _u28) | ( apply(_u30, _u32) != zero(_u27)) | element(skolem5(_u31, _u30, _u29, _u28, _u27, _u32), _u29) )).
% 9.31/9.47 cnf(matrix-40, plain, ( ~exact(_u31, _u30) | ~morphism(_u31, _u29, _u28) | ~morphism(_u30, _u28, _u27) | ~element(_u32, _u28) | ( apply(_u30, _u32) != zero(_u27)) | ( apply(_u31, skolem5(_u31, _u30, _u29, _u28, _u27, _u32)) = _u32) )).
% 9.31/9.47 cnf(matrix-41, plain, ( ~exact(_u31, _u30) | ~morphism(_u31, _u29, _u28) | ~morphism(_u30, _u28, _u27) | ~element(_u25, _u29) | ( apply(_u31, _u25) != _u33) | element(_u33, _u28) )).
% 9.31/9.47 cnf(matrix-42, plain, ( ~exact(_u31, _u30) | ~morphism(_u31, _u29, _u28) | ~morphism(_u30, _u28, _u27) | ~element(_u25, _u29) | ( apply(_u31, _u25) != _u33) | ( apply(_u30, _u33) = zero(_u27)) )).
% 9.31/9.47 cnf(matrix-43, plain, ( exact(_u41, _u40) | ~morphism(_u41, _u39, _u38) | ~morphism(_u40, _u38, _u37) | element(skolem6(_u41, _u40, _u39, _u38, _u37), _u38) | element(skolem8(_u41, _u40, _u39, _u38, _u37), _u39) )).
% 9.31/9.47 cnf(matrix-44, plain, ( exact(_u41, _u40) | ~morphism(_u41, _u39, _u38) | ~morphism(_u40, _u38, _u37) | element(skolem6(_u41, _u40, _u39, _u38, _u37), _u38) | ( apply(_u41, skolem8(_u41, _u40, _u39, _u38, _u37)) = skolem7(_u41, _u40, _u39, _u38, _u37)) )).
% 9.31/9.47 cnf(matrix-45, plain, ( exact(_u41, _u40) | ~morphism(_u41, _u39, _u38) | ~morphism(_u40, _u38, _u37) | ( apply(_u40, skolem6(_u41, _u40, _u39, _u38, _u37)) = zero(_u37)) | element(skolem8(_u41, _u40, _u39, _u38, _u37), _u39) )).
% 9.31/9.47 cnf(matrix-46, plain, ( exact(_u41, _u40) | ~morphism(_u41, _u39, _u38) | ~morphism(_u40, _u38, _u37) | ( apply(_u40, skolem6(_u41, _u40, _u39, _u38, _u37)) = zero(_u37)) | ( apply(_u41, skolem8(_u41, _u40, _u39, _u38, _u37)) = skolem7(_u41, _u40, _u39, _u38, _u37)) )).
% 9.31/9.47 cnf(matrix-47, plain, ( exact(_u41, _u40) | ~morphism(_u41, _u39, _u38) | ~morphism(_u40, _u38, _u37) | ~element(skolem7(_u41, _u40, _u39, _u38, _u37), _u38) | ( apply(_u40, skolem7(_u41, _u40, _u39, _u38, _u37)) != zero(_u37)) | element(skolem6(_u41, _u40, _u39, _u38, _u37), _u38) )).
% 9.31/9.47 cnf(matrix-48, plain, ( exact(_u41, _u40) | ~morphism(_u41, _u39, _u38) | ~morphism(_u40, _u38, _u37) | ~element(skolem7(_u41, _u40, _u39, _u38, _u37), _u38) | ( apply(_u40, skolem7(_u41, _u40, _u39, _u38, _u37)) != zero(_u37)) | ( apply(_u40, skolem6(_u41, _u40, _u39, _u38, _u37)) = zero(_u37)) )).
% 9.31/9.47 cnf(matrix-49, plain, ( exact(_u41, _u40) | ~morphism(_u41, _u39, _u38) | ~morphism(_u40, _u38, _u37) | ~element(_u34, _u39) | ( apply(_u41, _u34) != skolem6(_u41, _u40, _u39, _u38, _u37)) | element(skolem8(_u41, _u40, _u39, _u38, _u37), _u39) )).
% 9.31/9.47 cnf(matrix-50, plain, ( exact(_u41, _u40) | ~morphism(_u41, _u39, _u38) | ~morphism(_u40, _u38, _u37) | ~element(_u34, _u39) | ( apply(_u41, _u34) != skolem6(_u41, _u40, _u39, _u38, _u37)) | ( apply(_u41, skolem8(_u41, _u40, _u39, _u38, _u37)) = skolem7(_u41, _u40, _u39, _u38, _u37)) )).
% 9.31/9.47 cnf(matrix-51, plain, ( exact(_u41, _u40) | ~morphism(_u41, _u39, _u38) | ~morphism(_u40, _u38, _u37) | ~element(_u34, _u39) | ( apply(_u41, _u34) != skolem6(_u41, _u40, _u39, _u38, _u37)) | ~element(skolem7(_u41, _u40, _u39, _u38, _u37), _u38) | ( apply(_u40, skolem7(_u41, _u40, _u39, _u38, _u37)) != zero(_u37)) )).
% 9.31/9.47 cnf(matrix-52, plain, ( ~element(_u44, _u48) | ( apply(_u51, apply(_u52, _u44)) = apply(_u49, apply(_u50, _u44))) | ~commute(_u52, _u51, _u50, _u49) | ~morphism(_u52, _u48, _u47) | ~morphism(_u50, _u48, _u46) | ~morphism(_u51, _u47, _u45) | ~morphism(_u49, _u46, _u45) )).
% 9.31/9.47 cnf(matrix-53, plain, ( commute(_u61, _u60, _u59, _u58) | ~morphism(_u61, _u57, _u56) | ~morphism(_u59, _u57, _u55) | ~morphism(_u60, _u56, _u54) | ~morphism(_u58, _u55, _u54) | element(skolem9(_u61, _u60, _u59, _u58, _u57), _u57) )).
% 9.31/9.47 cnf(matrix-54, plain, ( commute(_u61, _u60, _u59, _u58) | ~morphism(_u61, _u57, _u56) | ~morphism(_u59, _u57, _u55) | ~morphism(_u60, _u56, _u54) | ~morphism(_u58, _u55, _u54) | ( apply(_u60, apply(_u61, skolem9(_u61, _u60, _u59, _u58, _u57))) != apply(_u58, apply(_u59, skolem9(_u61, _u60, _u59, _u58, _u57)))) )).
% 9.31/9.47 cnf(matrix-55, plain, ( ~element(_u63, _u64) | ~element(_u62, _u64) | element(subtract(_u64, _u63, _u62), _u64) )).
% 9.31/9.47 cnf(matrix-56, plain, ( ~element(_u65, _u66) | ( subtract(_u66, _u65, _u65) = zero(_u66)) )).
% 9.31/9.47 cnf(matrix-57, plain, ( ~element(_u68, _u69) | ~element(_u67, _u69) | ( subtract(_u69, _u68, subtract(_u69, _u68, _u67)) = _u67) )).
% 9.31/9.47 cnf(matrix-58, plain, ( ~morphism(_u74, _u73, _u72) | ~element(_u71, _u73) | ~element(_u70, _u73) | ( apply(_u74, subtract(_u73, _u71, _u70)) = subtract(_u72, apply(_u74, _u71), apply(_u74, _u70))) )).
% 9.31/9.47 cnf(matrix-59, plain, ( morphism(alpha, a, b) )).
% 9.31/9.47 cnf(matrix-60, plain, ( morphism(beta, b, c) )).
% 9.31/9.47 cnf(matrix-61, plain, ( morphism(gamma, d, e) )).
% 9.31/9.47 cnf(matrix-62, plain, ( morphism(delta, e, r) )).
% 9.31/9.47 cnf(matrix-63, plain, ( morphism(f, a, d) )).
% 9.31/9.47 cnf(matrix-64, plain, ( morphism(g, b, e) )).
% 9.31/9.47 cnf(matrix-65, plain, ( morphism(h, c, r) )).
% 9.31/9.47 cnf(matrix-66, plain, ( injection(alpha) )).
% 9.31/9.47 cnf(matrix-67, plain, ( injection(gamma) )).
% 9.31/9.47 cnf(matrix-68, plain, ( surjection(beta) )).
% 9.31/9.47 cnf(matrix-69, plain, ( surjection(delta) )).
% 9.31/9.47 cnf(matrix-70, plain, ( exact(alpha, beta) )).
% 9.31/9.47 cnf(matrix-71, plain, ( exact(gammma, delta) )).
% 9.31/9.47 cnf(matrix-72, plain, ( commute(alpha, g, f, gamma) )).
% 9.31/9.47 cnf(matrix-73, plain, ( commute(beta, h, g, delta) )).
% 9.31/9.47 cnf(matrix-74, plain, ( surjection(f) )).
% 9.31/9.47 cnf(matrix-75, plain, ( surjection(h) )).
% 9.31/9.47 cnf(matrix-76, plain, ( ~element(_u77, e) | element(skolem10(_u77), r) )).
% 9.31/9.47 cnf(matrix-77, plain, ( ~element(_u77, e) | ( apply(delta, _u77) = skolem10(_u77)) )).
% 9.31/9.47 cnf(matrix-78, plain, ( ~element(_u77, e) | element(skolem11(_u77), b) )).
% 9.31/9.47 cnf(matrix-79, plain, ( ~element(_u77, e) | ( apply(h, apply(beta, skolem11(_u77))) = skolem10(_u77)) )).
% 9.31/9.47 cnf(matrix-80, plain, ( ~element(_u77, e) | ( apply(delta, apply(g, skolem11(_u77))) = skolem10(_u77)) )).
% 9.31/9.47 cnf(matrix-81, plain, ( ~element(_u81, e) | element(skolem12(_u81), b) )).
% 9.31/9.47 cnf(matrix-82, plain, ( ~element(_u81, e) | element(skolem13(_u81), e) )).
% 9.31/9.47 cnf(matrix-83, plain, ( ~element(_u81, e) | ( subtract(e, apply(g, skolem12(_u81)), _u81) = skolem13(_u81)) )).
% 9.31/9.47 cnf(matrix-84, plain, ( ~element(_u81, e) | element(skolem14(_u81), a) )).
% 9.31/9.47 cnf(matrix-85, plain, ( ~element(_u81, e) | ( apply(gamma, apply(f, skolem14(_u81))) = skolem13(_u81)) )).
% 9.31/9.47 cnf(matrix-86, plain, ( ~element(_u81, e) | ( apply(g, apply(alpha, skolem14(_u81))) = skolem13(_u81)) )).
% 9.31/9.47 cnf(matrix-87, plain, ( ~element(_u84, e) | element(skolem15(_u84), b) )).
% 9.31/9.47 cnf(matrix-88, plain, ( ~element(_u84, e) | element(skolem16(_u84), b) )).
% 9.31/9.47 cnf(matrix-89, plain, ( ~element(_u84, e) | ( apply(g, subtract(b, skolem15(_u84), skolem16(_u84))) = _u84) )).
% 9.31/9.47 cnf(matrix-90, plain, ( ~surjection(g) )).
% 9.31/9.47
% 9.31/9.47 % Proof stack:
% 9.31/9.47 cnf(proof-stack, plain,
% 9.31/9.47 proof_stack(
% 9.31/9.47 start(90),
% 9.31/9.47 left_branch(0, 38, 0, 2),
% 9.31/9.47 left_branch(0, 89, 1, 3),
% 9.31/9.47 left_branch(0, 37, 2, 4),
% 9.31/9.47 reduction(0, 0),
% 9.31/9.47 left_branch(0, 64, 0, 6),
% 9.31/9.47 right_branch(6),
% 9.31/9.47 right_branch(4),
% 9.31/9.47 right_branch(3),
% 9.31/9.47 left_branch(0, 55, 2, 4),
% 9.31/9.47 left_branch(0, 87, 1, 5),
% 9.31/9.47 left_branch(0, 37, 2, 6),
% 9.31/9.47 reduction(0, 0),
% 9.31/9.47 left_branch(0, 64, 0, 8),
% 9.31/9.47 right_branch(8),
% 9.31/9.47 right_branch(6),
% 9.31/9.47 right_branch(5),
% 9.31/9.47 left_branch(0, 88, 1, 6),
% 9.31/9.47 left_branch(0, 37, 2, 7),
% 9.31/9.47 reduction(0, 0),
% 9.31/9.47 left_branch(0, 64, 0, 9),
% 9.31/9.47 right_branch(9),
% 9.31/9.47 right_branch(7),
% 9.31/9.47 right_branch(6),
% 9.31/9.47 right_branch(4),
% 9.31/9.47 left_branch(0, 64, 0, 5),
% 9.31/9.47 right_branch(5),
% 9.31/9.47 right_branch(2)
% 9.31/9.47 )).
% 9.31/9.47 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------