TSTP Solution File: GRA010+1 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : GRA010+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% Computer : n016.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 14:12:59 EDT 2024
% Result : Theorem 48.42s 48.62s
% Output : Proof 48.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRA010+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.06/0.12 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.33 % Computer : n016.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 : Thu Mar 21 00:46:54 EDT 2024
% 0.12/0.33 % CPUTime :
% 48.42/48.62 % SZS status Theorem for theBenchmark
% 48.42/48.62 % SZS output start Proof for theBenchmark
% 48.42/48.62
% 48.42/48.62 % Formula: no_loops ( axiom ) converted to clauses:
% 48.42/48.62 cnf(no_loops-1, axiom, ( ~edge(_u0) | ( head_of(_u0) != tail_of(_u0)) )).
% 48.42/48.62
% 48.42/48.62 % Formula: edge_ends_are_vertices ( axiom ) converted to clauses:
% 48.42/48.62 cnf(edge_ends_are_vertices-1, axiom, ( ~edge(_u1) | vertex(head_of(_u1)) )).
% 48.42/48.62 cnf(edge_ends_are_vertices-2, axiom, ( ~edge(_u1) | vertex(tail_of(_u1)) )).
% 48.42/48.62
% 48.42/48.62 % Formula: complete_properties ( axiom ) converted to clauses:
% 48.42/48.62 cnf(complete_properties-1, axiom, ( ~complete | ~vertex(_u4) | ~vertex(_u3) | ( _u4 = _u3) | edge(skolem1(_u4, _u3)) )).
% 48.42/48.62 cnf(complete_properties-2, axiom, ( ~complete | ~vertex(_u4) | ~vertex(_u3) | ( _u4 = _u3) | ( _u4 = head_of(skolem1(_u4, _u3))) | ( _u3 = head_of(skolem1(_u4, _u3))) )).
% 48.42/48.62 cnf(complete_properties-3, axiom, ( ~complete | ~vertex(_u4) | ~vertex(_u3) | ( _u4 = _u3) | ( _u4 = head_of(skolem1(_u4, _u3))) | ( _u4 = tail_of(skolem1(_u4, _u3))) )).
% 48.42/48.62 cnf(complete_properties-4, axiom, ( ~complete | ~vertex(_u4) | ~vertex(_u3) | ( _u4 = _u3) | ( _u3 = tail_of(skolem1(_u4, _u3))) | ( _u3 = head_of(skolem1(_u4, _u3))) )).
% 48.42/48.62 cnf(complete_properties-5, axiom, ( ~complete | ~vertex(_u4) | ~vertex(_u3) | ( _u4 = _u3) | ( _u3 = tail_of(skolem1(_u4, _u3))) | ( _u4 = tail_of(skolem1(_u4, _u3))) )).
% 48.42/48.62 cnf(complete_properties-6, axiom, ( ~complete | ~vertex(_u4) | ~vertex(_u3) | ( _u4 = _u3) | ( _u3 != head_of(skolem1(_u4, _u3))) | ( _u4 != tail_of(skolem1(_u4, _u3))) | ( _u4 != head_of(skolem1(_u4, _u3))) | ( _u3 != tail_of(skolem1(_u4, _u3))) )).
% 48.42/48.62
% 48.42/48.62 % Formula: path_defn ( axiom ) converted to clauses:
% 48.42/48.62 cnf(path_defn-1, axiom, ( path(_u9, _u8, _u7) | ~vertex(_u9) | ~vertex(_u8) | ~edge(_u6) | ( _u9 != tail_of(_u6)) | ( _u8 != head_of(_u6)) | ( _u7 != path_cons(_u6, empty)) )).
% 48.42/48.62 cnf(path_defn-2, axiom, ( path(_u9, _u8, _u7) | ~vertex(_u9) | ~vertex(_u8) | ~edge(_u6) | ( _u9 != tail_of(_u6)) | ~path(head_of(_u6), _u8, _u5) | ( _u7 != path_cons(_u6, _u5)) )).
% 48.42/48.62
% 48.42/48.62 % Formula: path_properties ( axiom ) converted to clauses:
% 48.42/48.62 cnf(path_properties-1, axiom, ( ~path(_u15, _u14, _u13) | vertex(_u15) )).
% 48.42/48.62 cnf(path_properties-2, axiom, ( ~path(_u15, _u14, _u13) | vertex(_u14) )).
% 48.42/48.62 cnf(path_properties-3, axiom, ( ~path(_u15, _u14, _u13) | edge(skolem2(_u15, _u14, _u13)) )).
% 48.42/48.62 cnf(path_properties-4, axiom, ( ~path(_u15, _u14, _u13) | ( _u15 = tail_of(skolem2(_u15, _u14, _u13))) )).
% 48.42/48.62 cnf(path_properties-5, axiom, ( ~path(_u15, _u14, _u13) | ( _u14 = head_of(skolem2(_u15, _u14, _u13))) | path(head_of(skolem2(_u15, _u14, _u13)), _u14, skolem3(_u15, _u14, _u13)) )).
% 48.42/48.62 cnf(path_properties-6, axiom, ( ~path(_u15, _u14, _u13) | ( _u14 = head_of(skolem2(_u15, _u14, _u13))) | ( _u13 = path_cons(skolem2(_u15, _u14, _u13), skolem3(_u15, _u14, _u13))) )).
% 48.42/48.62 cnf(path_properties-7, axiom, ( ~path(_u15, _u14, _u13) | ( _u13 = path_cons(skolem2(_u15, _u14, _u13), empty)) | path(head_of(skolem2(_u15, _u14, _u13)), _u14, skolem3(_u15, _u14, _u13)) )).
% 48.42/48.62 cnf(path_properties-8, axiom, ( ~path(_u15, _u14, _u13) | ( _u13 = path_cons(skolem2(_u15, _u14, _u13), empty)) | ( _u13 = path_cons(skolem2(_u15, _u14, _u13), skolem3(_u15, _u14, _u13))) )).
% 48.42/48.62 cnf(path_properties-9, axiom, ( ~path(_u15, _u14, _u13) | ~path(head_of(skolem2(_u15, _u14, _u13)), _u14, _u10) | ( _u13 != path_cons(skolem2(_u15, _u14, _u13), _u10)) | ( _u14 != head_of(skolem2(_u15, _u14, _u13))) | ( _u13 != path_cons(skolem2(_u15, _u14, _u13), empty)) )).
% 48.42/48.62 cnf(path_properties-10, axiom, ( ~path(_u15, _u14, _u13) | ~path(head_of(skolem2(_u15, _u14, _u13)), _u14, _u10) | ( _u13 != path_cons(skolem2(_u15, _u14, _u13), _u10)) | path(head_of(skolem2(_u15, _u14, _u13)), _u14, skolem3(_u15, _u14, _u13)) )).
% 48.42/48.62 cnf(path_properties-11, axiom, ( ~path(_u15, _u14, _u13) | ~path(head_of(skolem2(_u15, _u14, _u13)), _u14, _u10) | ( _u13 != path_cons(skolem2(_u15, _u14, _u13), _u10)) | ( _u13 = path_cons(skolem2(_u15, _u14, _u13), skolem3(_u15, _u14, _u13))) )).
% 48.42/48.62
% 48.42/48.62 % Formula: on_path_properties ( axiom ) converted to clauses:
% 48.42/48.62 cnf(on_path_properties-1, axiom, ( ~path(_u19, _u18, _u17) | ~on_path(_u16, _u17) | edge(_u16) )).
% 48.42/48.62 cnf(on_path_properties-2, axiom, ( ~path(_u19, _u18, _u17) | ~on_path(_u16, _u17) | in_path(head_of(_u16), _u17) )).
% 48.42/48.62 cnf(on_path_properties-3, axiom, ( ~path(_u19, _u18, _u17) | ~on_path(_u16, _u17) | in_path(tail_of(_u16), _u17) )).
% 48.42/48.62
% 48.42/48.62 % Formula: in_path_properties ( axiom ) converted to clauses:
% 48.42/48.62 cnf(in_path_properties-1, axiom, ( ~path(_u24, _u23, _u22) | ~in_path(_u21, _u22) | vertex(_u21) )).
% 48.42/48.62 cnf(in_path_properties-2, axiom, ( ~path(_u24, _u23, _u22) | ~in_path(_u21, _u22) | on_path(skolem4(_u24, _u23, _u22, _u21), _u22) )).
% 48.42/48.62 cnf(in_path_properties-3, axiom, ( ~path(_u24, _u23, _u22) | ~in_path(_u21, _u22) | ( _u21 = head_of(skolem4(_u24, _u23, _u22, _u21))) | ( _u21 = tail_of(skolem4(_u24, _u23, _u22, _u21))) )).
% 48.42/48.62
% 48.42/48.62 % Formula: sequential_defn ( axiom ) converted to clauses:
% 48.42/48.62 cnf(sequential_defn-1, axiom, ( ~sequential(_u29, _u27) | edge(_u29) )).
% 48.42/48.62 cnf(sequential_defn-2, axiom, ( ~sequential(_u29, _u27) | edge(_u27) )).
% 48.42/48.62 cnf(sequential_defn-3, axiom, ( ~sequential(_u29, _u27) | ( _u29 != _u27) )).
% 48.42/48.62 cnf(sequential_defn-4, axiom, ( ~sequential(_u29, _u27) | ( head_of(_u29) = tail_of(_u27)) )).
% 48.42/48.62 cnf(sequential_defn-5, axiom, ( ~edge(_u30) | ~edge(_u28) | ( _u30 = _u28) | ( head_of(_u30) != tail_of(_u28)) | sequential(_u30, _u28) )).
% 48.42/48.62
% 48.42/48.62 % Formula: precedes_defn ( axiom ) converted to clauses:
% 48.42/48.62 cnf(precedes_defn-1, axiom, ( ~path(_u35, _u34, _u36) | precedes(_u33, _u32, _u36) | ~on_path(_u33, _u36) | ~on_path(_u32, _u36) | ~sequential(_u33, _u32) )).
% 48.42/48.62 cnf(precedes_defn-2, axiom, ( ~path(_u35, _u34, _u36) | precedes(_u33, _u32, _u36) | ~on_path(_u33, _u36) | ~on_path(_u32, _u36) | ~sequential(_u33, _u31) | ~precedes(_u31, _u32, _u36) )).
% 48.42/48.62
% 48.42/48.62 % Formula: precedes_properties ( axiom ) converted to clauses:
% 48.42/48.62 cnf(precedes_properties-1, axiom, ( ~path(_u42, _u41, _u43) | ~precedes(_u40, _u39, _u43) | on_path(_u40, _u43) )).
% 48.42/48.62 cnf(precedes_properties-2, axiom, ( ~path(_u42, _u41, _u43) | ~precedes(_u40, _u39, _u43) | on_path(_u39, _u43) )).
% 48.42/48.62 cnf(precedes_properties-3, axiom, ( ~path(_u42, _u41, _u43) | ~precedes(_u40, _u39, _u43) | sequential(_u40, _u39) | sequential(_u40, skolem5(_u43, _u40, _u39)) )).
% 48.42/48.62 cnf(precedes_properties-4, axiom, ( ~path(_u42, _u41, _u43) | ~precedes(_u40, _u39, _u43) | sequential(_u40, _u39) | precedes(skolem5(_u43, _u40, _u39), _u39, _u43) )).
% 48.42/48.62 cnf(precedes_properties-5, axiom, ( ~path(_u42, _u41, _u43) | ~precedes(_u40, _u39, _u43) | ~sequential(_u40, _u37) | ~precedes(_u37, _u39, _u43) | ~sequential(_u40, _u39) )).
% 48.42/48.62 cnf(precedes_properties-6, axiom, ( ~path(_u42, _u41, _u43) | ~precedes(_u40, _u39, _u43) | ~sequential(_u40, _u37) | ~precedes(_u37, _u39, _u43) | sequential(_u40, skolem5(_u43, _u40, _u39)) )).
% 48.42/48.62 cnf(precedes_properties-7, axiom, ( ~path(_u42, _u41, _u43) | ~precedes(_u40, _u39, _u43) | ~sequential(_u40, _u37) | ~precedes(_u37, _u39, _u43) | precedes(skolem5(_u43, _u40, _u39), _u39, _u43) )).
% 48.42/48.62
% 48.42/48.62 % Formula: shortest_path_defn ( axiom ) converted to clauses:
% 48.42/48.62 cnf(shortest_path_defn-1, axiom, ( ~shortest_path(_u53, _u51, _u49) | path(_u53, _u51, _u49) )).
% 48.42/48.62 cnf(shortest_path_defn-2, axiom, ( ~shortest_path(_u53, _u51, _u49) | ( _u53 != _u51) )).
% 48.42/48.62 cnf(shortest_path_defn-3, axiom, ( ~shortest_path(_u53, _u51, _u49) | ~path(_u53, _u51, _u44) | less_or_equal(length_of(_u49), length_of(_u44)) )).
% 48.42/48.62 cnf(shortest_path_defn-4, axiom, ( shortest_path(_u54, _u52, _u50) | ~path(_u54, _u52, _u50) | ( _u54 = _u52) | path(_u54, _u52, skolem6(_u54, _u52, _u50)) )).
% 48.42/48.62 cnf(shortest_path_defn-5, axiom, ( shortest_path(_u54, _u52, _u50) | ~path(_u54, _u52, _u50) | ( _u54 = _u52) | ~less_or_equal(length_of(_u50), length_of(skolem6(_u54, _u52, _u50))) )).
% 48.42/48.62
% 48.42/48.62 % Formula: shortest_path_properties ( axiom ) converted to clauses:
% 48.42/48.62 cnf(shortest_path_properties-1, axiom, ( ~shortest_path(_u60, _u59, _u56) | ~precedes(_u58, _u57, _u56) | ( tail_of(_u55) != tail_of(_u58)) | ( head_of(_u55) != head_of(_u57)) )).
% 48.42/48.62 cnf(shortest_path_properties-2, axiom, ( ~shortest_path(_u60, _u59, _u56) | ~precedes(_u58, _u57, _u56) | ~precedes(_u57, _u58, _u56) )).
% 48.42/48.62
% 48.42/48.62 % Formula: triangle_defn ( axiom ) converted to clauses:
% 48.42/48.62 cnf(triangle_defn-1, axiom, ( ~triangle(_u68, _u66, _u64) | edge(_u68) )).
% 48.42/48.62 cnf(triangle_defn-2, axiom, ( ~triangle(_u68, _u66, _u64) | edge(_u66) )).
% 48.42/48.62 cnf(triangle_defn-3, axiom, ( ~triangle(_u68, _u66, _u64) | edge(_u64) )).
% 48.42/48.62 cnf(triangle_defn-4, axiom, ( ~triangle(_u68, _u66, _u64) | sequential(_u68, _u66) )).
% 48.42/48.62 cnf(triangle_defn-5, axiom, ( ~triangle(_u68, _u66, _u64) | sequential(_u66, _u64) )).
% 48.42/48.62 cnf(triangle_defn-6, axiom, ( ~triangle(_u68, _u66, _u64) | sequential(_u64, _u68) )).
% 48.42/48.62 cnf(triangle_defn-7, axiom, ( ~edge(_u69) | ~edge(_u67) | ~edge(_u65) | ~sequential(_u69, _u67) | ~sequential(_u67, _u65) | ~sequential(_u65, _u69) | triangle(_u69, _u67, _u65) )).
% 48.42/48.62
% 48.42/48.62 % Formula: length_defn ( axiom ) converted to clauses:
% 48.42/48.62 cnf(length_defn-1, axiom, ( ~path(_u72, _u71, _u70) | ( length_of(_u70) = number_of_in(edges, _u70)) )).
% 48.42/48.62
% 48.42/48.62 % Formula: path_length_sequential_pairs ( axiom ) converted to clauses:
% 48.42/48.62 cnf(path_length_sequential_pairs-1, axiom, ( ~path(_u75, _u74, _u73) | ( number_of_in(sequential_pairs, _u73) = minus(length_of(_u73), n1)) )).
% 48.42/48.62
% 48.42/48.62 % Formula: sequential_pairs_and_triangles ( axiom ) converted to clauses:
% 48.42/48.62 cnf(sequential_pairs_and_triangles-1, axiom, ( ( number_of_in(sequential_pairs, _u81) = number_of_in(triangles, _u81)) | ~path(_u80, _u79, _u81) | on_path(skolem7(_u81), _u81) )).
% 48.42/48.62 cnf(sequential_pairs_and_triangles-2, axiom, ( ( number_of_in(sequential_pairs, _u81) = number_of_in(triangles, _u81)) | ~path(_u80, _u79, _u81) | on_path(skolem8(_u81), _u81) )).
% 48.42/48.62 cnf(sequential_pairs_and_triangles-3, axiom, ( ( number_of_in(sequential_pairs, _u81) = number_of_in(triangles, _u81)) | ~path(_u80, _u79, _u81) | sequential(skolem7(_u81), skolem8(_u81)) )).
% 48.42/48.62 cnf(sequential_pairs_and_triangles-4, axiom, ( ( number_of_in(sequential_pairs, _u81) = number_of_in(triangles, _u81)) | ~path(_u80, _u79, _u81) | ~triangle(skolem7(_u81), skolem8(_u81), _u76) )).
% 48.42/48.62
% 48.42/48.62 % Formula: graph_has_them_all ( axiom ) converted to clauses:
% 48.42/48.62 cnf(graph_has_them_all-1, axiom, ( less_or_equal(number_of_in(_u83, _u82), number_of_in(_u83, graph)) )).
% 48.42/48.62
% 48.42/48.62 % Formula: complete_means_sequential_pairs_and_triangles ( conjecture ) (definitionally) converted to clauses:
% 48.42/48.62 cnf(complete_means_sequential_pairs_and_triangles-1, negated_conjecture, ( complete )).
% 48.42/48.62 cnf(complete_means_sequential_pairs_and_triangles-2, negated_conjecture, ( path(skolem10, skolem11, skolem9) )).
% 48.42/48.62 cnf(complete_means_sequential_pairs_and_triangles-3, negated_conjecture, ( ~on_path(_u86, skolem9) | ~on_path(_u85, skolem9) | ~sequential(_u86, _u85) | triangle(_u86, _u85, skolem12(_u86, _u85)) )).
% 48.42/48.62 cnf(complete_means_sequential_pairs_and_triangles-4, negated_conjecture, ( ( number_of_in(sequential_pairs, skolem9) != number_of_in(triangles, skolem9)) )).
% 48.42/48.62
% 48.42/48.62 % Problem matrix:
% 48.42/48.62 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 48.42/48.62 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 48.42/48.62 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 48.42/48.62 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( head_of(__eqx_0) = head_of(__eqy_0)) )).
% 48.42/48.62 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( tail_of(__eqx_0) = tail_of(__eqy_0)) )).
% 48.42/48.62 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( path_cons(__eqx_0, __eqx_1) = path_cons(__eqy_0, __eqy_1)) )).
% 48.42/48.62 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( length_of(__eqx_0) = length_of(__eqy_0)) )).
% 48.42/48.62 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( number_of_in(__eqx_0, __eqx_1) = number_of_in(__eqy_0, __eqy_1)) )).
% 48.42/48.62 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( minus(__eqx_0, __eqx_1) = minus(__eqy_0, __eqy_1)) )).
% 48.42/48.62 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 48.42/48.62 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem2(__eqx_0, __eqx_1, __eqx_2) = skolem2(__eqy_0, __eqy_1, __eqy_2)) )).
% 48.42/48.62 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem3(__eqx_0, __eqx_1, __eqx_2) = skolem3(__eqy_0, __eqy_1, __eqy_2)) )).
% 48.42/48.62 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( skolem4(__eqx_0, __eqx_1, __eqx_2, __eqx_3) = skolem4(__eqy_0, __eqy_1, __eqy_2, __eqy_3)) )).
% 48.42/48.62 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem5(__eqx_0, __eqx_1, __eqx_2) = skolem5(__eqy_0, __eqy_1, __eqy_2)) )).
% 48.42/48.62 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem6(__eqx_0, __eqx_1, __eqx_2) = skolem6(__eqy_0, __eqy_1, __eqy_2)) )).
% 48.42/48.62 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( skolem7(__eqx_0) = skolem7(__eqy_0)) )).
% 48.42/48.62 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( skolem8(__eqx_0) = skolem8(__eqy_0)) )).
% 48.42/48.62 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem12(__eqx_0, __eqx_1) = skolem12(__eqy_0, __eqy_1)) )).
% 48.42/48.62 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ~edge(__eqx_0) | edge(__eqy_0) )).
% 48.42/48.62 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ~vertex(__eqx_0) | vertex(__eqy_0) )).
% 48.42/48.62 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~path(__eqx_0, __eqx_1, __eqx_2) | path(__eqy_0, __eqy_1, __eqy_2) )).
% 48.42/48.62 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~on_path(__eqx_0, __eqx_1) | on_path(__eqy_0, __eqy_1) )).
% 48.42/48.62 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in_path(__eqx_0, __eqx_1) | in_path(__eqy_0, __eqy_1) )).
% 48.42/48.62 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~sequential(__eqx_0, __eqx_1) | sequential(__eqy_0, __eqy_1) )).
% 48.42/48.62 cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~precedes(__eqx_0, __eqx_1, __eqx_2) | precedes(__eqy_0, __eqy_1, __eqy_2) )).
% 48.42/48.62 cnf(matrix-25, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~shortest_path(__eqx_0, __eqx_1, __eqx_2) | shortest_path(__eqy_0, __eqy_1, __eqy_2) )).
% 48.42/48.62 cnf(matrix-26, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~less_or_equal(__eqx_0, __eqx_1) | less_or_equal(__eqy_0, __eqy_1) )).
% 48.42/48.62 cnf(matrix-27, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~triangle(__eqx_0, __eqx_1, __eqx_2) | triangle(__eqy_0, __eqy_1, __eqy_2) )).
% 48.42/48.62 cnf(matrix-28, plain, ( ~edge(_u0) | ( head_of(_u0) != tail_of(_u0)) )).
% 48.42/48.62 cnf(matrix-29, plain, ( ~edge(_u1) | vertex(head_of(_u1)) )).
% 48.42/48.62 cnf(matrix-30, plain, ( ~edge(_u1) | vertex(tail_of(_u1)) )).
% 48.42/48.62 cnf(matrix-31, plain, ( ~complete | ~vertex(_u4) | ~vertex(_u3) | ( _u4 = _u3) | edge(skolem1(_u4, _u3)) )).
% 48.42/48.62 cnf(matrix-32, plain, ( ~complete | ~vertex(_u4) | ~vertex(_u3) | ( _u4 = _u3) | ( _u4 = head_of(skolem1(_u4, _u3))) | ( _u3 = head_of(skolem1(_u4, _u3))) )).
% 48.42/48.62 cnf(matrix-33, plain, ( ~complete | ~vertex(_u4) | ~vertex(_u3) | ( _u4 = _u3) | ( _u4 = head_of(skolem1(_u4, _u3))) | ( _u4 = tail_of(skolem1(_u4, _u3))) )).
% 48.42/48.62 cnf(matrix-34, plain, ( ~complete | ~vertex(_u4) | ~vertex(_u3) | ( _u4 = _u3) | ( _u3 = tail_of(skolem1(_u4, _u3))) | ( _u3 = head_of(skolem1(_u4, _u3))) )).
% 48.42/48.62 cnf(matrix-35, plain, ( ~complete | ~vertex(_u4) | ~vertex(_u3) | ( _u4 = _u3) | ( _u3 = tail_of(skolem1(_u4, _u3))) | ( _u4 = tail_of(skolem1(_u4, _u3))) )).
% 48.42/48.62 cnf(matrix-36, plain, ( ~complete | ~vertex(_u4) | ~vertex(_u3) | ( _u4 = _u3) | ( _u3 != head_of(skolem1(_u4, _u3))) | ( _u4 != tail_of(skolem1(_u4, _u3))) | ( _u4 != head_of(skolem1(_u4, _u3))) | ( _u3 != tail_of(skolem1(_u4, _u3))) )).
% 48.42/48.62 cnf(matrix-37, plain, ( path(_u9, _u8, _u7) | ~vertex(_u9) | ~vertex(_u8) | ~edge(_u6) | ( _u9 != tail_of(_u6)) | ( _u8 != head_of(_u6)) | ( _u7 != path_cons(_u6, empty)) )).
% 48.42/48.62 cnf(matrix-38, plain, ( path(_u9, _u8, _u7) | ~vertex(_u9) | ~vertex(_u8) | ~edge(_u6) | ( _u9 != tail_of(_u6)) | ~path(head_of(_u6), _u8, _u5) | ( _u7 != path_cons(_u6, _u5)) )).
% 48.42/48.62 cnf(matrix-39, plain, ( ~path(_u15, _u14, _u13) | vertex(_u15) )).
% 48.42/48.62 cnf(matrix-40, plain, ( ~path(_u15, _u14, _u13) | vertex(_u14) )).
% 48.42/48.62 cnf(matrix-41, plain, ( ~path(_u15, _u14, _u13) | edge(skolem2(_u15, _u14, _u13)) )).
% 48.42/48.62 cnf(matrix-42, plain, ( ~path(_u15, _u14, _u13) | ( _u15 = tail_of(skolem2(_u15, _u14, _u13))) )).
% 48.42/48.62 cnf(matrix-43, plain, ( ~path(_u15, _u14, _u13) | ( _u14 = head_of(skolem2(_u15, _u14, _u13))) | path(head_of(skolem2(_u15, _u14, _u13)), _u14, skolem3(_u15, _u14, _u13)) )).
% 48.42/48.62 cnf(matrix-44, plain, ( ~path(_u15, _u14, _u13) | ( _u14 = head_of(skolem2(_u15, _u14, _u13))) | ( _u13 = path_cons(skolem2(_u15, _u14, _u13), skolem3(_u15, _u14, _u13))) )).
% 48.42/48.62 cnf(matrix-45, plain, ( ~path(_u15, _u14, _u13) | ( _u13 = path_cons(skolem2(_u15, _u14, _u13), empty)) | path(head_of(skolem2(_u15, _u14, _u13)), _u14, skolem3(_u15, _u14, _u13)) )).
% 48.42/48.62 cnf(matrix-46, plain, ( ~path(_u15, _u14, _u13) | ( _u13 = path_cons(skolem2(_u15, _u14, _u13), empty)) | ( _u13 = path_cons(skolem2(_u15, _u14, _u13), skolem3(_u15, _u14, _u13))) )).
% 48.42/48.62 cnf(matrix-47, plain, ( ~path(_u15, _u14, _u13) | ~path(head_of(skolem2(_u15, _u14, _u13)), _u14, _u10) | ( _u13 != path_cons(skolem2(_u15, _u14, _u13), _u10)) | ( _u14 != head_of(skolem2(_u15, _u14, _u13))) | ( _u13 != path_cons(skolem2(_u15, _u14, _u13), empty)) )).
% 48.42/48.62 cnf(matrix-48, plain, ( ~path(_u15, _u14, _u13) | ~path(head_of(skolem2(_u15, _u14, _u13)), _u14, _u10) | ( _u13 != path_cons(skolem2(_u15, _u14, _u13), _u10)) | path(head_of(skolem2(_u15, _u14, _u13)), _u14, skolem3(_u15, _u14, _u13)) )).
% 48.42/48.62 cnf(matrix-49, plain, ( ~path(_u15, _u14, _u13) | ~path(head_of(skolem2(_u15, _u14, _u13)), _u14, _u10) | ( _u13 != path_cons(skolem2(_u15, _u14, _u13), _u10)) | ( _u13 = path_cons(skolem2(_u15, _u14, _u13), skolem3(_u15, _u14, _u13))) )).
% 48.42/48.62 cnf(matrix-50, plain, ( ~path(_u19, _u18, _u17) | ~on_path(_u16, _u17) | edge(_u16) )).
% 48.42/48.62 cnf(matrix-51, plain, ( ~path(_u19, _u18, _u17) | ~on_path(_u16, _u17) | in_path(head_of(_u16), _u17) )).
% 48.42/48.62 cnf(matrix-52, plain, ( ~path(_u19, _u18, _u17) | ~on_path(_u16, _u17) | in_path(tail_of(_u16), _u17) )).
% 48.42/48.62 cnf(matrix-53, plain, ( ~path(_u24, _u23, _u22) | ~in_path(_u21, _u22) | vertex(_u21) )).
% 48.42/48.62 cnf(matrix-54, plain, ( ~path(_u24, _u23, _u22) | ~in_path(_u21, _u22) | on_path(skolem4(_u24, _u23, _u22, _u21), _u22) )).
% 48.42/48.62 cnf(matrix-55, plain, ( ~path(_u24, _u23, _u22) | ~in_path(_u21, _u22) | ( _u21 = head_of(skolem4(_u24, _u23, _u22, _u21))) | ( _u21 = tail_of(skolem4(_u24, _u23, _u22, _u21))) )).
% 48.42/48.62 cnf(matrix-56, plain, ( ~sequential(_u29, _u27) | edge(_u29) )).
% 48.42/48.62 cnf(matrix-57, plain, ( ~sequential(_u29, _u27) | edge(_u27) )).
% 48.42/48.62 cnf(matrix-58, plain, ( ~sequential(_u29, _u27) | ( _u29 != _u27) )).
% 48.42/48.62 cnf(matrix-59, plain, ( ~sequential(_u29, _u27) | ( head_of(_u29) = tail_of(_u27)) )).
% 48.42/48.62 cnf(matrix-60, plain, ( ~edge(_u30) | ~edge(_u28) | ( _u30 = _u28) | ( head_of(_u30) != tail_of(_u28)) | sequential(_u30, _u28) )).
% 48.42/48.62 cnf(matrix-61, plain, ( ~path(_u35, _u34, _u36) | precedes(_u33, _u32, _u36) | ~on_path(_u33, _u36) | ~on_path(_u32, _u36) | ~sequential(_u33, _u32) )).
% 48.42/48.62 cnf(matrix-62, plain, ( ~path(_u35, _u34, _u36) | precedes(_u33, _u32, _u36) | ~on_path(_u33, _u36) | ~on_path(_u32, _u36) | ~sequential(_u33, _u31) | ~precedes(_u31, _u32, _u36) )).
% 48.42/48.62 cnf(matrix-63, plain, ( ~path(_u42, _u41, _u43) | ~precedes(_u40, _u39, _u43) | on_path(_u40, _u43) )).
% 48.42/48.62 cnf(matrix-64, plain, ( ~path(_u42, _u41, _u43) | ~precedes(_u40, _u39, _u43) | on_path(_u39, _u43) )).
% 48.42/48.62 cnf(matrix-65, plain, ( ~path(_u42, _u41, _u43) | ~precedes(_u40, _u39, _u43) | sequential(_u40, _u39) | sequential(_u40, skolem5(_u43, _u40, _u39)) )).
% 48.42/48.62 cnf(matrix-66, plain, ( ~path(_u42, _u41, _u43) | ~precedes(_u40, _u39, _u43) | sequential(_u40, _u39) | precedes(skolem5(_u43, _u40, _u39), _u39, _u43) )).
% 48.42/48.62 cnf(matrix-67, plain, ( ~path(_u42, _u41, _u43) | ~precedes(_u40, _u39, _u43) | ~sequential(_u40, _u37) | ~precedes(_u37, _u39, _u43) | ~sequential(_u40, _u39) )).
% 48.42/48.62 cnf(matrix-68, plain, ( ~path(_u42, _u41, _u43) | ~precedes(_u40, _u39, _u43) | ~sequential(_u40, _u37) | ~precedes(_u37, _u39, _u43) | sequential(_u40, skolem5(_u43, _u40, _u39)) )).
% 48.42/48.62 cnf(matrix-69, plain, ( ~path(_u42, _u41, _u43) | ~precedes(_u40, _u39, _u43) | ~sequential(_u40, _u37) | ~precedes(_u37, _u39, _u43) | precedes(skolem5(_u43, _u40, _u39), _u39, _u43) )).
% 48.42/48.62 cnf(matrix-70, plain, ( ~shortest_path(_u53, _u51, _u49) | path(_u53, _u51, _u49) )).
% 48.42/48.62 cnf(matrix-71, plain, ( ~shortest_path(_u53, _u51, _u49) | ( _u53 != _u51) )).
% 48.42/48.62 cnf(matrix-72, plain, ( ~shortest_path(_u53, _u51, _u49) | ~path(_u53, _u51, _u44) | less_or_equal(length_of(_u49), length_of(_u44)) )).
% 48.42/48.62 cnf(matrix-73, plain, ( shortest_path(_u54, _u52, _u50) | ~path(_u54, _u52, _u50) | ( _u54 = _u52) | path(_u54, _u52, skolem6(_u54, _u52, _u50)) )).
% 48.42/48.62 cnf(matrix-74, plain, ( shortest_path(_u54, _u52, _u50) | ~path(_u54, _u52, _u50) | ( _u54 = _u52) | ~less_or_equal(length_of(_u50), length_of(skolem6(_u54, _u52, _u50))) )).
% 48.42/48.62 cnf(matrix-75, plain, ( ~shortest_path(_u60, _u59, _u56) | ~precedes(_u58, _u57, _u56) | ( tail_of(_u55) != tail_of(_u58)) | ( head_of(_u55) != head_of(_u57)) )).
% 48.42/48.62 cnf(matrix-76, plain, ( ~shortest_path(_u60, _u59, _u56) | ~precedes(_u58, _u57, _u56) | ~precedes(_u57, _u58, _u56) )).
% 48.42/48.62 cnf(matrix-77, plain, ( ~triangle(_u68, _u66, _u64) | edge(_u68) )).
% 48.42/48.62 cnf(matrix-78, plain, ( ~triangle(_u68, _u66, _u64) | edge(_u66) )).
% 48.42/48.62 cnf(matrix-79, plain, ( ~triangle(_u68, _u66, _u64) | edge(_u64) )).
% 48.42/48.62 cnf(matrix-80, plain, ( ~triangle(_u68, _u66, _u64) | sequential(_u68, _u66) )).
% 48.42/48.62 cnf(matrix-81, plain, ( ~triangle(_u68, _u66, _u64) | sequential(_u66, _u64) )).
% 48.42/48.62 cnf(matrix-82, plain, ( ~triangle(_u68, _u66, _u64) | sequential(_u64, _u68) )).
% 48.42/48.62 cnf(matrix-83, plain, ( ~edge(_u69) | ~edge(_u67) | ~edge(_u65) | ~sequential(_u69, _u67) | ~sequential(_u67, _u65) | ~sequential(_u65, _u69) | triangle(_u69, _u67, _u65) )).
% 48.42/48.62 cnf(matrix-84, plain, ( ~path(_u72, _u71, _u70) | ( length_of(_u70) = number_of_in(edges, _u70)) )).
% 48.42/48.62 cnf(matrix-85, plain, ( ~path(_u75, _u74, _u73) | ( number_of_in(sequential_pairs, _u73) = minus(length_of(_u73), n1)) )).
% 48.42/48.62 cnf(matrix-86, plain, ( ( number_of_in(sequential_pairs, _u81) = number_of_in(triangles, _u81)) | ~path(_u80, _u79, _u81) | on_path(skolem7(_u81), _u81) )).
% 48.42/48.62 cnf(matrix-87, plain, ( ( number_of_in(sequential_pairs, _u81) = number_of_in(triangles, _u81)) | ~path(_u80, _u79, _u81) | on_path(skolem8(_u81), _u81) )).
% 48.42/48.62 cnf(matrix-88, plain, ( ( number_of_in(sequential_pairs, _u81) = number_of_in(triangles, _u81)) | ~path(_u80, _u79, _u81) | sequential(skolem7(_u81), skolem8(_u81)) )).
% 48.42/48.62 cnf(matrix-89, plain, ( ( number_of_in(sequential_pairs, _u81) = number_of_in(triangles, _u81)) | ~path(_u80, _u79, _u81) | ~triangle(skolem7(_u81), skolem8(_u81), _u76) )).
% 48.42/48.62 cnf(matrix-90, plain, ( less_or_equal(number_of_in(_u83, _u82), number_of_in(_u83, graph)) )).
% 48.42/48.62 cnf(matrix-91, plain, ( complete )).
% 48.42/48.62 cnf(matrix-92, plain, ( path(skolem10, skolem11, skolem9) )).
% 48.42/48.62 cnf(matrix-93, plain, ( ~on_path(_u86, skolem9) | ~on_path(_u85, skolem9) | ~sequential(_u86, _u85) | triangle(_u86, _u85, skolem12(_u86, _u85)) )).
% 48.42/48.62 cnf(matrix-94, plain, ( ( number_of_in(sequential_pairs, skolem9) != number_of_in(triangles, skolem9)) )).
% 48.42/48.62
% 48.42/48.62 % Proof stack:
% 48.42/48.62 cnf(proof-stack, plain,
% 48.42/48.62 proof_stack(
% 48.42/48.62 start(92),
% 48.42/48.62 left_branch(0, 89, 1, 2),
% 48.42/48.62 left_branch(0, 94, 0, 3),
% 48.42/48.62 right_branch(3),
% 48.42/48.62 left_branch(0, 93, 3, 4),
% 48.42/48.62 left_branch(0, 86, 2, 5),
% 48.42/48.62 lemmata(0, 0),
% 48.42/48.62 reduction(0, 0),
% 48.42/48.62 right_branch(5),
% 48.42/48.62 left_branch(0, 88, 2, 6),
% 48.42/48.62 lemmata(0, 0),
% 48.42/48.62 reduction(0, 0),
% 48.42/48.62 right_branch(6),
% 48.42/48.62 left_branch(0, 87, 2, 7),
% 48.42/48.62 lemmata(0, 0),
% 48.42/48.62 reduction(0, 0),
% 48.42/48.62 right_branch(7),
% 48.42/48.62 right_branch(4),
% 48.42/48.62 right_branch(2)
% 48.42/48.62 )).
% 48.42/48.62 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------