TSTP Solution File: SET638+3 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SET638+3 : TPTP v8.1.2. Released v2.2.0.
% 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 14:32:10 EDT 2024
% Result : Theorem 8.15s 8.31s
% Output : Proof 8.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET638+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.13 % 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 : Wed Mar 20 22:47:54 EDT 2024
% 0.12/0.34 % CPUTime :
% 8.15/8.31 % SZS status Theorem for theBenchmark
% 8.15/8.31 % SZS output start Proof for theBenchmark
% 8.15/8.31
% 8.15/8.31 % Formula: intersection_is_subset ( axiom ) converted to clauses:
% 8.15/8.31 cnf(intersection_is_subset-1, axiom, ( subset(intersection(_u1, _u0), _u1) )).
% 8.15/8.31
% 8.15/8.31 % Formula: subset_intersection ( axiom ) converted to clauses:
% 8.15/8.31 cnf(subset_intersection-1, axiom, ( ~subset(_u3, _u2) | ( intersection(_u3, _u2) = _u3) )).
% 8.15/8.31
% 8.15/8.31 % Formula: union_empty_set ( axiom ) converted to clauses:
% 8.15/8.31 cnf(union_empty_set-1, axiom, ( ( union(_u4, empty_set) = _u4) )).
% 8.15/8.31
% 8.15/8.31 % Formula: intersection_distributes_over_union ( axiom ) converted to clauses:
% 8.15/8.31 cnf(intersection_distributes_over_union-1, axiom, ( ( intersection(_u7, union(_u6, _u5)) = union(intersection(_u7, _u6), intersection(_u7, _u5))) )).
% 8.15/8.31
% 8.15/8.31 % Formula: union_defn ( axiom ) converted to clauses:
% 8.15/8.31 cnf(union_defn-1, axiom, ( ~member(_u11, union(_u15, _u13)) | member(_u11, _u15) | member(_u11, _u13) )).
% 8.15/8.31 cnf(union_defn-2, axiom, ( member(_u12, union(_u16, _u14)) | ~member(_u12, _u16) )).
% 8.15/8.31 cnf(union_defn-3, axiom, ( member(_u12, union(_u16, _u14)) | ~member(_u12, _u14) )).
% 8.15/8.31
% 8.15/8.31 % Formula: empty_set_defn ( axiom ) converted to clauses:
% 8.15/8.31 cnf(empty_set_defn-1, axiom, ( ~member(_u17, empty_set) )).
% 8.15/8.31
% 8.15/8.31 % Formula: intersection_defn ( axiom ) converted to clauses:
% 8.15/8.31 cnf(intersection_defn-1, axiom, ( ~member(_u21, intersection(_u25, _u23)) | member(_u21, _u25) )).
% 8.15/8.31 cnf(intersection_defn-2, axiom, ( ~member(_u21, intersection(_u25, _u23)) | member(_u21, _u23) )).
% 8.15/8.31 cnf(intersection_defn-3, axiom, ( ~member(_u22, _u26) | ~member(_u22, _u24) | member(_u22, intersection(_u26, _u24)) )).
% 8.15/8.31
% 8.15/8.31 % Formula: subset_defn ( axiom ) converted to clauses:
% 8.15/8.31 cnf(subset_defn-1, axiom, ( ~subset(_u33, _u31) | ~member(_u27, _u33) | member(_u27, _u31) )).
% 8.15/8.31 cnf(subset_defn-2, axiom, ( subset(_u34, _u32) | member(skolem1(_u34, _u32), _u34) )).
% 8.15/8.31 cnf(subset_defn-3, axiom, ( subset(_u34, _u32) | ~member(skolem1(_u34, _u32), _u32) )).
% 8.15/8.31
% 8.15/8.31 % Formula: equal_defn ( axiom ) converted to clauses:
% 8.15/8.31 cnf(equal_defn-1, axiom, ( ( _u39 != _u37) | subset(_u39, _u37) )).
% 8.15/8.31 cnf(equal_defn-2, axiom, ( ( _u39 != _u37) | subset(_u37, _u39) )).
% 8.15/8.31 cnf(equal_defn-3, axiom, ( ~subset(_u40, _u38) | ~subset(_u38, _u40) | ( _u40 = _u38) )).
% 8.15/8.31
% 8.15/8.31 % Formula: commutativity_of_union ( axiom ) converted to clauses:
% 8.15/8.31 cnf(commutativity_of_union-1, axiom, ( ( union(_u42, _u41) = union(_u41, _u42)) )).
% 8.15/8.31
% 8.15/8.31 % Formula: commutativity_of_intersection ( axiom ) converted to clauses:
% 8.15/8.31 cnf(commutativity_of_intersection-1, axiom, ( ( intersection(_u44, _u43) = intersection(_u43, _u44)) )).
% 8.15/8.31
% 8.15/8.31 % Formula: reflexivity_of_subset ( axiom ) converted to clauses:
% 8.15/8.31 cnf(reflexivity_of_subset-1, axiom, ( subset(_u45, _u45) )).
% 8.15/8.31
% 8.15/8.31 % Formula: empty_defn ( axiom ) converted to clauses:
% 8.15/8.31 cnf(empty_defn-1, axiom, ( ~empty(_u49) | ~member(_u46, _u49) )).
% 8.15/8.31 cnf(empty_defn-2, axiom, ( member(skolem2(_u50), _u50) | empty(_u50) )).
% 8.15/8.31
% 8.15/8.31 % Formula: equal_member_defn ( axiom ) converted to clauses:
% 8.15/8.31 cnf(equal_member_defn-1, axiom, ( ( _u61 != _u59) | ~member(_u55, _u61) | member(_u55, _u59) )).
% 8.15/8.31 cnf(equal_member_defn-2, axiom, ( ( _u61 != _u59) | ~member(_u56, _u59) | member(_u56, _u61) )).
% 8.15/8.31 cnf(equal_member_defn-3, axiom, ( ( _u62 = _u60) | member(skolem3(_u62, _u60), _u62) | member(skolem4(_u62, _u60), _u60) )).
% 8.15/8.31 cnf(equal_member_defn-4, axiom, ( ( _u62 = _u60) | member(skolem3(_u62, _u60), _u62) | ~member(skolem4(_u62, _u60), _u62) )).
% 8.15/8.31 cnf(equal_member_defn-5, axiom, ( ( _u62 = _u60) | ~member(skolem3(_u62, _u60), _u60) | member(skolem4(_u62, _u60), _u60) )).
% 8.15/8.31 cnf(equal_member_defn-6, axiom, ( ( _u62 = _u60) | ~member(skolem3(_u62, _u60), _u60) | ~member(skolem4(_u62, _u60), _u62) )).
% 8.15/8.31
% 8.15/8.31 % Formula: prove_th120 ( conjecture ) (definitionally) converted to clauses:
% 8.15/8.31 cnf(prove_th120-1, negated_conjecture, ( subset(skolem5, union(skolem6, skolem7)) )).
% 8.15/8.31 cnf(prove_th120-2, negated_conjecture, ( ( intersection(skolem5, skolem7) = empty_set) )).
% 8.15/8.31 cnf(prove_th120-3, negated_conjecture, ( ~subset(skolem5, skolem6) )).
% 8.15/8.31
% 8.15/8.31 % Problem matrix:
% 8.15/8.31 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 8.15/8.31 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 8.15/8.31 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 8.15/8.31 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( intersection(__eqx_0, __eqx_1) = intersection(__eqy_0, __eqy_1)) )).
% 8.15/8.31 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( union(__eqx_0, __eqx_1) = union(__eqy_0, __eqy_1)) )).
% 8.15/8.31 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 8.15/8.31 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( skolem2(__eqx_0) = skolem2(__eqy_0)) )).
% 8.15/8.31 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem3(__eqx_0, __eqx_1) = skolem3(__eqy_0, __eqy_1)) )).
% 8.15/8.31 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem4(__eqx_0, __eqx_1) = skolem4(__eqy_0, __eqy_1)) )).
% 8.15/8.31 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 8.15/8.31 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~member(__eqx_0, __eqx_1) | member(__eqy_0, __eqy_1) )).
% 8.15/8.31 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 8.15/8.31 cnf(matrix-12, plain, ( subset(intersection(_u1, _u0), _u1) )).
% 8.15/8.31 cnf(matrix-13, plain, ( ~subset(_u3, _u2) | ( intersection(_u3, _u2) = _u3) )).
% 8.15/8.31 cnf(matrix-14, plain, ( ( union(_u4, empty_set) = _u4) )).
% 8.15/8.31 cnf(matrix-15, plain, ( ( intersection(_u7, union(_u6, _u5)) = union(intersection(_u7, _u6), intersection(_u7, _u5))) )).
% 8.15/8.31 cnf(matrix-16, plain, ( ~member(_u11, union(_u15, _u13)) | member(_u11, _u15) | member(_u11, _u13) )).
% 8.15/8.31 cnf(matrix-17, plain, ( member(_u12, union(_u16, _u14)) | ~member(_u12, _u16) )).
% 8.15/8.31 cnf(matrix-18, plain, ( member(_u12, union(_u16, _u14)) | ~member(_u12, _u14) )).
% 8.15/8.31 cnf(matrix-19, plain, ( ~member(_u17, empty_set) )).
% 8.15/8.31 cnf(matrix-20, plain, ( ~member(_u21, intersection(_u25, _u23)) | member(_u21, _u25) )).
% 8.15/8.31 cnf(matrix-21, plain, ( ~member(_u21, intersection(_u25, _u23)) | member(_u21, _u23) )).
% 8.15/8.31 cnf(matrix-22, plain, ( ~member(_u22, _u26) | ~member(_u22, _u24) | member(_u22, intersection(_u26, _u24)) )).
% 8.15/8.31 cnf(matrix-23, plain, ( ~subset(_u33, _u31) | ~member(_u27, _u33) | member(_u27, _u31) )).
% 8.15/8.31 cnf(matrix-24, plain, ( subset(_u34, _u32) | member(skolem1(_u34, _u32), _u34) )).
% 8.15/8.31 cnf(matrix-25, plain, ( subset(_u34, _u32) | ~member(skolem1(_u34, _u32), _u32) )).
% 8.15/8.31 cnf(matrix-26, plain, ( ( _u39 != _u37) | subset(_u39, _u37) )).
% 8.15/8.31 cnf(matrix-27, plain, ( ( _u39 != _u37) | subset(_u37, _u39) )).
% 8.15/8.31 cnf(matrix-28, plain, ( ~subset(_u40, _u38) | ~subset(_u38, _u40) | ( _u40 = _u38) )).
% 8.15/8.31 cnf(matrix-29, plain, ( ( union(_u42, _u41) = union(_u41, _u42)) )).
% 8.15/8.31 cnf(matrix-30, plain, ( ( intersection(_u44, _u43) = intersection(_u43, _u44)) )).
% 8.15/8.31 cnf(matrix-31, plain, ( subset(_u45, _u45) )).
% 8.15/8.31 cnf(matrix-32, plain, ( ~empty(_u49) | ~member(_u46, _u49) )).
% 8.15/8.31 cnf(matrix-33, plain, ( member(skolem2(_u50), _u50) | empty(_u50) )).
% 8.15/8.31 cnf(matrix-34, plain, ( ( _u61 != _u59) | ~member(_u55, _u61) | member(_u55, _u59) )).
% 8.15/8.31 cnf(matrix-35, plain, ( ( _u61 != _u59) | ~member(_u56, _u59) | member(_u56, _u61) )).
% 8.15/8.31 cnf(matrix-36, plain, ( ( _u62 = _u60) | member(skolem3(_u62, _u60), _u62) | member(skolem4(_u62, _u60), _u60) )).
% 8.15/8.31 cnf(matrix-37, plain, ( ( _u62 = _u60) | member(skolem3(_u62, _u60), _u62) | ~member(skolem4(_u62, _u60), _u62) )).
% 8.15/8.31 cnf(matrix-38, plain, ( ( _u62 = _u60) | ~member(skolem3(_u62, _u60), _u60) | member(skolem4(_u62, _u60), _u60) )).
% 8.15/8.31 cnf(matrix-39, plain, ( ( _u62 = _u60) | ~member(skolem3(_u62, _u60), _u60) | ~member(skolem4(_u62, _u60), _u62) )).
% 8.15/8.31 cnf(matrix-40, plain, ( subset(skolem5, union(skolem6, skolem7)) )).
% 8.15/8.31 cnf(matrix-41, plain, ( ( intersection(skolem5, skolem7) = empty_set) )).
% 8.15/8.31 cnf(matrix-42, plain, ( ~subset(skolem5, skolem6) )).
% 8.15/8.31
% 8.15/8.31 % Proof stack:
% 8.15/8.31 cnf(proof-stack, plain,
% 8.15/8.31 proof_stack(
% 8.15/8.31 start(19),
% 8.15/8.31 left_branch(0, 34, 2, 2),
% 8.15/8.31 left_branch(0, 41, 0, 3),
% 8.15/8.31 right_branch(3),
% 8.15/8.31 left_branch(0, 22, 2, 4),
% 8.15/8.31 left_branch(0, 24, 1, 5),
% 8.15/8.31 left_branch(0, 42, 0, 6),
% 8.15/8.31 right_branch(6),
% 8.15/8.31 right_branch(5),
% 8.15/8.31 left_branch(0, 16, 2, 6),
% 8.15/8.31 left_branch(0, 23, 2, 7),
% 8.15/8.31 left_branch(0, 40, 0, 8),
% 8.15/8.31 right_branch(8),
% 8.15/8.31 lemmata(0, 1),
% 8.15/8.31 right_branch(7),
% 8.15/8.31 left_branch(0, 25, 1, 8),
% 8.15/8.31 left_branch(0, 42, 0, 9),
% 8.15/8.31 right_branch(9),
% 8.15/8.31 right_branch(8),
% 8.15/8.31 right_branch(6),
% 8.15/8.31 right_branch(4),
% 8.15/8.31 right_branch(2)
% 8.15/8.31 )).
% 8.15/8.31 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------