TSTP Solution File: SET624+3 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SET624+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 : n028.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 14:32:08 EDT 2024
% Result : Theorem 21.42s 21.60s
% Output : Proof 21.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET624+3 : TPTP v8.1.2. Released v2.2.0.
% 0.04/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Mar 20 22:25:54 EDT 2024
% 0.13/0.33 % CPUTime :
% 21.42/21.60 % SZS status Theorem for theBenchmark
% 21.42/21.60 % SZS output start Proof for theBenchmark
% 21.42/21.60
% 21.42/21.60 % Formula: union_defn ( axiom ) converted to clauses:
% 21.42/21.60 cnf(union_defn-1, axiom, ( ~member(_u3, union(_u7, _u5)) | member(_u3, _u7) | member(_u3, _u5) )).
% 21.42/21.60 cnf(union_defn-2, axiom, ( member(_u4, union(_u8, _u6)) | ~member(_u4, _u8) )).
% 21.42/21.60 cnf(union_defn-3, axiom, ( member(_u4, union(_u8, _u6)) | ~member(_u4, _u6) )).
% 21.42/21.60
% 21.42/21.60 % Formula: intersect_defn ( axiom ) converted to clauses:
% 21.42/21.60 cnf(intersect_defn-1, axiom, ( ~intersect(_u15, _u13) | member(skolem1(_u15, _u13), _u15) )).
% 21.42/21.60 cnf(intersect_defn-2, axiom, ( ~intersect(_u15, _u13) | member(skolem1(_u15, _u13), _u13) )).
% 21.42/21.60 cnf(intersect_defn-3, axiom, ( ~member(_u10, _u16) | ~member(_u10, _u14) | intersect(_u16, _u14) )).
% 21.42/21.60
% 21.42/21.60 % Formula: commutativity_of_union ( axiom ) converted to clauses:
% 21.42/21.60 cnf(commutativity_of_union-1, axiom, ( ( union(_u18, _u17) = union(_u17, _u18)) )).
% 21.42/21.60
% 21.42/21.60 % Formula: symmetry_of_intersect ( axiom ) converted to clauses:
% 21.42/21.60 cnf(symmetry_of_intersect-1, axiom, ( ~intersect(_u20, _u19) | intersect(_u19, _u20) )).
% 21.42/21.60
% 21.42/21.60 % Formula: equal_member_defn ( axiom ) converted to clauses:
% 21.42/21.60 cnf(equal_member_defn-1, axiom, ( ( _u31 != _u29) | ~member(_u25, _u31) | member(_u25, _u29) )).
% 21.42/21.60 cnf(equal_member_defn-2, axiom, ( ( _u31 != _u29) | ~member(_u26, _u29) | member(_u26, _u31) )).
% 21.42/21.60 cnf(equal_member_defn-3, axiom, ( ( _u32 = _u30) | member(skolem2(_u32, _u30), _u32) | member(skolem3(_u32, _u30), _u30) )).
% 21.42/21.60 cnf(equal_member_defn-4, axiom, ( ( _u32 = _u30) | member(skolem2(_u32, _u30), _u32) | ~member(skolem3(_u32, _u30), _u32) )).
% 21.42/21.60 cnf(equal_member_defn-5, axiom, ( ( _u32 = _u30) | ~member(skolem2(_u32, _u30), _u30) | member(skolem3(_u32, _u30), _u30) )).
% 21.42/21.60 cnf(equal_member_defn-6, axiom, ( ( _u32 = _u30) | ~member(skolem2(_u32, _u30), _u30) | ~member(skolem3(_u32, _u30), _u32) )).
% 21.42/21.60
% 21.42/21.60 % Formula: prove_intersect_with_union ( conjecture ) (definitionally) converted to clauses:
% 21.42/21.60 cnf(prove_intersect_with_union-1, negated_conjecture, ( ~_def0 | ~_def1 )).
% 21.42/21.60 cnf(prove_intersect_with_union-2, negated_conjecture, ( _def0 | intersect(skolem4, union(skolem5, skolem6)) )).
% 21.42/21.60 cnf(prove_intersect_with_union-3, negated_conjecture, ( _def0 | ~intersect(skolem4, skolem5) )).
% 21.42/21.60 cnf(prove_intersect_with_union-4, negated_conjecture, ( _def0 | ~intersect(skolem4, skolem6) )).
% 21.42/21.60 cnf(prove_intersect_with_union-5, negated_conjecture, ( _def1 | intersect(skolem4, skolem5) | intersect(skolem4, skolem6) )).
% 21.42/21.60 cnf(prove_intersect_with_union-6, negated_conjecture, ( _def1 | ~intersect(skolem4, union(skolem5, skolem6)) )).
% 21.42/21.60
% 21.42/21.60 % Problem matrix:
% 21.42/21.60 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 21.42/21.60 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 21.42/21.60 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 21.42/21.60 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( union(__eqx_0, __eqx_1) = union(__eqy_0, __eqy_1)) )).
% 21.42/21.60 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 21.42/21.60 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem2(__eqx_0, __eqx_1) = skolem2(__eqy_0, __eqy_1)) )).
% 21.42/21.60 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem3(__eqx_0, __eqx_1) = skolem3(__eqy_0, __eqy_1)) )).
% 21.42/21.60 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~member(__eqx_0, __eqx_1) | member(__eqy_0, __eqy_1) )).
% 21.42/21.60 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~intersect(__eqx_0, __eqx_1) | intersect(__eqy_0, __eqy_1) )).
% 21.42/21.60 cnf(matrix-9, plain, ( ~member(_u3, union(_u7, _u5)) | member(_u3, _u7) | member(_u3, _u5) )).
% 21.42/21.60 cnf(matrix-10, plain, ( member(_u4, union(_u8, _u6)) | ~member(_u4, _u8) )).
% 21.42/21.60 cnf(matrix-11, plain, ( member(_u4, union(_u8, _u6)) | ~member(_u4, _u6) )).
% 21.42/21.60 cnf(matrix-12, plain, ( ~intersect(_u15, _u13) | member(skolem1(_u15, _u13), _u15) )).
% 21.42/21.60 cnf(matrix-13, plain, ( ~intersect(_u15, _u13) | member(skolem1(_u15, _u13), _u13) )).
% 21.42/21.60 cnf(matrix-14, plain, ( ~member(_u10, _u16) | ~member(_u10, _u14) | intersect(_u16, _u14) )).
% 21.42/21.60 cnf(matrix-15, plain, ( ( union(_u18, _u17) = union(_u17, _u18)) )).
% 21.42/21.60 cnf(matrix-16, plain, ( ~intersect(_u20, _u19) | intersect(_u19, _u20) )).
% 21.42/21.60 cnf(matrix-17, plain, ( ( _u31 != _u29) | ~member(_u25, _u31) | member(_u25, _u29) )).
% 21.42/21.60 cnf(matrix-18, plain, ( ( _u31 != _u29) | ~member(_u26, _u29) | member(_u26, _u31) )).
% 21.42/21.60 cnf(matrix-19, plain, ( ( _u32 = _u30) | member(skolem2(_u32, _u30), _u32) | member(skolem3(_u32, _u30), _u30) )).
% 21.42/21.60 cnf(matrix-20, plain, ( ( _u32 = _u30) | member(skolem2(_u32, _u30), _u32) | ~member(skolem3(_u32, _u30), _u32) )).
% 21.42/21.60 cnf(matrix-21, plain, ( ( _u32 = _u30) | ~member(skolem2(_u32, _u30), _u30) | member(skolem3(_u32, _u30), _u30) )).
% 21.42/21.60 cnf(matrix-22, plain, ( ( _u32 = _u30) | ~member(skolem2(_u32, _u30), _u30) | ~member(skolem3(_u32, _u30), _u32) )).
% 21.42/21.60 cnf(matrix-23, plain, ( ~_def0 | ~_def1 )).
% 21.42/21.60 cnf(matrix-24, plain, ( _def0 | intersect(skolem4, union(skolem5, skolem6)) )).
% 21.42/21.60 cnf(matrix-25, plain, ( _def0 | ~intersect(skolem4, skolem5) )).
% 21.42/21.60 cnf(matrix-26, plain, ( _def0 | ~intersect(skolem4, skolem6) )).
% 21.42/21.60 cnf(matrix-27, plain, ( _def1 | intersect(skolem4, skolem5) | intersect(skolem4, skolem6) )).
% 21.42/21.60 cnf(matrix-28, plain, ( _def1 | ~intersect(skolem4, union(skolem5, skolem6)) )).
% 21.42/21.60
% 21.42/21.60 % Proof stack:
% 21.42/21.60 cnf(proof-stack, plain,
% 21.42/21.60 proof_stack(
% 21.42/21.60 start(23),
% 21.42/21.60 left_branch(0, 26, 0, 2),
% 21.42/21.60 left_branch(0, 14, 2, 3),
% 21.42/21.60 left_branch(0, 13, 1, 4),
% 21.42/21.60 left_branch(0, 16, 1, 5),
% 21.42/21.60 left_branch(0, 24, 1, 6),
% 21.42/21.60 reduction(0, 0),
% 21.42/21.60 right_branch(6),
% 21.42/21.60 right_branch(5),
% 21.42/21.60 right_branch(4),
% 21.42/21.60 left_branch(0, 9, 2, 5),
% 21.42/21.60 left_branch(0, 12, 1, 6),
% 21.42/21.60 left_branch(0, 16, 1, 7),
% 21.42/21.60 left_branch(0, 24, 1, 8),
% 21.42/21.60 reduction(0, 0),
% 21.42/21.60 right_branch(8),
% 21.42/21.60 right_branch(7),
% 21.42/21.60 right_branch(6),
% 21.42/21.60 left_branch(0, 14, 0, 7),
% 21.42/21.60 left_branch(0, 16, 0, 8),
% 21.42/21.60 left_branch(0, 25, 1, 9),
% 21.42/21.60 reduction(0, 0),
% 21.42/21.60 right_branch(9),
% 21.42/21.60 right_branch(8),
% 21.42/21.60 lemmata(0, 0),
% 21.42/21.60 right_branch(7),
% 21.42/21.60 right_branch(5),
% 21.42/21.60 right_branch(3),
% 21.42/21.60 right_branch(2),
% 21.42/21.60 left_branch(0, 27, 0, 3),
% 21.42/21.60 left_branch(0, 16, 0, 4),
% 21.42/21.60 left_branch(0, 13, 0, 5),
% 21.42/21.60 left_branch(0, 14, 0, 6),
% 21.42/21.60 left_branch(0, 28, 1, 7),
% 21.42/21.60 reduction(0, 0),
% 21.42/21.60 right_branch(7),
% 21.42/21.60 left_branch(0, 11, 0, 8),
% 21.42/21.60 left_branch(0, 12, 1, 9),
% 21.42/21.60 reduction(0, 2),
% 21.42/21.60 right_branch(9),
% 21.42/21.60 right_branch(8),
% 21.42/21.60 right_branch(6),
% 21.42/21.60 right_branch(5),
% 21.42/21.60 right_branch(4),
% 21.42/21.60 left_branch(0, 16, 0, 5),
% 21.42/21.60 left_branch(0, 13, 0, 6),
% 21.42/21.60 left_branch(0, 14, 0, 7),
% 21.42/21.60 left_branch(0, 28, 1, 8),
% 21.42/21.60 reduction(0, 0),
% 21.42/21.60 right_branch(8),
% 21.42/21.60 left_branch(0, 10, 0, 9),
% 21.42/21.60 left_branch(0, 12, 1, 10),
% 21.42/21.60 reduction(0, 2),
% 21.42/21.60 right_branch(10),
% 21.42/21.60 right_branch(9),
% 21.42/21.60 right_branch(7),
% 21.42/21.60 right_branch(6),
% 21.42/21.60 right_branch(5),
% 21.42/21.60 right_branch(3)
% 21.42/21.60 )).
% 21.42/21.60 % SZS output end Proof for theBenchmark
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