TSTP Solution File: SET008+3 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SET008+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 : n014.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 14:30:39 EDT 2024
% Result : Theorem 5.92s 6.09s
% Output : Proof 5.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET008+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Mar 20 22:08:00 EDT 2024
% 0.13/0.34 % CPUTime :
% 5.92/6.09 % SZS status Theorem for theBenchmark
% 5.92/6.09 % SZS output start Proof for theBenchmark
% 5.92/6.09
% 5.92/6.09 % Formula: intersection_defn ( axiom ) converted to clauses:
% 5.92/6.09 cnf(intersection_defn-1, axiom, ( ~member(_u3, intersection(_u7, _u5)) | member(_u3, _u7) )).
% 5.92/6.09 cnf(intersection_defn-2, axiom, ( ~member(_u3, intersection(_u7, _u5)) | member(_u3, _u5) )).
% 5.92/6.09 cnf(intersection_defn-3, axiom, ( ~member(_u4, _u8) | ~member(_u4, _u6) | member(_u4, intersection(_u8, _u6)) )).
% 5.92/6.09
% 5.92/6.09 % Formula: difference_defn ( axiom ) converted to clauses:
% 5.92/6.09 cnf(difference_defn-1, axiom, ( ~member(_u12, difference(_u16, _u14)) | member(_u12, _u16) )).
% 5.92/6.09 cnf(difference_defn-2, axiom, ( ~member(_u12, difference(_u16, _u14)) | ~member(_u12, _u14) )).
% 5.92/6.09 cnf(difference_defn-3, axiom, ( ~member(_u13, _u17) | member(_u13, _u15) | member(_u13, difference(_u17, _u15)) )).
% 5.92/6.09
% 5.92/6.09 % Formula: empty_set_defn ( axiom ) converted to clauses:
% 5.92/6.09 cnf(empty_set_defn-1, axiom, ( ~member(_u18, empty_set) )).
% 5.92/6.09
% 5.92/6.09 % Formula: equal_defn ( axiom ) converted to clauses:
% 5.92/6.09 cnf(equal_defn-1, axiom, ( ( _u23 != _u21) | subset(_u23, _u21) )).
% 5.92/6.09 cnf(equal_defn-2, axiom, ( ( _u23 != _u21) | subset(_u21, _u23) )).
% 5.92/6.09 cnf(equal_defn-3, axiom, ( ~subset(_u24, _u22) | ~subset(_u22, _u24) | ( _u24 = _u22) )).
% 5.92/6.09
% 5.92/6.09 % Formula: commutativity_of_intersection ( axiom ) converted to clauses:
% 5.92/6.09 cnf(commutativity_of_intersection-1, axiom, ( ( intersection(_u26, _u25) = intersection(_u25, _u26)) )).
% 5.92/6.09
% 5.92/6.09 % Formula: subset_defn ( axiom ) converted to clauses:
% 5.92/6.09 cnf(subset_defn-1, axiom, ( ~subset(_u33, _u31) | ~member(_u27, _u33) | member(_u27, _u31) )).
% 5.92/6.09 cnf(subset_defn-2, axiom, ( subset(_u34, _u32) | member(skolem1(_u34, _u32), _u34) )).
% 5.92/6.09 cnf(subset_defn-3, axiom, ( subset(_u34, _u32) | ~member(skolem1(_u34, _u32), _u32) )).
% 5.92/6.09
% 5.92/6.09 % Formula: reflexivity_of_subset ( axiom ) converted to clauses:
% 5.92/6.09 cnf(reflexivity_of_subset-1, axiom, ( subset(_u35, _u35) )).
% 5.92/6.09
% 5.92/6.09 % Formula: empty_defn ( axiom ) converted to clauses:
% 5.92/6.09 cnf(empty_defn-1, axiom, ( ~empty(_u39) | ~member(_u36, _u39) )).
% 5.92/6.09 cnf(empty_defn-2, axiom, ( member(skolem2(_u40), _u40) | empty(_u40) )).
% 5.92/6.09
% 5.92/6.09 % Formula: equal_member_defn ( axiom ) converted to clauses:
% 5.92/6.09 cnf(equal_member_defn-1, axiom, ( ( _u51 != _u49) | ~member(_u45, _u51) | member(_u45, _u49) )).
% 5.92/6.09 cnf(equal_member_defn-2, axiom, ( ( _u51 != _u49) | ~member(_u46, _u49) | member(_u46, _u51) )).
% 5.92/6.09 cnf(equal_member_defn-3, axiom, ( ( _u52 = _u50) | member(skolem3(_u52, _u50), _u52) | member(skolem4(_u52, _u50), _u50) )).
% 5.92/6.09 cnf(equal_member_defn-4, axiom, ( ( _u52 = _u50) | member(skolem3(_u52, _u50), _u52) | ~member(skolem4(_u52, _u50), _u52) )).
% 5.92/6.09 cnf(equal_member_defn-5, axiom, ( ( _u52 = _u50) | ~member(skolem3(_u52, _u50), _u50) | member(skolem4(_u52, _u50), _u50) )).
% 5.92/6.09 cnf(equal_member_defn-6, axiom, ( ( _u52 = _u50) | ~member(skolem3(_u52, _u50), _u50) | ~member(skolem4(_u52, _u50), _u52) )).
% 5.92/6.09
% 5.92/6.09 % Formula: prove_intersection_difference_empty_set ( conjecture ) (definitionally) converted to clauses:
% 5.92/6.09 cnf(prove_intersection_difference_empty_set-1, negated_conjecture, ( ( intersection(difference(skolem5, skolem6), skolem6) != empty_set) )).
% 5.92/6.09
% 5.92/6.09 % Problem matrix:
% 5.92/6.09 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 5.92/6.09 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 5.92/6.09 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 5.92/6.09 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( intersection(__eqx_0, __eqx_1) = intersection(__eqy_0, __eqy_1)) )).
% 5.92/6.09 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( difference(__eqx_0, __eqx_1) = difference(__eqy_0, __eqy_1)) )).
% 5.92/6.09 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 5.92/6.09 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( skolem2(__eqx_0) = skolem2(__eqy_0)) )).
% 5.92/6.09 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem3(__eqx_0, __eqx_1) = skolem3(__eqy_0, __eqy_1)) )).
% 5.92/6.09 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem4(__eqx_0, __eqx_1) = skolem4(__eqy_0, __eqy_1)) )).
% 5.92/6.09 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~member(__eqx_0, __eqx_1) | member(__eqy_0, __eqy_1) )).
% 5.92/6.09 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 5.92/6.09 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 5.92/6.09 cnf(matrix-12, plain, ( ~member(_u3, intersection(_u7, _u5)) | member(_u3, _u7) )).
% 5.92/6.09 cnf(matrix-13, plain, ( ~member(_u3, intersection(_u7, _u5)) | member(_u3, _u5) )).
% 5.92/6.09 cnf(matrix-14, plain, ( ~member(_u4, _u8) | ~member(_u4, _u6) | member(_u4, intersection(_u8, _u6)) )).
% 5.92/6.09 cnf(matrix-15, plain, ( ~member(_u12, difference(_u16, _u14)) | member(_u12, _u16) )).
% 5.92/6.09 cnf(matrix-16, plain, ( ~member(_u12, difference(_u16, _u14)) | ~member(_u12, _u14) )).
% 5.92/6.09 cnf(matrix-17, plain, ( ~member(_u13, _u17) | member(_u13, _u15) | member(_u13, difference(_u17, _u15)) )).
% 5.92/6.09 cnf(matrix-18, plain, ( ~member(_u18, empty_set) )).
% 5.92/6.09 cnf(matrix-19, plain, ( ( _u23 != _u21) | subset(_u23, _u21) )).
% 5.92/6.09 cnf(matrix-20, plain, ( ( _u23 != _u21) | subset(_u21, _u23) )).
% 5.92/6.09 cnf(matrix-21, plain, ( ~subset(_u24, _u22) | ~subset(_u22, _u24) | ( _u24 = _u22) )).
% 5.92/6.09 cnf(matrix-22, plain, ( ( intersection(_u26, _u25) = intersection(_u25, _u26)) )).
% 5.92/6.09 cnf(matrix-23, plain, ( ~subset(_u33, _u31) | ~member(_u27, _u33) | member(_u27, _u31) )).
% 5.92/6.09 cnf(matrix-24, plain, ( subset(_u34, _u32) | member(skolem1(_u34, _u32), _u34) )).
% 5.92/6.09 cnf(matrix-25, plain, ( subset(_u34, _u32) | ~member(skolem1(_u34, _u32), _u32) )).
% 5.92/6.09 cnf(matrix-26, plain, ( subset(_u35, _u35) )).
% 5.92/6.09 cnf(matrix-27, plain, ( ~empty(_u39) | ~member(_u36, _u39) )).
% 5.92/6.09 cnf(matrix-28, plain, ( member(skolem2(_u40), _u40) | empty(_u40) )).
% 5.92/6.09 cnf(matrix-29, plain, ( ( _u51 != _u49) | ~member(_u45, _u51) | member(_u45, _u49) )).
% 5.92/6.09 cnf(matrix-30, plain, ( ( _u51 != _u49) | ~member(_u46, _u49) | member(_u46, _u51) )).
% 5.92/6.09 cnf(matrix-31, plain, ( ( _u52 = _u50) | member(skolem3(_u52, _u50), _u52) | member(skolem4(_u52, _u50), _u50) )).
% 5.92/6.09 cnf(matrix-32, plain, ( ( _u52 = _u50) | member(skolem3(_u52, _u50), _u52) | ~member(skolem4(_u52, _u50), _u52) )).
% 5.92/6.09 cnf(matrix-33, plain, ( ( _u52 = _u50) | ~member(skolem3(_u52, _u50), _u50) | member(skolem4(_u52, _u50), _u50) )).
% 5.92/6.09 cnf(matrix-34, plain, ( ( _u52 = _u50) | ~member(skolem3(_u52, _u50), _u50) | ~member(skolem4(_u52, _u50), _u52) )).
% 5.92/6.09 cnf(matrix-35, plain, ( ( intersection(difference(skolem5, skolem6), skolem6) != empty_set) )).
% 5.92/6.09
% 5.92/6.09 % Proof stack:
% 5.92/6.09 cnf(proof-stack, plain,
% 5.92/6.09 proof_stack(
% 5.92/6.09 start(18),
% 5.92/6.09 left_branch(0, 31, 2, 2),
% 5.92/6.09 left_branch(0, 35, 0, 3),
% 5.92/6.09 right_branch(3),
% 5.92/6.09 left_branch(0, 13, 0, 4),
% 5.92/6.09 left_branch(0, 16, 1, 5),
% 5.92/6.09 left_branch(0, 12, 1, 6),
% 5.92/6.09 reduction(0, 1),
% 5.92/6.09 right_branch(6),
% 5.92/6.09 right_branch(5),
% 5.92/6.09 right_branch(4),
% 5.92/6.09 right_branch(2)
% 5.92/6.09 )).
% 5.92/6.09 % SZS output end Proof for theBenchmark
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