TSTP Solution File: SET611+3 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SET611+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 : n024.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 14:32:05 EDT 2024
% Result : Theorem 189.52s 189.70s
% Output : Proof 189.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET611+3 : TPTP v8.1.2. Released v2.2.0.
% 0.08/0.12 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.33 % Computer : n024.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 21:52:31 EDT 2024
% 0.12/0.33 % CPUTime :
% 189.52/189.70 % SZS status Theorem for theBenchmark
% 189.52/189.70 % SZS output start Proof for theBenchmark
% 189.52/189.70
% 189.52/189.70 % Formula: member_equal ( axiom ) converted to clauses:
% 189.52/189.70 cnf(member_equal-1, axiom, ( ( _u2 = _u1) | member(skolem1(_u2, _u1), _u2) | member(skolem2(_u2, _u1), _u1) )).
% 189.52/189.70 cnf(member_equal-2, axiom, ( ( _u2 = _u1) | member(skolem1(_u2, _u1), _u2) | ~member(skolem2(_u2, _u1), _u2) )).
% 189.52/189.70 cnf(member_equal-3, axiom, ( ( _u2 = _u1) | ~member(skolem1(_u2, _u1), _u1) | member(skolem2(_u2, _u1), _u1) )).
% 189.52/189.70 cnf(member_equal-4, axiom, ( ( _u2 = _u1) | ~member(skolem1(_u2, _u1), _u1) | ~member(skolem2(_u2, _u1), _u2) )).
% 189.52/189.70
% 189.52/189.70 % Formula: intersection_defn ( axiom ) converted to clauses:
% 189.52/189.70 cnf(intersection_defn-1, axiom, ( ~member(_u8, intersection(_u12, _u10)) | member(_u8, _u12) )).
% 189.52/189.70 cnf(intersection_defn-2, axiom, ( ~member(_u8, intersection(_u12, _u10)) | member(_u8, _u10) )).
% 189.52/189.70 cnf(intersection_defn-3, axiom, ( ~member(_u9, _u13) | ~member(_u9, _u11) | member(_u9, intersection(_u13, _u11)) )).
% 189.52/189.70
% 189.52/189.70 % Formula: difference_defn ( axiom ) converted to clauses:
% 189.52/189.70 cnf(difference_defn-1, axiom, ( ~member(_u17, difference(_u21, _u19)) | member(_u17, _u21) )).
% 189.52/189.70 cnf(difference_defn-2, axiom, ( ~member(_u17, difference(_u21, _u19)) | ~member(_u17, _u19) )).
% 189.52/189.70 cnf(difference_defn-3, axiom, ( ~member(_u18, _u22) | member(_u18, _u20) | member(_u18, difference(_u22, _u20)) )).
% 189.52/189.70
% 189.52/189.70 % Formula: empty_set_defn ( axiom ) converted to clauses:
% 189.52/189.70 cnf(empty_set_defn-1, axiom, ( ~member(_u23, empty_set) )).
% 189.52/189.70
% 189.52/189.70 % Formula: equal_defn ( axiom ) converted to clauses:
% 189.52/189.70 cnf(equal_defn-1, axiom, ( ( _u28 != _u26) | subset(_u28, _u26) )).
% 189.52/189.70 cnf(equal_defn-2, axiom, ( ( _u28 != _u26) | subset(_u26, _u28) )).
% 189.52/189.70 cnf(equal_defn-3, axiom, ( ~subset(_u29, _u27) | ~subset(_u27, _u29) | ( _u29 = _u27) )).
% 189.52/189.70
% 189.52/189.70 % Formula: commutativity_of_intersection ( axiom ) converted to clauses:
% 189.52/189.70 cnf(commutativity_of_intersection-1, axiom, ( ( intersection(_u31, _u30) = intersection(_u30, _u31)) )).
% 189.52/189.70
% 189.52/189.70 % Formula: equal_member_defn ( axiom ) converted to clauses:
% 189.52/189.70 cnf(equal_member_defn-1, axiom, ( ( _u42 != _u40) | ~member(_u36, _u42) | member(_u36, _u40) )).
% 189.52/189.70 cnf(equal_member_defn-2, axiom, ( ( _u42 != _u40) | ~member(_u37, _u40) | member(_u37, _u42) )).
% 189.52/189.70 cnf(equal_member_defn-3, axiom, ( ( _u43 = _u41) | member(skolem3(_u43, _u41), _u43) | member(skolem4(_u43, _u41), _u41) )).
% 189.52/189.70 cnf(equal_member_defn-4, axiom, ( ( _u43 = _u41) | member(skolem3(_u43, _u41), _u43) | ~member(skolem4(_u43, _u41), _u43) )).
% 189.52/189.70 cnf(equal_member_defn-5, axiom, ( ( _u43 = _u41) | ~member(skolem3(_u43, _u41), _u41) | member(skolem4(_u43, _u41), _u41) )).
% 189.52/189.70 cnf(equal_member_defn-6, axiom, ( ( _u43 = _u41) | ~member(skolem3(_u43, _u41), _u41) | ~member(skolem4(_u43, _u41), _u43) )).
% 189.52/189.70
% 189.52/189.70 % Formula: subset_defn ( axiom ) converted to clauses:
% 189.52/189.70 cnf(subset_defn-1, axiom, ( ~subset(_u50, _u48) | ~member(_u44, _u50) | member(_u44, _u48) )).
% 189.52/189.70 cnf(subset_defn-2, axiom, ( subset(_u51, _u49) | member(skolem5(_u51, _u49), _u51) )).
% 189.52/189.70 cnf(subset_defn-3, axiom, ( subset(_u51, _u49) | ~member(skolem5(_u51, _u49), _u49) )).
% 189.52/189.70
% 189.52/189.70 % Formula: reflexivity_of_subset ( axiom ) converted to clauses:
% 189.52/189.70 cnf(reflexivity_of_subset-1, axiom, ( subset(_u52, _u52) )).
% 189.52/189.70
% 189.52/189.70 % Formula: empty_defn ( axiom ) converted to clauses:
% 189.52/189.70 cnf(empty_defn-1, axiom, ( ~empty(_u56) | ~member(_u53, _u56) )).
% 189.52/189.70 cnf(empty_defn-2, axiom, ( member(skolem6(_u57), _u57) | empty(_u57) )).
% 189.52/189.70
% 189.52/189.70 % Formula: prove_th84 ( conjecture ) (definitionally) converted to clauses:
% 189.52/189.70 cnf(prove_th84-1, negated_conjecture, ( ~_def0 | ~_def1 )).
% 189.52/189.70 cnf(prove_th84-2, negated_conjecture, ( _def0 | ( intersection(skolem7, skolem8) = empty_set) )).
% 189.52/189.70 cnf(prove_th84-3, negated_conjecture, ( _def0 | ( difference(skolem7, skolem8) != skolem7) )).
% 189.52/189.70 cnf(prove_th84-4, negated_conjecture, ( _def1 | ( difference(skolem7, skolem8) = skolem7) )).
% 189.52/189.70 cnf(prove_th84-5, negated_conjecture, ( _def1 | ( intersection(skolem7, skolem8) != empty_set) )).
% 189.52/189.70
% 189.52/189.70 % Problem matrix:
% 189.52/189.70 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 189.52/189.70 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 189.52/189.70 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 189.52/189.70 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( intersection(__eqx_0, __eqx_1) = intersection(__eqy_0, __eqy_1)) )).
% 189.52/189.70 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( difference(__eqx_0, __eqx_1) = difference(__eqy_0, __eqy_1)) )).
% 189.52/189.70 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 189.52/189.70 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem2(__eqx_0, __eqx_1) = skolem2(__eqy_0, __eqy_1)) )).
% 189.52/189.70 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem3(__eqx_0, __eqx_1) = skolem3(__eqy_0, __eqy_1)) )).
% 189.52/189.70 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem4(__eqx_0, __eqx_1) = skolem4(__eqy_0, __eqy_1)) )).
% 189.52/189.70 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem5(__eqx_0, __eqx_1) = skolem5(__eqy_0, __eqy_1)) )).
% 189.52/189.70 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( skolem6(__eqx_0) = skolem6(__eqy_0)) )).
% 189.52/189.70 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~member(__eqx_0, __eqx_1) | member(__eqy_0, __eqy_1) )).
% 189.52/189.70 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 189.52/189.70 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 189.52/189.70 cnf(matrix-14, plain, ( ( _u2 = _u1) | member(skolem1(_u2, _u1), _u2) | member(skolem2(_u2, _u1), _u1) )).
% 189.52/189.70 cnf(matrix-15, plain, ( ( _u2 = _u1) | member(skolem1(_u2, _u1), _u2) | ~member(skolem2(_u2, _u1), _u2) )).
% 189.52/189.70 cnf(matrix-16, plain, ( ( _u2 = _u1) | ~member(skolem1(_u2, _u1), _u1) | member(skolem2(_u2, _u1), _u1) )).
% 189.52/189.70 cnf(matrix-17, plain, ( ( _u2 = _u1) | ~member(skolem1(_u2, _u1), _u1) | ~member(skolem2(_u2, _u1), _u2) )).
% 189.52/189.70 cnf(matrix-18, plain, ( ~member(_u8, intersection(_u12, _u10)) | member(_u8, _u12) )).
% 189.52/189.70 cnf(matrix-19, plain, ( ~member(_u8, intersection(_u12, _u10)) | member(_u8, _u10) )).
% 189.52/189.70 cnf(matrix-20, plain, ( ~member(_u9, _u13) | ~member(_u9, _u11) | member(_u9, intersection(_u13, _u11)) )).
% 189.52/189.70 cnf(matrix-21, plain, ( ~member(_u17, difference(_u21, _u19)) | member(_u17, _u21) )).
% 189.52/189.70 cnf(matrix-22, plain, ( ~member(_u17, difference(_u21, _u19)) | ~member(_u17, _u19) )).
% 189.52/189.70 cnf(matrix-23, plain, ( ~member(_u18, _u22) | member(_u18, _u20) | member(_u18, difference(_u22, _u20)) )).
% 189.52/189.70 cnf(matrix-24, plain, ( ~member(_u23, empty_set) )).
% 189.52/189.70 cnf(matrix-25, plain, ( ( _u28 != _u26) | subset(_u28, _u26) )).
% 189.52/189.70 cnf(matrix-26, plain, ( ( _u28 != _u26) | subset(_u26, _u28) )).
% 189.52/189.70 cnf(matrix-27, plain, ( ~subset(_u29, _u27) | ~subset(_u27, _u29) | ( _u29 = _u27) )).
% 189.52/189.70 cnf(matrix-28, plain, ( ( intersection(_u31, _u30) = intersection(_u30, _u31)) )).
% 189.52/189.70 cnf(matrix-29, plain, ( ( _u42 != _u40) | ~member(_u36, _u42) | member(_u36, _u40) )).
% 189.52/189.70 cnf(matrix-30, plain, ( ( _u42 != _u40) | ~member(_u37, _u40) | member(_u37, _u42) )).
% 189.52/189.70 cnf(matrix-31, plain, ( ( _u43 = _u41) | member(skolem3(_u43, _u41), _u43) | member(skolem4(_u43, _u41), _u41) )).
% 189.52/189.70 cnf(matrix-32, plain, ( ( _u43 = _u41) | member(skolem3(_u43, _u41), _u43) | ~member(skolem4(_u43, _u41), _u43) )).
% 189.52/189.70 cnf(matrix-33, plain, ( ( _u43 = _u41) | ~member(skolem3(_u43, _u41), _u41) | member(skolem4(_u43, _u41), _u41) )).
% 189.52/189.70 cnf(matrix-34, plain, ( ( _u43 = _u41) | ~member(skolem3(_u43, _u41), _u41) | ~member(skolem4(_u43, _u41), _u43) )).
% 189.52/189.70 cnf(matrix-35, plain, ( ~subset(_u50, _u48) | ~member(_u44, _u50) | member(_u44, _u48) )).
% 189.52/189.70 cnf(matrix-36, plain, ( subset(_u51, _u49) | member(skolem5(_u51, _u49), _u51) )).
% 189.52/189.70 cnf(matrix-37, plain, ( subset(_u51, _u49) | ~member(skolem5(_u51, _u49), _u49) )).
% 189.52/189.70 cnf(matrix-38, plain, ( subset(_u52, _u52) )).
% 189.52/189.70 cnf(matrix-39, plain, ( ~empty(_u56) | ~member(_u53, _u56) )).
% 189.52/189.70 cnf(matrix-40, plain, ( member(skolem6(_u57), _u57) | empty(_u57) )).
% 189.52/189.70 cnf(matrix-41, plain, ( ~_def0 | ~_def1 )).
% 189.52/189.70 cnf(matrix-42, plain, ( _def0 | ( intersection(skolem7, skolem8) = empty_set) )).
% 189.52/189.70 cnf(matrix-43, plain, ( _def0 | ( difference(skolem7, skolem8) != skolem7) )).
% 189.52/189.70 cnf(matrix-44, plain, ( _def1 | ( difference(skolem7, skolem8) = skolem7) )).
% 189.52/189.70 cnf(matrix-45, plain, ( _def1 | ( intersection(skolem7, skolem8) != empty_set) )).
% 189.52/189.70
% 189.52/189.70 % Proof stack:
% 189.52/189.70 cnf(proof-stack, plain,
% 189.52/189.70 proof_stack(
% 189.52/189.70 start(41),
% 189.52/189.70 left_branch(0, 43, 0, 2),
% 189.52/189.70 left_branch(0, 33, 0, 3),
% 189.52/189.70 left_branch(0, 23, 0, 4),
% 189.52/189.70 left_branch(0, 34, 2, 5),
% 189.52/189.70 reduction(0, 1),
% 189.52/189.70 left_branch(0, 21, 1, 7),
% 189.52/189.70 left_branch(0, 32, 1, 8),
% 189.52/189.70 lemmata(0, 0),
% 189.52/189.70 reduction(0, 3),
% 189.52/189.70 right_branch(8),
% 189.52/189.70 right_branch(7),
% 189.52/189.70 right_branch(5),
% 189.52/189.70 left_branch(0, 20, 0, 6),
% 189.52/189.70 left_branch(0, 30, 1, 7),
% 189.52/189.70 left_branch(0, 28, 0, 8),
% 189.52/189.70 right_branch(8),
% 189.52/189.70 left_branch(0, 18, 0, 9),
% 189.52/189.70 left_branch(0, 24, 0, 10),
% 189.52/189.70 right_branch(10),
% 189.52/189.70 right_branch(9),
% 189.52/189.70 right_branch(7),
% 189.52/189.70 left_branch(0, 29, 2, 8),
% 189.52/189.70 left_branch(0, 42, 1, 9),
% 189.52/189.70 reduction(0, 0),
% 189.52/189.70 right_branch(9),
% 189.52/189.70 left_branch(0, 20, 2, 10),
% 189.52/189.70 reduction(0, 2),
% 189.52/189.70 reduction(0, 3),
% 189.52/189.70 right_branch(10),
% 189.52/189.70 right_branch(8),
% 189.52/189.70 right_branch(6),
% 189.52/189.70 right_branch(4),
% 189.52/189.70 left_branch(0, 23, 1, 5),
% 189.52/189.70 left_branch(0, 32, 1, 6),
% 189.52/189.70 reduction(0, 1),
% 189.52/189.70 left_branch(0, 23, 1, 8),
% 189.52/189.70 left_branch(0, 31, 2, 9),
% 189.52/189.70 lemmata(0, 1),
% 189.52/189.70 reduction(0, 3),
% 189.52/189.70 right_branch(9),
% 189.52/189.70 left_branch(0, 21, 0, 10),
% 189.52/189.70 lemmata(0, 0),
% 189.52/189.70 right_branch(10),
% 189.52/189.70 right_branch(8),
% 189.52/189.70 right_branch(6),
% 189.52/189.70 left_branch(0, 21, 0, 7),
% 189.52/189.70 left_branch(0, 21, 0, 8),
% 189.52/189.70 reduction(0, 2),
% 189.52/189.70 right_branch(8),
% 189.52/189.70 right_branch(7),
% 189.52/189.70 right_branch(5),
% 189.52/189.70 right_branch(3),
% 189.52/189.70 right_branch(2),
% 189.52/189.70 left_branch(0, 45, 0, 3),
% 189.52/189.70 left_branch(0, 31, 0, 4),
% 189.52/189.70 left_branch(0, 39, 1, 5),
% 189.52/189.70 left_branch(0, 40, 1, 6),
% 189.52/189.70 left_branch(0, 24, 0, 7),
% 189.52/189.70 right_branch(7),
% 189.52/189.70 right_branch(6),
% 189.52/189.70 right_branch(5),
% 189.52/189.70 left_branch(0, 19, 0, 6),
% 189.52/189.70 left_branch(0, 22, 1, 7),
% 189.52/189.70 left_branch(0, 30, 2, 8),
% 189.52/189.70 left_branch(0, 44, 1, 9),
% 189.52/189.70 reduction(0, 0),
% 189.52/189.70 right_branch(9),
% 189.52/189.70 left_branch(0, 18, 1, 10),
% 189.52/189.70 reduction(0, 2),
% 189.52/189.70 right_branch(10),
% 189.52/189.70 right_branch(8),
% 189.52/189.70 right_branch(7),
% 189.52/189.70 right_branch(6),
% 189.52/189.70 right_branch(4),
% 189.52/189.70 right_branch(3)
% 189.52/189.70 )).
% 189.52/189.70 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------