TSTP Solution File: SET587+3 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SET587+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 : n002.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 14:31:57 EDT 2024
% Result : Theorem 17.70s 17.86s
% Output : Proof 17.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET587+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.33 % Computer : n002.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Mar 20 21:35:08 EDT 2024
% 0.13/0.34 % CPUTime :
% 17.70/17.86 % SZS status Theorem for theBenchmark
% 17.70/17.86 % SZS output start Proof for theBenchmark
% 17.70/17.86
% 17.70/17.86 % Formula: member_equal ( axiom ) converted to clauses:
% 17.70/17.86 cnf(member_equal-1, axiom, ( ( _u2 = _u1) | member(skolem1(_u2, _u1), _u2) | member(skolem2(_u2, _u1), _u1) )).
% 17.70/17.86 cnf(member_equal-2, axiom, ( ( _u2 = _u1) | member(skolem1(_u2, _u1), _u2) | ~member(skolem2(_u2, _u1), _u2) )).
% 17.70/17.86 cnf(member_equal-3, axiom, ( ( _u2 = _u1) | ~member(skolem1(_u2, _u1), _u1) | member(skolem2(_u2, _u1), _u1) )).
% 17.70/17.86 cnf(member_equal-4, axiom, ( ( _u2 = _u1) | ~member(skolem1(_u2, _u1), _u1) | ~member(skolem2(_u2, _u1), _u2) )).
% 17.70/17.86
% 17.70/17.86 % Formula: difference_defn ( axiom ) converted to clauses:
% 17.70/17.86 cnf(difference_defn-1, axiom, ( ~member(_u8, difference(_u12, _u10)) | member(_u8, _u12) )).
% 17.70/17.86 cnf(difference_defn-2, axiom, ( ~member(_u8, difference(_u12, _u10)) | ~member(_u8, _u10) )).
% 17.70/17.86 cnf(difference_defn-3, axiom, ( ~member(_u9, _u13) | member(_u9, _u11) | member(_u9, difference(_u13, _u11)) )).
% 17.70/17.86
% 17.70/17.86 % Formula: empty_set_defn ( axiom ) converted to clauses:
% 17.70/17.86 cnf(empty_set_defn-1, axiom, ( ~member(_u14, empty_set) )).
% 17.70/17.86
% 17.70/17.86 % Formula: subset_defn ( axiom ) converted to clauses:
% 17.70/17.86 cnf(subset_defn-1, axiom, ( ~subset(_u21, _u19) | ~member(_u15, _u21) | member(_u15, _u19) )).
% 17.70/17.86 cnf(subset_defn-2, axiom, ( subset(_u22, _u20) | member(skolem3(_u22, _u20), _u22) )).
% 17.70/17.86 cnf(subset_defn-3, axiom, ( subset(_u22, _u20) | ~member(skolem3(_u22, _u20), _u20) )).
% 17.70/17.86
% 17.70/17.86 % Formula: equal_defn ( axiom ) converted to clauses:
% 17.70/17.86 cnf(equal_defn-1, axiom, ( ( _u27 != _u25) | subset(_u27, _u25) )).
% 17.70/17.86 cnf(equal_defn-2, axiom, ( ( _u27 != _u25) | subset(_u25, _u27) )).
% 17.70/17.86 cnf(equal_defn-3, axiom, ( ~subset(_u28, _u26) | ~subset(_u26, _u28) | ( _u28 = _u26) )).
% 17.70/17.86
% 17.70/17.86 % Formula: equal_member_defn ( axiom ) converted to clauses:
% 17.70/17.86 cnf(equal_member_defn-1, axiom, ( ( _u39 != _u37) | ~member(_u33, _u39) | member(_u33, _u37) )).
% 17.70/17.86 cnf(equal_member_defn-2, axiom, ( ( _u39 != _u37) | ~member(_u34, _u37) | member(_u34, _u39) )).
% 17.70/17.86 cnf(equal_member_defn-3, axiom, ( ( _u40 = _u38) | member(skolem4(_u40, _u38), _u40) | member(skolem5(_u40, _u38), _u38) )).
% 17.70/17.86 cnf(equal_member_defn-4, axiom, ( ( _u40 = _u38) | member(skolem4(_u40, _u38), _u40) | ~member(skolem5(_u40, _u38), _u40) )).
% 17.70/17.86 cnf(equal_member_defn-5, axiom, ( ( _u40 = _u38) | ~member(skolem4(_u40, _u38), _u38) | member(skolem5(_u40, _u38), _u38) )).
% 17.70/17.86 cnf(equal_member_defn-6, axiom, ( ( _u40 = _u38) | ~member(skolem4(_u40, _u38), _u38) | ~member(skolem5(_u40, _u38), _u40) )).
% 17.70/17.86
% 17.70/17.86 % Formula: reflexivity_of_subset ( axiom ) converted to clauses:
% 17.70/17.86 cnf(reflexivity_of_subset-1, axiom, ( subset(_u41, _u41) )).
% 17.70/17.86
% 17.70/17.86 % Formula: empty_defn ( axiom ) converted to clauses:
% 17.70/17.86 cnf(empty_defn-1, axiom, ( ~empty(_u45) | ~member(_u42, _u45) )).
% 17.70/17.86 cnf(empty_defn-2, axiom, ( member(skolem6(_u46), _u46) | empty(_u46) )).
% 17.70/17.86
% 17.70/17.86 % Formula: prove_difference_empty_set ( conjecture ) (definitionally) converted to clauses:
% 17.70/17.86 cnf(prove_difference_empty_set-1, negated_conjecture, ( ~_def0 | ~_def1 )).
% 17.70/17.86 cnf(prove_difference_empty_set-2, negated_conjecture, ( _def0 | ( difference(skolem7, skolem8) = empty_set) )).
% 17.70/17.86 cnf(prove_difference_empty_set-3, negated_conjecture, ( _def0 | ~subset(skolem7, skolem8) )).
% 17.70/17.86 cnf(prove_difference_empty_set-4, negated_conjecture, ( _def1 | subset(skolem7, skolem8) )).
% 17.70/17.86 cnf(prove_difference_empty_set-5, negated_conjecture, ( _def1 | ( difference(skolem7, skolem8) != empty_set) )).
% 17.70/17.86
% 17.70/17.86 % Problem matrix:
% 17.70/17.86 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 17.70/17.86 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 17.70/17.86 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 17.70/17.86 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( difference(__eqx_0, __eqx_1) = difference(__eqy_0, __eqy_1)) )).
% 17.70/17.86 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 17.70/17.86 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem2(__eqx_0, __eqx_1) = skolem2(__eqy_0, __eqy_1)) )).
% 17.70/17.86 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem3(__eqx_0, __eqx_1) = skolem3(__eqy_0, __eqy_1)) )).
% 17.70/17.86 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem4(__eqx_0, __eqx_1) = skolem4(__eqy_0, __eqy_1)) )).
% 17.70/17.86 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem5(__eqx_0, __eqx_1) = skolem5(__eqy_0, __eqy_1)) )).
% 17.70/17.86 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( skolem6(__eqx_0) = skolem6(__eqy_0)) )).
% 17.70/17.86 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~member(__eqx_0, __eqx_1) | member(__eqy_0, __eqy_1) )).
% 17.70/17.86 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 17.70/17.86 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 17.70/17.86 cnf(matrix-13, plain, ( ( _u2 = _u1) | member(skolem1(_u2, _u1), _u2) | member(skolem2(_u2, _u1), _u1) )).
% 17.70/17.86 cnf(matrix-14, plain, ( ( _u2 = _u1) | member(skolem1(_u2, _u1), _u2) | ~member(skolem2(_u2, _u1), _u2) )).
% 17.70/17.86 cnf(matrix-15, plain, ( ( _u2 = _u1) | ~member(skolem1(_u2, _u1), _u1) | member(skolem2(_u2, _u1), _u1) )).
% 17.70/17.86 cnf(matrix-16, plain, ( ( _u2 = _u1) | ~member(skolem1(_u2, _u1), _u1) | ~member(skolem2(_u2, _u1), _u2) )).
% 17.70/17.86 cnf(matrix-17, plain, ( ~member(_u8, difference(_u12, _u10)) | member(_u8, _u12) )).
% 17.70/17.86 cnf(matrix-18, plain, ( ~member(_u8, difference(_u12, _u10)) | ~member(_u8, _u10) )).
% 17.70/17.86 cnf(matrix-19, plain, ( ~member(_u9, _u13) | member(_u9, _u11) | member(_u9, difference(_u13, _u11)) )).
% 17.70/17.86 cnf(matrix-20, plain, ( ~member(_u14, empty_set) )).
% 17.70/17.86 cnf(matrix-21, plain, ( ~subset(_u21, _u19) | ~member(_u15, _u21) | member(_u15, _u19) )).
% 17.70/17.86 cnf(matrix-22, plain, ( subset(_u22, _u20) | member(skolem3(_u22, _u20), _u22) )).
% 17.70/17.86 cnf(matrix-23, plain, ( subset(_u22, _u20) | ~member(skolem3(_u22, _u20), _u20) )).
% 17.70/17.86 cnf(matrix-24, plain, ( ( _u27 != _u25) | subset(_u27, _u25) )).
% 17.70/17.86 cnf(matrix-25, plain, ( ( _u27 != _u25) | subset(_u25, _u27) )).
% 17.70/17.86 cnf(matrix-26, plain, ( ~subset(_u28, _u26) | ~subset(_u26, _u28) | ( _u28 = _u26) )).
% 17.70/17.86 cnf(matrix-27, plain, ( ( _u39 != _u37) | ~member(_u33, _u39) | member(_u33, _u37) )).
% 17.70/17.86 cnf(matrix-28, plain, ( ( _u39 != _u37) | ~member(_u34, _u37) | member(_u34, _u39) )).
% 17.70/17.86 cnf(matrix-29, plain, ( ( _u40 = _u38) | member(skolem4(_u40, _u38), _u40) | member(skolem5(_u40, _u38), _u38) )).
% 17.70/17.86 cnf(matrix-30, plain, ( ( _u40 = _u38) | member(skolem4(_u40, _u38), _u40) | ~member(skolem5(_u40, _u38), _u40) )).
% 17.70/17.86 cnf(matrix-31, plain, ( ( _u40 = _u38) | ~member(skolem4(_u40, _u38), _u38) | member(skolem5(_u40, _u38), _u38) )).
% 17.70/17.86 cnf(matrix-32, plain, ( ( _u40 = _u38) | ~member(skolem4(_u40, _u38), _u38) | ~member(skolem5(_u40, _u38), _u40) )).
% 17.70/17.86 cnf(matrix-33, plain, ( subset(_u41, _u41) )).
% 17.70/17.86 cnf(matrix-34, plain, ( ~empty(_u45) | ~member(_u42, _u45) )).
% 17.70/17.86 cnf(matrix-35, plain, ( member(skolem6(_u46), _u46) | empty(_u46) )).
% 17.70/17.86 cnf(matrix-36, plain, ( ~_def0 | ~_def1 )).
% 17.70/17.86 cnf(matrix-37, plain, ( _def0 | ( difference(skolem7, skolem8) = empty_set) )).
% 17.70/17.86 cnf(matrix-38, plain, ( _def0 | ~subset(skolem7, skolem8) )).
% 17.70/17.86 cnf(matrix-39, plain, ( _def1 | subset(skolem7, skolem8) )).
% 17.70/17.86 cnf(matrix-40, plain, ( _def1 | ( difference(skolem7, skolem8) != empty_set) )).
% 17.70/17.86
% 17.70/17.86 % Proof stack:
% 17.70/17.86 cnf(proof-stack, plain,
% 17.70/17.86 proof_stack(
% 17.70/17.86 start(36),
% 17.70/17.86 left_branch(0, 38, 0, 2),
% 17.70/17.86 left_branch(0, 23, 0, 3),
% 17.70/17.86 left_branch(0, 19, 1, 4),
% 17.70/17.86 left_branch(0, 22, 1, 5),
% 17.70/17.86 reduction(0, 1),
% 17.70/17.86 right_branch(5),
% 17.70/17.86 left_branch(0, 27, 1, 6),
% 17.70/17.86 left_branch(0, 37, 1, 7),
% 17.70/17.86 reduction(0, 0),
% 17.70/17.86 right_branch(7),
% 17.70/17.86 left_branch(0, 20, 0, 8),
% 17.70/17.86 right_branch(8),
% 17.70/17.86 right_branch(6),
% 17.70/17.86 right_branch(4),
% 17.70/17.86 right_branch(3),
% 17.70/17.86 right_branch(2),
% 17.70/17.86 left_branch(0, 40, 0, 3),
% 17.70/17.86 left_branch(0, 29, 0, 4),
% 17.70/17.86 left_branch(0, 34, 1, 5),
% 17.70/17.86 left_branch(0, 35, 1, 6),
% 17.70/17.86 left_branch(0, 20, 0, 7),
% 17.70/17.86 right_branch(7),
% 17.70/17.86 right_branch(6),
% 17.70/17.86 right_branch(5),
% 17.70/17.86 left_branch(0, 18, 0, 6),
% 17.70/17.86 left_branch(0, 21, 2, 7),
% 17.70/17.86 left_branch(0, 39, 1, 8),
% 17.70/17.86 reduction(0, 0),
% 17.70/17.86 right_branch(8),
% 17.70/17.86 left_branch(0, 17, 1, 9),
% 17.70/17.86 reduction(0, 2),
% 17.70/17.86 right_branch(9),
% 17.70/17.86 right_branch(7),
% 17.70/17.86 right_branch(6),
% 17.70/17.86 right_branch(4),
% 17.70/17.86 right_branch(3)
% 17.70/17.86 )).
% 17.70/17.86 % SZS output end Proof for theBenchmark
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