TSTP Solution File: SET162+3 by ConnectPP---0.2.2
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%------------------------------------------------------------------------------
% File : ConnectPP---0.2.2
% Problem : SET162+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 : n022.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 : Wed Mar 6 09:18:54 EST 2024
% Result : Theorem 5.74s 5.96s
% Output : Proof 5.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET162+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Mar 3 19:54:18 EST 2024
% 0.12/0.34 % CPUTime :
% 5.74/5.96 % SZS status Theorem for theBenchmark
% 5.74/5.96 % SZS output start Proof for theBenchmark
% 5.74/5.96
% 5.74/5.96 % Formula: union_defn ( axiom ) converted to clauses:
% 5.74/5.96 cnf(union_defn-1, axiom, ( ~member(_u3, union(_u7, _u5)) | member(_u3, _u7) | member(_u3, _u5) )).
% 5.74/5.96 cnf(union_defn-2, axiom, ( member(_u4, union(_u8, _u6)) | ~member(_u4, _u8) )).
% 5.74/5.96 cnf(union_defn-3, axiom, ( member(_u4, union(_u8, _u6)) | ~member(_u4, _u6) )).
% 5.74/5.96
% 5.74/5.96 % Formula: empty_set_defn ( axiom ) converted to clauses:
% 5.74/5.96 cnf(empty_set_defn-1, axiom, ( ~member(_u9, empty_set) )).
% 5.74/5.96
% 5.74/5.96 % Formula: equal_defn ( axiom ) converted to clauses:
% 5.74/5.96 cnf(equal_defn-1, axiom, ( ( _u14 != _u12) | subset(_u14, _u12) )).
% 5.74/5.96 cnf(equal_defn-2, axiom, ( ( _u14 != _u12) | subset(_u12, _u14) )).
% 5.74/5.96 cnf(equal_defn-3, axiom, ( ~subset(_u15, _u13) | ~subset(_u13, _u15) | ( _u15 = _u13) )).
% 5.74/5.96
% 5.74/5.96 % Formula: commutativity_of_union ( axiom ) converted to clauses:
% 5.74/5.96 cnf(commutativity_of_union-1, axiom, ( ( union(_u17, _u16) = union(_u16, _u17)) )).
% 5.74/5.96
% 5.74/5.96 % Formula: subset_defn ( axiom ) converted to clauses:
% 5.74/5.96 cnf(subset_defn-1, axiom, ( ~subset(_u24, _u22) | ~member(_u18, _u24) | member(_u18, _u22) )).
% 5.74/5.96 cnf(subset_defn-2, axiom, ( subset(_u25, _u23) | member(skolem1(_u25, _u23), _u25) )).
% 5.74/5.96 cnf(subset_defn-3, axiom, ( subset(_u25, _u23) | ~member(skolem1(_u25, _u23), _u23) )).
% 5.74/5.96
% 5.74/5.96 % Formula: reflexivity_of_subset ( axiom ) converted to clauses:
% 5.74/5.96 cnf(reflexivity_of_subset-1, axiom, ( subset(_u26, _u26) )).
% 5.74/5.96
% 5.74/5.96 % Formula: empty_defn ( axiom ) converted to clauses:
% 5.74/5.96 cnf(empty_defn-1, axiom, ( ~empty(_u30) | ~member(_u27, _u30) )).
% 5.74/5.96 cnf(empty_defn-2, axiom, ( member(skolem2(_u31), _u31) | empty(_u31) )).
% 5.74/5.96
% 5.74/5.96 % Formula: equal_member_defn ( axiom ) converted to clauses:
% 5.74/5.96 cnf(equal_member_defn-1, axiom, ( ( _u42 != _u40) | ~member(_u36, _u42) | member(_u36, _u40) )).
% 5.74/5.96 cnf(equal_member_defn-2, axiom, ( ( _u42 != _u40) | ~member(_u37, _u40) | member(_u37, _u42) )).
% 5.74/5.96 cnf(equal_member_defn-3, axiom, ( ( _u43 = _u41) | member(skolem3(_u43, _u41), _u43) | member(skolem4(_u43, _u41), _u41) )).
% 5.74/5.96 cnf(equal_member_defn-4, axiom, ( ( _u43 = _u41) | member(skolem3(_u43, _u41), _u43) | ~member(skolem4(_u43, _u41), _u43) )).
% 5.74/5.96 cnf(equal_member_defn-5, axiom, ( ( _u43 = _u41) | ~member(skolem3(_u43, _u41), _u41) | member(skolem4(_u43, _u41), _u41) )).
% 5.74/5.96 cnf(equal_member_defn-6, axiom, ( ( _u43 = _u41) | ~member(skolem3(_u43, _u41), _u41) | ~member(skolem4(_u43, _u41), _u43) )).
% 5.74/5.96
% 5.74/5.96 % Formula: prove_union_empty_set ( conjecture ) converted to clauses:
% 5.74/5.96 cnf(prove_union_empty_set-1, negated_conjecture, ( ( union(skolem5, empty_set) != skolem5) )).
% 5.74/5.96
% 5.74/5.96 % Problem matrix:
% 5.74/5.96 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 5.74/5.96 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 5.74/5.96 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 5.74/5.96 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( union(__eqx_0, __eqx_1) = union(__eqy_0, __eqy_1)) )).
% 5.74/5.96 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 5.74/5.96 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( skolem2(__eqx_0) = skolem2(__eqy_0)) )).
% 5.74/5.96 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem3(__eqx_0, __eqx_1) = skolem3(__eqy_0, __eqy_1)) )).
% 5.74/5.96 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem4(__eqx_0, __eqx_1) = skolem4(__eqy_0, __eqy_1)) )).
% 5.74/5.96 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~member(__eqx_0, __eqx_1) | member(__eqy_0, __eqy_1) )).
% 5.74/5.96 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 5.74/5.96 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 5.74/5.96 cnf(matrix-11, plain, ( ~member(_u3, union(_u7, _u5)) | member(_u3, _u7) | member(_u3, _u5) )).
% 5.74/5.96 cnf(matrix-12, plain, ( member(_u4, union(_u8, _u6)) | ~member(_u4, _u8) )).
% 5.74/5.96 cnf(matrix-13, plain, ( member(_u4, union(_u8, _u6)) | ~member(_u4, _u6) )).
% 5.74/5.96 cnf(matrix-14, plain, ( ~member(_u9, empty_set) )).
% 5.74/5.96 cnf(matrix-15, plain, ( ( _u14 != _u12) | subset(_u14, _u12) )).
% 5.74/5.96 cnf(matrix-16, plain, ( ( _u14 != _u12) | subset(_u12, _u14) )).
% 5.74/5.96 cnf(matrix-17, plain, ( ~subset(_u15, _u13) | ~subset(_u13, _u15) | ( _u15 = _u13) )).
% 5.74/5.96 cnf(matrix-18, plain, ( ( union(_u17, _u16) = union(_u16, _u17)) )).
% 5.74/5.96 cnf(matrix-19, plain, ( ~subset(_u24, _u22) | ~member(_u18, _u24) | member(_u18, _u22) )).
% 5.74/5.96 cnf(matrix-20, plain, ( subset(_u25, _u23) | member(skolem1(_u25, _u23), _u25) )).
% 5.74/5.96 cnf(matrix-21, plain, ( subset(_u25, _u23) | ~member(skolem1(_u25, _u23), _u23) )).
% 5.74/5.96 cnf(matrix-22, plain, ( subset(_u26, _u26) )).
% 5.74/5.96 cnf(matrix-23, plain, ( ~empty(_u30) | ~member(_u27, _u30) )).
% 5.74/5.96 cnf(matrix-24, plain, ( member(skolem2(_u31), _u31) | empty(_u31) )).
% 5.74/5.96 cnf(matrix-25, plain, ( ( _u42 != _u40) | ~member(_u36, _u42) | member(_u36, _u40) )).
% 5.74/5.96 cnf(matrix-26, plain, ( ( _u42 != _u40) | ~member(_u37, _u40) | member(_u37, _u42) )).
% 5.74/5.96 cnf(matrix-27, plain, ( ( _u43 = _u41) | member(skolem3(_u43, _u41), _u43) | member(skolem4(_u43, _u41), _u41) )).
% 5.74/5.96 cnf(matrix-28, plain, ( ( _u43 = _u41) | member(skolem3(_u43, _u41), _u43) | ~member(skolem4(_u43, _u41), _u43) )).
% 5.74/5.96 cnf(matrix-29, plain, ( ( _u43 = _u41) | ~member(skolem3(_u43, _u41), _u41) | member(skolem4(_u43, _u41), _u41) )).
% 5.74/5.96 cnf(matrix-30, plain, ( ( _u43 = _u41) | ~member(skolem3(_u43, _u41), _u41) | ~member(skolem4(_u43, _u41), _u43) )).
% 5.74/5.96 cnf(matrix-31, plain, ( ( union(skolem5, empty_set) != skolem5) )).
% 5.74/5.96
% 5.74/5.96 % Proof stack:
% 5.74/5.96 cnf(proof-stack, plain,
% 5.74/5.96 proof_stack(
% 5.74/5.96 start(14),
% 5.74/5.96 left_branch(0, 11, 2, 2),
% 5.74/5.96 left_branch(0, 29, 2, 3),
% 5.74/5.96 left_branch(0, 1, 0, 4),
% 5.74/5.96 left_branch(0, 31, 0, 5),
% 5.74/5.96 right_branch(5),
% 5.74/5.96 right_branch(4),
% 5.74/5.96 left_branch(0, 12, 0, 5),
% 5.74/5.96 left_branch(0, 27, 1, 6),
% 5.74/5.96 lemmata(0, 0),
% 5.74/5.96 reduction(0, 1),
% 5.74/5.96 right_branch(6),
% 5.74/5.96 right_branch(5),
% 5.74/5.96 right_branch(3),
% 5.74/5.96 left_branch(0, 30, 2, 4),
% 5.74/5.96 left_branch(0, 1, 0, 5),
% 5.74/5.96 left_branch(0, 31, 0, 6),
% 5.74/5.96 right_branch(6),
% 5.74/5.96 right_branch(5),
% 5.74/5.96 left_branch(0, 12, 0, 6),
% 5.74/5.96 left_branch(0, 28, 1, 7),
% 5.74/5.96 lemmata(0, 1),
% 5.74/5.96 reduction(0, 1),
% 5.74/5.96 right_branch(7),
% 5.74/5.96 right_branch(6),
% 5.74/5.96 right_branch(4),
% 5.74/5.96 right_branch(2)
% 5.74/5.96 )).
% 5.74/5.96 % SZS output end Proof for theBenchmark
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