TSTP Solution File: SET909+1 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SET909+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% Computer : n015.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 14:32:46 EDT 2024
% Result : Theorem 1.15s 1.36s
% Output : Proof 1.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET909+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.34 % Computer : n015.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 : Wed Mar 20 22:19:04 EDT 2024
% 0.12/0.34 % CPUTime :
% 1.15/1.36 % SZS status Theorem for theBenchmark
% 1.15/1.36 % SZS output start Proof for theBenchmark
% 1.15/1.36
% 1.15/1.36 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 1.15/1.36 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 1.15/1.36
% 1.15/1.36 % Formula: commutativity_k2_tarski ( axiom ) converted to clauses:
% 1.15/1.36 cnf(commutativity_k2_tarski-1, axiom, ( ( unordered_pair(_u3, _u2) = unordered_pair(_u2, _u3)) )).
% 1.15/1.36
% 1.15/1.36 % Formula: commutativity_k2_xboole_0 ( axiom ) converted to clauses:
% 1.15/1.36 cnf(commutativity_k2_xboole_0-1, axiom, ( ( set_union2(_u5, _u4) = set_union2(_u4, _u5)) )).
% 1.15/1.36
% 1.15/1.36 % Formula: d1_xboole_0 ( axiom ) converted to clauses:
% 1.15/1.36 cnf(d1_xboole_0-1, axiom, ( ( _u9 != empty_set) | ~in(_u6, _u9) )).
% 1.15/1.36 cnf(d1_xboole_0-2, axiom, ( in(skolem1(_u10), _u10) | ( _u10 = empty_set) )).
% 1.15/1.36
% 1.15/1.36 % Formula: d2_tarski ( axiom ) converted to clauses:
% 1.15/1.36 cnf(d2_tarski-1, axiom, ( ( _u20 != unordered_pair(_u24, _u22)) | ~in(_u16, _u20) | ( _u16 = _u24) | ( _u16 = _u22) )).
% 1.15/1.36 cnf(d2_tarski-2, axiom, ( ( _u20 != unordered_pair(_u24, _u22)) | in(_u17, _u20) | ( _u17 != _u24) )).
% 1.15/1.36 cnf(d2_tarski-3, axiom, ( ( _u20 != unordered_pair(_u24, _u22)) | in(_u17, _u20) | ( _u17 != _u22) )).
% 1.15/1.36 cnf(d2_tarski-4, axiom, ( ( _u21 = unordered_pair(_u25, _u23)) | in(skolem2(_u25, _u23, _u21), _u21) | ( skolem3(_u25, _u23, _u21) = _u25) | ( skolem3(_u25, _u23, _u21) = _u23) )).
% 1.15/1.36 cnf(d2_tarski-5, axiom, ( ( _u21 = unordered_pair(_u25, _u23)) | in(skolem2(_u25, _u23, _u21), _u21) | ~in(skolem3(_u25, _u23, _u21), _u21) )).
% 1.15/1.36 cnf(d2_tarski-6, axiom, ( ( _u21 = unordered_pair(_u25, _u23)) | ( skolem3(_u25, _u23, _u21) = _u25) | ( skolem3(_u25, _u23, _u21) = _u23) | ( skolem2(_u25, _u23, _u21) != _u25) )).
% 1.15/1.36 cnf(d2_tarski-7, axiom, ( ( _u21 = unordered_pair(_u25, _u23)) | ( skolem3(_u25, _u23, _u21) = _u25) | ( skolem3(_u25, _u23, _u21) = _u23) | ( skolem2(_u25, _u23, _u21) != _u23) )).
% 1.15/1.36 cnf(d2_tarski-8, axiom, ( ( _u21 = unordered_pair(_u25, _u23)) | ~in(skolem3(_u25, _u23, _u21), _u21) | ( skolem2(_u25, _u23, _u21) != _u25) )).
% 1.15/1.36 cnf(d2_tarski-9, axiom, ( ( _u21 = unordered_pair(_u25, _u23)) | ~in(skolem3(_u25, _u23, _u21), _u21) | ( skolem2(_u25, _u23, _u21) != _u23) )).
% 1.15/1.36
% 1.15/1.36 % Formula: d2_xboole_0 ( axiom ) converted to clauses:
% 1.15/1.36 cnf(d2_xboole_0-1, axiom, ( ( _u35 != set_union2(_u39, _u37)) | ~in(_u31, _u35) | in(_u31, _u39) | in(_u31, _u37) )).
% 1.15/1.36 cnf(d2_xboole_0-2, axiom, ( ( _u35 != set_union2(_u39, _u37)) | in(_u32, _u35) | ~in(_u32, _u39) )).
% 1.15/1.36 cnf(d2_xboole_0-3, axiom, ( ( _u35 != set_union2(_u39, _u37)) | in(_u32, _u35) | ~in(_u32, _u37) )).
% 1.15/1.36 cnf(d2_xboole_0-4, axiom, ( ( _u36 = set_union2(_u40, _u38)) | in(skolem4(_u40, _u38, _u36), _u36) | in(skolem5(_u40, _u38, _u36), _u40) | in(skolem5(_u40, _u38, _u36), _u38) )).
% 1.15/1.36 cnf(d2_xboole_0-5, axiom, ( ( _u36 = set_union2(_u40, _u38)) | in(skolem4(_u40, _u38, _u36), _u36) | ~in(skolem5(_u40, _u38, _u36), _u36) )).
% 1.15/1.36 cnf(d2_xboole_0-6, axiom, ( ( _u36 = set_union2(_u40, _u38)) | in(skolem5(_u40, _u38, _u36), _u40) | in(skolem5(_u40, _u38, _u36), _u38) | ~in(skolem4(_u40, _u38, _u36), _u40) )).
% 1.15/1.36 cnf(d2_xboole_0-7, axiom, ( ( _u36 = set_union2(_u40, _u38)) | in(skolem5(_u40, _u38, _u36), _u40) | in(skolem5(_u40, _u38, _u36), _u38) | ~in(skolem4(_u40, _u38, _u36), _u38) )).
% 1.15/1.36 cnf(d2_xboole_0-8, axiom, ( ( _u36 = set_union2(_u40, _u38)) | ~in(skolem5(_u40, _u38, _u36), _u36) | ~in(skolem4(_u40, _u38, _u36), _u40) )).
% 1.15/1.36 cnf(d2_xboole_0-9, axiom, ( ( _u36 = set_union2(_u40, _u38)) | ~in(skolem5(_u40, _u38, _u36), _u36) | ~in(skolem4(_u40, _u38, _u36), _u38) )).
% 1.15/1.36
% 1.15/1.36 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 1.15/1.36 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 1.15/1.36
% 1.15/1.36 % Formula: fc2_xboole_0 ( axiom ) converted to clauses:
% 1.15/1.36 cnf(fc2_xboole_0-1, axiom, ( empty(_u42) | ~empty(set_union2(_u42, _u41)) )).
% 1.15/1.36
% 1.15/1.36 % Formula: fc3_xboole_0 ( axiom ) converted to clauses:
% 1.15/1.36 cnf(fc3_xboole_0-1, axiom, ( empty(_u44) | ~empty(set_union2(_u43, _u44)) )).
% 1.15/1.36
% 1.15/1.36 % Formula: idempotence_k2_xboole_0 ( axiom ) converted to clauses:
% 1.15/1.36 cnf(idempotence_k2_xboole_0-1, axiom, ( ( set_union2(_u46, _u46) = _u46) )).
% 1.15/1.36
% 1.15/1.36 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 1.15/1.36 cnf(rc1_xboole_0-1, axiom, ( empty(skolem6) )).
% 1.15/1.36
% 1.15/1.36 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 1.15/1.36 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem7) )).
% 1.15/1.36
% 1.15/1.36 % Formula: t50_zfmisc_1 ( conjecture ) (definitionally) converted to clauses:
% 1.15/1.36 cnf(t50_zfmisc_1-1, negated_conjecture, ( ( set_union2(unordered_pair(skolem8, skolem9), skolem10) = empty_set) )).
% 1.15/1.36
% 1.15/1.36 % Problem matrix:
% 1.15/1.36 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 1.15/1.36 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 1.15/1.36 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 1.15/1.36 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( unordered_pair(__eqx_0, __eqx_1) = unordered_pair(__eqy_0, __eqy_1)) )).
% 1.15/1.36 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_union2(__eqx_0, __eqx_1) = set_union2(__eqy_0, __eqy_1)) )).
% 1.15/1.36 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( skolem1(__eqx_0) = skolem1(__eqy_0)) )).
% 1.15/1.36 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem2(__eqx_0, __eqx_1, __eqx_2) = skolem2(__eqy_0, __eqy_1, __eqy_2)) )).
% 1.15/1.36 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem3(__eqx_0, __eqx_1, __eqx_2) = skolem3(__eqy_0, __eqy_1, __eqy_2)) )).
% 1.15/1.36 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem4(__eqx_0, __eqx_1, __eqx_2) = skolem4(__eqy_0, __eqy_1, __eqy_2)) )).
% 1.15/1.36 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem5(__eqx_0, __eqx_1, __eqx_2) = skolem5(__eqy_0, __eqy_1, __eqy_2)) )).
% 1.15/1.36 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 1.15/1.36 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 1.15/1.36 cnf(matrix-12, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 1.15/1.36 cnf(matrix-13, plain, ( ( unordered_pair(_u3, _u2) = unordered_pair(_u2, _u3)) )).
% 1.15/1.36 cnf(matrix-14, plain, ( ( set_union2(_u5, _u4) = set_union2(_u4, _u5)) )).
% 1.15/1.36 cnf(matrix-15, plain, ( ( _u9 != empty_set) | ~in(_u6, _u9) )).
% 1.15/1.36 cnf(matrix-16, plain, ( in(skolem1(_u10), _u10) | ( _u10 = empty_set) )).
% 1.15/1.36 cnf(matrix-17, plain, ( ( _u20 != unordered_pair(_u24, _u22)) | ~in(_u16, _u20) | ( _u16 = _u24) | ( _u16 = _u22) )).
% 1.15/1.36 cnf(matrix-18, plain, ( ( _u20 != unordered_pair(_u24, _u22)) | in(_u17, _u20) | ( _u17 != _u24) )).
% 1.15/1.36 cnf(matrix-19, plain, ( ( _u20 != unordered_pair(_u24, _u22)) | in(_u17, _u20) | ( _u17 != _u22) )).
% 1.15/1.36 cnf(matrix-20, plain, ( ( _u21 = unordered_pair(_u25, _u23)) | in(skolem2(_u25, _u23, _u21), _u21) | ( skolem3(_u25, _u23, _u21) = _u25) | ( skolem3(_u25, _u23, _u21) = _u23) )).
% 1.15/1.36 cnf(matrix-21, plain, ( ( _u21 = unordered_pair(_u25, _u23)) | in(skolem2(_u25, _u23, _u21), _u21) | ~in(skolem3(_u25, _u23, _u21), _u21) )).
% 1.15/1.36 cnf(matrix-22, plain, ( ( _u21 = unordered_pair(_u25, _u23)) | ( skolem3(_u25, _u23, _u21) = _u25) | ( skolem3(_u25, _u23, _u21) = _u23) | ( skolem2(_u25, _u23, _u21) != _u25) )).
% 1.15/1.36 cnf(matrix-23, plain, ( ( _u21 = unordered_pair(_u25, _u23)) | ( skolem3(_u25, _u23, _u21) = _u25) | ( skolem3(_u25, _u23, _u21) = _u23) | ( skolem2(_u25, _u23, _u21) != _u23) )).
% 1.15/1.36 cnf(matrix-24, plain, ( ( _u21 = unordered_pair(_u25, _u23)) | ~in(skolem3(_u25, _u23, _u21), _u21) | ( skolem2(_u25, _u23, _u21) != _u25) )).
% 1.15/1.36 cnf(matrix-25, plain, ( ( _u21 = unordered_pair(_u25, _u23)) | ~in(skolem3(_u25, _u23, _u21), _u21) | ( skolem2(_u25, _u23, _u21) != _u23) )).
% 1.15/1.36 cnf(matrix-26, plain, ( ( _u35 != set_union2(_u39, _u37)) | ~in(_u31, _u35) | in(_u31, _u39) | in(_u31, _u37) )).
% 1.15/1.36 cnf(matrix-27, plain, ( ( _u35 != set_union2(_u39, _u37)) | in(_u32, _u35) | ~in(_u32, _u39) )).
% 1.15/1.36 cnf(matrix-28, plain, ( ( _u35 != set_union2(_u39, _u37)) | in(_u32, _u35) | ~in(_u32, _u37) )).
% 1.15/1.36 cnf(matrix-29, plain, ( ( _u36 = set_union2(_u40, _u38)) | in(skolem4(_u40, _u38, _u36), _u36) | in(skolem5(_u40, _u38, _u36), _u40) | in(skolem5(_u40, _u38, _u36), _u38) )).
% 1.15/1.36 cnf(matrix-30, plain, ( ( _u36 = set_union2(_u40, _u38)) | in(skolem4(_u40, _u38, _u36), _u36) | ~in(skolem5(_u40, _u38, _u36), _u36) )).
% 1.15/1.36 cnf(matrix-31, plain, ( ( _u36 = set_union2(_u40, _u38)) | in(skolem5(_u40, _u38, _u36), _u40) | in(skolem5(_u40, _u38, _u36), _u38) | ~in(skolem4(_u40, _u38, _u36), _u40) )).
% 1.15/1.36 cnf(matrix-32, plain, ( ( _u36 = set_union2(_u40, _u38)) | in(skolem5(_u40, _u38, _u36), _u40) | in(skolem5(_u40, _u38, _u36), _u38) | ~in(skolem4(_u40, _u38, _u36), _u38) )).
% 1.15/1.36 cnf(matrix-33, plain, ( ( _u36 = set_union2(_u40, _u38)) | ~in(skolem5(_u40, _u38, _u36), _u36) | ~in(skolem4(_u40, _u38, _u36), _u40) )).
% 1.15/1.36 cnf(matrix-34, plain, ( ( _u36 = set_union2(_u40, _u38)) | ~in(skolem5(_u40, _u38, _u36), _u36) | ~in(skolem4(_u40, _u38, _u36), _u38) )).
% 1.15/1.36 cnf(matrix-35, plain, ( empty(empty_set) )).
% 1.15/1.36 cnf(matrix-36, plain, ( empty(_u42) | ~empty(set_union2(_u42, _u41)) )).
% 1.15/1.36 cnf(matrix-37, plain, ( empty(_u44) | ~empty(set_union2(_u43, _u44)) )).
% 1.15/1.36 cnf(matrix-38, plain, ( ( set_union2(_u46, _u46) = _u46) )).
% 1.15/1.36 cnf(matrix-39, plain, ( empty(skolem6) )).
% 1.15/1.36 cnf(matrix-40, plain, ( ~empty(skolem7) )).
% 1.15/1.36 cnf(matrix-41, plain, ( ( set_union2(unordered_pair(skolem8, skolem9), skolem10) = empty_set) )).
% 1.15/1.36
% 1.15/1.36 % Proof stack:
% 1.15/1.36 cnf(proof-stack, plain,
% 1.15/1.36 proof_stack(
% 1.15/1.36 start(15),
% 1.15/1.36 left_branch(0, 41, 0, 2),
% 1.15/1.36 right_branch(2),
% 1.15/1.36 left_branch(0, 28, 1, 3),
% 1.15/1.36 left_branch(0, 14, 0, 4),
% 1.15/1.36 right_branch(4),
% 1.15/1.36 left_branch(0, 19, 1, 5),
% 1.15/1.36 left_branch(0, 13, 0, 6),
% 1.15/1.36 right_branch(6),
% 1.15/1.36 left_branch(0, 38, 0, 7),
% 1.15/1.36 right_branch(7),
% 1.15/1.36 right_branch(5),
% 1.15/1.36 right_branch(3)
% 1.15/1.36 )).
% 1.15/1.36 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------