TSTP Solution File: SET920+1 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SET920+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 : n004.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 14:32:48 EDT 2024
% Result : Theorem 3.23s 3.38s
% Output : Proof 3.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET920+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.33 % Computer : n004.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
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Mar 20 21:48:39 EDT 2024
% 0.13/0.33 % CPUTime :
% 3.23/3.38 % SZS status Theorem for theBenchmark
% 3.23/3.38 % SZS output start Proof for theBenchmark
% 3.23/3.38
% 3.23/3.38 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 3.23/3.38 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 3.23/3.38
% 3.23/3.38 % Formula: commutativity_k2_tarski ( axiom ) converted to clauses:
% 3.23/3.38 cnf(commutativity_k2_tarski-1, axiom, ( ( unordered_pair(_u3, _u2) = unordered_pair(_u2, _u3)) )).
% 3.23/3.38
% 3.23/3.38 % Formula: commutativity_k3_xboole_0 ( axiom ) converted to clauses:
% 3.23/3.38 cnf(commutativity_k3_xboole_0-1, axiom, ( ( set_intersection2(_u5, _u4) = set_intersection2(_u4, _u5)) )).
% 3.23/3.38
% 3.23/3.38 % Formula: d2_tarski ( axiom ) converted to clauses:
% 3.23/3.38 cnf(d2_tarski-1, axiom, ( ( _u15 != unordered_pair(_u19, _u17)) | ~in(_u11, _u15) | ( _u11 = _u19) | ( _u11 = _u17) )).
% 3.23/3.38 cnf(d2_tarski-2, axiom, ( ( _u15 != unordered_pair(_u19, _u17)) | in(_u12, _u15) | ( _u12 != _u19) )).
% 3.23/3.38 cnf(d2_tarski-3, axiom, ( ( _u15 != unordered_pair(_u19, _u17)) | in(_u12, _u15) | ( _u12 != _u17) )).
% 3.23/3.38 cnf(d2_tarski-4, axiom, ( ( _u16 = unordered_pair(_u20, _u18)) | in(skolem1(_u20, _u18, _u16), _u16) | ( skolem2(_u20, _u18, _u16) = _u20) | ( skolem2(_u20, _u18, _u16) = _u18) )).
% 3.23/3.38 cnf(d2_tarski-5, axiom, ( ( _u16 = unordered_pair(_u20, _u18)) | in(skolem1(_u20, _u18, _u16), _u16) | ~in(skolem2(_u20, _u18, _u16), _u16) )).
% 3.23/3.38 cnf(d2_tarski-6, axiom, ( ( _u16 = unordered_pair(_u20, _u18)) | ( skolem2(_u20, _u18, _u16) = _u20) | ( skolem2(_u20, _u18, _u16) = _u18) | ( skolem1(_u20, _u18, _u16) != _u20) )).
% 3.23/3.38 cnf(d2_tarski-7, axiom, ( ( _u16 = unordered_pair(_u20, _u18)) | ( skolem2(_u20, _u18, _u16) = _u20) | ( skolem2(_u20, _u18, _u16) = _u18) | ( skolem1(_u20, _u18, _u16) != _u18) )).
% 3.23/3.38 cnf(d2_tarski-8, axiom, ( ( _u16 = unordered_pair(_u20, _u18)) | ~in(skolem2(_u20, _u18, _u16), _u16) | ( skolem1(_u20, _u18, _u16) != _u20) )).
% 3.23/3.38 cnf(d2_tarski-9, axiom, ( ( _u16 = unordered_pair(_u20, _u18)) | ~in(skolem2(_u20, _u18, _u16), _u16) | ( skolem1(_u20, _u18, _u16) != _u18) )).
% 3.23/3.38
% 3.23/3.38 % Formula: d3_xboole_0 ( axiom ) converted to clauses:
% 3.23/3.38 cnf(d3_xboole_0-1, axiom, ( ( _u30 != set_intersection2(_u34, _u32)) | ~in(_u26, _u30) | in(_u26, _u34) )).
% 3.23/3.38 cnf(d3_xboole_0-2, axiom, ( ( _u30 != set_intersection2(_u34, _u32)) | ~in(_u26, _u30) | in(_u26, _u32) )).
% 3.23/3.38 cnf(d3_xboole_0-3, axiom, ( ( _u30 != set_intersection2(_u34, _u32)) | ~in(_u27, _u34) | ~in(_u27, _u32) | in(_u27, _u30) )).
% 3.23/3.38 cnf(d3_xboole_0-4, axiom, ( ( _u31 = set_intersection2(_u35, _u33)) | in(skolem3(_u35, _u33, _u31), _u31) | in(skolem4(_u35, _u33, _u31), _u35) )).
% 3.23/3.38 cnf(d3_xboole_0-5, axiom, ( ( _u31 = set_intersection2(_u35, _u33)) | in(skolem3(_u35, _u33, _u31), _u31) | in(skolem4(_u35, _u33, _u31), _u33) )).
% 3.23/3.38 cnf(d3_xboole_0-6, axiom, ( ( _u31 = set_intersection2(_u35, _u33)) | in(skolem3(_u35, _u33, _u31), _u31) | ~in(skolem4(_u35, _u33, _u31), _u31) )).
% 3.23/3.38 cnf(d3_xboole_0-7, axiom, ( ( _u31 = set_intersection2(_u35, _u33)) | ~in(skolem3(_u35, _u33, _u31), _u35) | ~in(skolem3(_u35, _u33, _u31), _u33) | in(skolem4(_u35, _u33, _u31), _u35) )).
% 3.23/3.38 cnf(d3_xboole_0-8, axiom, ( ( _u31 = set_intersection2(_u35, _u33)) | ~in(skolem3(_u35, _u33, _u31), _u35) | ~in(skolem3(_u35, _u33, _u31), _u33) | in(skolem4(_u35, _u33, _u31), _u33) )).
% 3.23/3.38 cnf(d3_xboole_0-9, axiom, ( ( _u31 = set_intersection2(_u35, _u33)) | ~in(skolem3(_u35, _u33, _u31), _u35) | ~in(skolem3(_u35, _u33, _u31), _u33) | ~in(skolem4(_u35, _u33, _u31), _u31) )).
% 3.23/3.38
% 3.23/3.38 % Formula: idempotence_k3_xboole_0 ( axiom ) converted to clauses:
% 3.23/3.38 cnf(idempotence_k3_xboole_0-1, axiom, ( ( set_intersection2(_u37, _u37) = _u37) )).
% 3.23/3.38
% 3.23/3.38 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 3.23/3.38 cnf(rc1_xboole_0-1, axiom, ( empty(skolem5) )).
% 3.23/3.38
% 3.23/3.38 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 3.23/3.38 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem6) )).
% 3.23/3.38
% 3.23/3.38 % Formula: t63_zfmisc_1 ( conjecture ) (definitionally) converted to clauses:
% 3.23/3.38 cnf(t63_zfmisc_1-1, negated_conjecture, ( ( set_intersection2(unordered_pair(skolem7, skolem8), skolem9) = unordered_pair(skolem7, skolem8)) )).
% 3.23/3.38 cnf(t63_zfmisc_1-2, negated_conjecture, ( ~in(skolem7, skolem9) )).
% 3.23/3.38
% 3.23/3.38 % Problem matrix:
% 3.23/3.38 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 3.23/3.38 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 3.23/3.38 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 3.23/3.38 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( unordered_pair(__eqx_0, __eqx_1) = unordered_pair(__eqy_0, __eqy_1)) )).
% 3.23/3.38 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_intersection2(__eqx_0, __eqx_1) = set_intersection2(__eqy_0, __eqy_1)) )).
% 3.23/3.38 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem1(__eqx_0, __eqx_1, __eqx_2) = skolem1(__eqy_0, __eqy_1, __eqy_2)) )).
% 3.23/3.38 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)) )).
% 3.23/3.38 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)) )).
% 3.23/3.38 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)) )).
% 3.23/3.38 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 3.23/3.38 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 3.23/3.38 cnf(matrix-11, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 3.23/3.38 cnf(matrix-12, plain, ( ( unordered_pair(_u3, _u2) = unordered_pair(_u2, _u3)) )).
% 3.23/3.38 cnf(matrix-13, plain, ( ( set_intersection2(_u5, _u4) = set_intersection2(_u4, _u5)) )).
% 3.23/3.38 cnf(matrix-14, plain, ( ( _u15 != unordered_pair(_u19, _u17)) | ~in(_u11, _u15) | ( _u11 = _u19) | ( _u11 = _u17) )).
% 3.23/3.38 cnf(matrix-15, plain, ( ( _u15 != unordered_pair(_u19, _u17)) | in(_u12, _u15) | ( _u12 != _u19) )).
% 3.23/3.38 cnf(matrix-16, plain, ( ( _u15 != unordered_pair(_u19, _u17)) | in(_u12, _u15) | ( _u12 != _u17) )).
% 3.23/3.38 cnf(matrix-17, plain, ( ( _u16 = unordered_pair(_u20, _u18)) | in(skolem1(_u20, _u18, _u16), _u16) | ( skolem2(_u20, _u18, _u16) = _u20) | ( skolem2(_u20, _u18, _u16) = _u18) )).
% 3.23/3.38 cnf(matrix-18, plain, ( ( _u16 = unordered_pair(_u20, _u18)) | in(skolem1(_u20, _u18, _u16), _u16) | ~in(skolem2(_u20, _u18, _u16), _u16) )).
% 3.23/3.38 cnf(matrix-19, plain, ( ( _u16 = unordered_pair(_u20, _u18)) | ( skolem2(_u20, _u18, _u16) = _u20) | ( skolem2(_u20, _u18, _u16) = _u18) | ( skolem1(_u20, _u18, _u16) != _u20) )).
% 3.23/3.38 cnf(matrix-20, plain, ( ( _u16 = unordered_pair(_u20, _u18)) | ( skolem2(_u20, _u18, _u16) = _u20) | ( skolem2(_u20, _u18, _u16) = _u18) | ( skolem1(_u20, _u18, _u16) != _u18) )).
% 3.23/3.38 cnf(matrix-21, plain, ( ( _u16 = unordered_pair(_u20, _u18)) | ~in(skolem2(_u20, _u18, _u16), _u16) | ( skolem1(_u20, _u18, _u16) != _u20) )).
% 3.23/3.38 cnf(matrix-22, plain, ( ( _u16 = unordered_pair(_u20, _u18)) | ~in(skolem2(_u20, _u18, _u16), _u16) | ( skolem1(_u20, _u18, _u16) != _u18) )).
% 3.23/3.38 cnf(matrix-23, plain, ( ( _u30 != set_intersection2(_u34, _u32)) | ~in(_u26, _u30) | in(_u26, _u34) )).
% 3.23/3.38 cnf(matrix-24, plain, ( ( _u30 != set_intersection2(_u34, _u32)) | ~in(_u26, _u30) | in(_u26, _u32) )).
% 3.23/3.38 cnf(matrix-25, plain, ( ( _u30 != set_intersection2(_u34, _u32)) | ~in(_u27, _u34) | ~in(_u27, _u32) | in(_u27, _u30) )).
% 3.23/3.38 cnf(matrix-26, plain, ( ( _u31 = set_intersection2(_u35, _u33)) | in(skolem3(_u35, _u33, _u31), _u31) | in(skolem4(_u35, _u33, _u31), _u35) )).
% 3.23/3.38 cnf(matrix-27, plain, ( ( _u31 = set_intersection2(_u35, _u33)) | in(skolem3(_u35, _u33, _u31), _u31) | in(skolem4(_u35, _u33, _u31), _u33) )).
% 3.23/3.38 cnf(matrix-28, plain, ( ( _u31 = set_intersection2(_u35, _u33)) | in(skolem3(_u35, _u33, _u31), _u31) | ~in(skolem4(_u35, _u33, _u31), _u31) )).
% 3.23/3.38 cnf(matrix-29, plain, ( ( _u31 = set_intersection2(_u35, _u33)) | ~in(skolem3(_u35, _u33, _u31), _u35) | ~in(skolem3(_u35, _u33, _u31), _u33) | in(skolem4(_u35, _u33, _u31), _u35) )).
% 3.23/3.38 cnf(matrix-30, plain, ( ( _u31 = set_intersection2(_u35, _u33)) | ~in(skolem3(_u35, _u33, _u31), _u35) | ~in(skolem3(_u35, _u33, _u31), _u33) | in(skolem4(_u35, _u33, _u31), _u33) )).
% 3.23/3.38 cnf(matrix-31, plain, ( ( _u31 = set_intersection2(_u35, _u33)) | ~in(skolem3(_u35, _u33, _u31), _u35) | ~in(skolem3(_u35, _u33, _u31), _u33) | ~in(skolem4(_u35, _u33, _u31), _u31) )).
% 3.23/3.38 cnf(matrix-32, plain, ( ( set_intersection2(_u37, _u37) = _u37) )).
% 3.23/3.38 cnf(matrix-33, plain, ( empty(skolem5) )).
% 3.23/3.38 cnf(matrix-34, plain, ( ~empty(skolem6) )).
% 3.23/3.38 cnf(matrix-35, plain, ( ( set_intersection2(unordered_pair(skolem7, skolem8), skolem9) = unordered_pair(skolem7, skolem8)) )).
% 3.23/3.38 cnf(matrix-36, plain, ( ~in(skolem7, skolem9) )).
% 3.23/3.38
% 3.23/3.38 % Proof stack:
% 3.23/3.38 cnf(proof-stack, plain,
% 3.23/3.38 proof_stack(
% 3.23/3.38 start(36),
% 3.23/3.38 left_branch(0, 24, 2, 2),
% 3.23/3.38 left_branch(0, 32, 0, 3),
% 3.23/3.38 right_branch(3),
% 3.23/3.38 left_branch(0, 15, 1, 4),
% 3.23/3.38 left_branch(0, 2, 2, 5),
% 3.23/3.38 left_branch(0, 32, 0, 6),
% 3.23/3.38 right_branch(6),
% 3.23/3.38 left_branch(0, 35, 0, 7),
% 3.23/3.38 right_branch(7),
% 3.23/3.38 right_branch(5),
% 3.23/3.38 left_branch(0, 0, 0, 6),
% 3.23/3.38 right_branch(6),
% 3.23/3.38 right_branch(4),
% 3.23/3.38 right_branch(2)
% 3.23/3.38 )).
% 3.23/3.38 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------