TSTP Solution File: SEU323+1 by ConnectPP---0.2.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ConnectPP---0.2.2
% Problem : SEU323+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% Computer : n021.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 09:20:51 EST 2024
% Result : Theorem 2.25s 2.43s
% Output : Proof 2.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU323+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 : Sun Mar 3 11:13:03 EST 2024
% 0.13/0.34 % CPUTime :
% 2.25/2.43 % SZS status Theorem for theBenchmark
% 2.25/2.43 % SZS output start Proof for theBenchmark
% 2.25/2.43
% 2.25/2.43 % Formula: fc3_tops_1 ( axiom ) converted to clauses:
% 2.25/2.43 cnf(fc3_tops_1-1, axiom, ( ~topological_space(_u1) | ~top_str(_u1) | ~closed_subset(_u0, _u1) | ~element(_u0, powerset(the_carrier(_u1))) | open_subset(subset_complement(the_carrier(_u1), _u0), _u1) )).
% 2.25/2.43
% 2.25/2.43 % Formula: rc6_pre_topc ( axiom ) converted to clauses:
% 2.25/2.43 cnf(rc6_pre_topc-1, axiom, ( ~topological_space(_u3) | ~top_str(_u3) | element(skolem1(_u3), powerset(the_carrier(_u3))) )).
% 2.25/2.43 cnf(rc6_pre_topc-2, axiom, ( ~topological_space(_u3) | ~top_str(_u3) | closed_subset(skolem1(_u3), _u3) )).
% 2.25/2.43
% 2.25/2.43 % Formula: involutiveness_k3_subset_1 ( axiom ) converted to clauses:
% 2.25/2.43 cnf(involutiveness_k3_subset_1-1, axiom, ( ~element(_u4, powerset(_u5)) | ( subset_complement(_u5, subset_complement(_u5, _u4)) = _u4) )).
% 2.25/2.43
% 2.25/2.43 % Formula: reflexivity_r1_tarski ( axiom ) converted to clauses:
% 2.25/2.43 cnf(reflexivity_r1_tarski-1, axiom, ( subset(_u7, _u7) )).
% 2.25/2.43
% 2.25/2.43 % Formula: existence_l1_struct_0 ( axiom ) converted to clauses:
% 2.25/2.43 cnf(existence_l1_struct_0-1, axiom, ( one_sorted_str(skolem2) )).
% 2.25/2.43
% 2.25/2.43 % Formula: dt_k3_subset_1 ( axiom ) converted to clauses:
% 2.25/2.43 cnf(dt_k3_subset_1-1, axiom, ( ~element(_u9, powerset(_u10)) | element(subset_complement(_u10, _u9), powerset(_u10)) )).
% 2.25/2.43
% 2.25/2.43 % Formula: dt_k6_pre_topc ( axiom ) converted to clauses:
% 2.25/2.43 cnf(dt_k6_pre_topc-1, axiom, ( ~top_str(_u12) | ~element(_u11, powerset(the_carrier(_u12))) | element(topstr_closure(_u12, _u11), powerset(the_carrier(_u12))) )).
% 2.25/2.43
% 2.25/2.43 % Formula: dt_l1_struct_0 ( axiom ) converted to clauses:
% 2.25/2.43
% 2.25/2.43 % Formula: fc2_tops_1 ( axiom ) converted to clauses:
% 2.25/2.43 cnf(fc2_tops_1-1, axiom, ( ~topological_space(_u14) | ~top_str(_u14) | ~element(_u13, powerset(the_carrier(_u14))) | closed_subset(topstr_closure(_u14, _u13), _u14) )).
% 2.25/2.43
% 2.25/2.43 % Formula: fc4_tops_1 ( axiom ) converted to clauses:
% 2.25/2.43 cnf(fc4_tops_1-1, axiom, ( ~topological_space(_u16) | ~top_str(_u16) | ~open_subset(_u15, _u16) | ~element(_u15, powerset(the_carrier(_u16))) | closed_subset(subset_complement(the_carrier(_u16), _u15), _u16) )).
% 2.25/2.43
% 2.25/2.43 % Formula: existence_l1_pre_topc ( axiom ) converted to clauses:
% 2.25/2.43 cnf(existence_l1_pre_topc-1, axiom, ( top_str(skolem3) )).
% 2.25/2.43
% 2.25/2.43 % Formula: existence_m1_subset_1 ( axiom ) converted to clauses:
% 2.25/2.43 cnf(existence_m1_subset_1-1, axiom, ( element(skolem4(_u19), _u19) )).
% 2.25/2.43
% 2.25/2.43 % Formula: dt_k1_tops_1 ( axiom ) converted to clauses:
% 2.25/2.43 cnf(dt_k1_tops_1-1, axiom, ( ~top_str(_u21) | ~element(_u20, powerset(the_carrier(_u21))) | element(interior(_u21, _u20), powerset(the_carrier(_u21))) )).
% 2.25/2.43
% 2.25/2.43 % Formula: dt_k1_zfmisc_1 ( axiom ) converted to clauses:
% 2.25/2.43
% 2.25/2.43 % Formula: dt_l1_pre_topc ( axiom ) converted to clauses:
% 2.25/2.43 cnf(dt_l1_pre_topc-1, axiom, ( ~top_str(_u22) | one_sorted_str(_u22) )).
% 2.25/2.43
% 2.25/2.43 % Formula: dt_m1_subset_1 ( axiom ) converted to clauses:
% 2.25/2.43
% 2.25/2.43 % Formula: dt_u1_struct_0 ( axiom ) converted to clauses:
% 2.25/2.43
% 2.25/2.43 % Formula: rc1_tops_1 ( axiom ) converted to clauses:
% 2.25/2.43 cnf(rc1_tops_1-1, axiom, ( ~topological_space(_u24) | ~top_str(_u24) | element(skolem5(_u24), powerset(the_carrier(_u24))) )).
% 2.25/2.43 cnf(rc1_tops_1-2, axiom, ( ~topological_space(_u24) | ~top_str(_u24) | open_subset(skolem5(_u24), _u24) )).
% 2.25/2.43
% 2.25/2.43 % Formula: t3_subset ( axiom ) converted to clauses:
% 2.25/2.43 cnf(t3_subset-1, axiom, ( ~element(_u29, powerset(_u27)) | subset(_u29, _u27) )).
% 2.25/2.43 cnf(t3_subset-2, axiom, ( ~subset(_u30, _u28) | element(_u30, powerset(_u28)) )).
% 2.25/2.43
% 2.25/2.43 % Formula: d1_tops_1 ( axiom ) converted to clauses:
% 2.25/2.43 cnf(d1_tops_1-1, axiom, ( ~top_str(_u32) | ~element(_u31, powerset(the_carrier(_u32))) | ( interior(_u32, _u31) = subset_complement(the_carrier(_u32), topstr_closure(_u32, subset_complement(the_carrier(_u32), _u31)))) )).
% 2.25/2.43
% 2.25/2.43 % Formula: t51_tops_1 ( conjecture ) converted to clauses:
% 2.25/2.43 cnf(t51_tops_1-1, negated_conjecture, ( topological_space(skolem6) )).
% 2.25/2.43 cnf(t51_tops_1-2, negated_conjecture, ( top_str(skolem6) )).
% 2.25/2.43 cnf(t51_tops_1-3, negated_conjecture, ( element(skolem7, powerset(the_carrier(skolem6))) )).
% 2.25/2.43 cnf(t51_tops_1-4, negated_conjecture, ( ~open_subset(interior(skolem6, skolem7), skolem6) )).
% 2.25/2.43
% 2.25/2.43 % Problem matrix:
% 2.25/2.43 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 2.25/2.43 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 2.25/2.43 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 2.25/2.43 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( the_carrier(__eqx_0) = the_carrier(__eqy_0)) )).
% 2.25/2.43 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( powerset(__eqx_0) = powerset(__eqy_0)) )).
% 2.25/2.43 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( subset_complement(__eqx_0, __eqx_1) = subset_complement(__eqy_0, __eqy_1)) )).
% 2.25/2.43 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( topstr_closure(__eqx_0, __eqx_1) = topstr_closure(__eqy_0, __eqy_1)) )).
% 2.25/2.43 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( interior(__eqx_0, __eqx_1) = interior(__eqy_0, __eqy_1)) )).
% 2.25/2.43 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( skolem1(__eqx_0) = skolem1(__eqy_0)) )).
% 2.25/2.43 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( skolem4(__eqx_0) = skolem4(__eqy_0)) )).
% 2.25/2.43 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( skolem5(__eqx_0) = skolem5(__eqy_0)) )).
% 2.25/2.43 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ~topological_space(__eqx_0) | topological_space(__eqy_0) )).
% 2.25/2.43 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ~top_str(__eqx_0) | top_str(__eqy_0) )).
% 2.25/2.43 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~closed_subset(__eqx_0, __eqx_1) | closed_subset(__eqy_0, __eqy_1) )).
% 2.25/2.43 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~element(__eqx_0, __eqx_1) | element(__eqy_0, __eqy_1) )).
% 2.25/2.43 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~open_subset(__eqx_0, __eqx_1) | open_subset(__eqy_0, __eqy_1) )).
% 2.25/2.43 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 2.25/2.43 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ~one_sorted_str(__eqx_0) | one_sorted_str(__eqy_0) )).
% 2.25/2.43 cnf(matrix-18, plain, ( ~topological_space(_u1) | ~top_str(_u1) | ~closed_subset(_u0, _u1) | ~element(_u0, powerset(the_carrier(_u1))) | open_subset(subset_complement(the_carrier(_u1), _u0), _u1) )).
% 2.25/2.43 cnf(matrix-19, plain, ( ~topological_space(_u3) | ~top_str(_u3) | element(skolem1(_u3), powerset(the_carrier(_u3))) )).
% 2.25/2.43 cnf(matrix-20, plain, ( ~topological_space(_u3) | ~top_str(_u3) | closed_subset(skolem1(_u3), _u3) )).
% 2.25/2.43 cnf(matrix-21, plain, ( ~element(_u4, powerset(_u5)) | ( subset_complement(_u5, subset_complement(_u5, _u4)) = _u4) )).
% 2.25/2.43 cnf(matrix-22, plain, ( subset(_u7, _u7) )).
% 2.25/2.43 cnf(matrix-23, plain, ( one_sorted_str(skolem2) )).
% 2.25/2.43 cnf(matrix-24, plain, ( ~element(_u9, powerset(_u10)) | element(subset_complement(_u10, _u9), powerset(_u10)) )).
% 2.25/2.43 cnf(matrix-25, plain, ( ~top_str(_u12) | ~element(_u11, powerset(the_carrier(_u12))) | element(topstr_closure(_u12, _u11), powerset(the_carrier(_u12))) )).
% 2.25/2.43 cnf(matrix-26, plain, ( ~topological_space(_u14) | ~top_str(_u14) | ~element(_u13, powerset(the_carrier(_u14))) | closed_subset(topstr_closure(_u14, _u13), _u14) )).
% 2.25/2.43 cnf(matrix-27, plain, ( ~topological_space(_u16) | ~top_str(_u16) | ~open_subset(_u15, _u16) | ~element(_u15, powerset(the_carrier(_u16))) | closed_subset(subset_complement(the_carrier(_u16), _u15), _u16) )).
% 2.25/2.43 cnf(matrix-28, plain, ( top_str(skolem3) )).
% 2.25/2.43 cnf(matrix-29, plain, ( element(skolem4(_u19), _u19) )).
% 2.25/2.43 cnf(matrix-30, plain, ( ~top_str(_u21) | ~element(_u20, powerset(the_carrier(_u21))) | element(interior(_u21, _u20), powerset(the_carrier(_u21))) )).
% 2.25/2.43 cnf(matrix-31, plain, ( ~top_str(_u22) | one_sorted_str(_u22) )).
% 2.25/2.43 cnf(matrix-32, plain, ( ~topological_space(_u24) | ~top_str(_u24) | element(skolem5(_u24), powerset(the_carrier(_u24))) )).
% 2.25/2.43 cnf(matrix-33, plain, ( ~topological_space(_u24) | ~top_str(_u24) | open_subset(skolem5(_u24), _u24) )).
% 2.25/2.43 cnf(matrix-34, plain, ( ~element(_u29, powerset(_u27)) | subset(_u29, _u27) )).
% 2.25/2.43 cnf(matrix-35, plain, ( ~subset(_u30, _u28) | element(_u30, powerset(_u28)) )).
% 2.25/2.43 cnf(matrix-36, plain, ( ~top_str(_u32) | ~element(_u31, powerset(the_carrier(_u32))) | ( interior(_u32, _u31) = subset_complement(the_carrier(_u32), topstr_closure(_u32, subset_complement(the_carrier(_u32), _u31)))) )).
% 2.25/2.43 cnf(matrix-37, plain, ( topological_space(skolem6) )).
% 2.25/2.43 cnf(matrix-38, plain, ( top_str(skolem6) )).
% 2.25/2.43 cnf(matrix-39, plain, ( element(skolem7, powerset(the_carrier(skolem6))) )).
% 2.25/2.43 cnf(matrix-40, plain, ( ~open_subset(interior(skolem6, skolem7), skolem6) )).
% 2.25/2.43
% 2.25/2.43 % Proof stack:
% 2.25/2.43 cnf(proof-stack, plain,
% 2.25/2.43 proof_stack(
% 2.25/2.43 start(40),
% 2.25/2.43 left_branch(0, 15, 3, 2),
% 2.25/2.43 left_branch(0, 2, 2, 3),
% 2.25/2.43 left_branch(0, 1, 1, 4),
% 2.25/2.43 left_branch(0, 36, 2, 5),
% 2.25/2.43 left_branch(0, 38, 0, 6),
% 2.25/2.43 right_branch(6),
% 2.25/2.43 left_branch(0, 39, 0, 7),
% 2.25/2.43 right_branch(7),
% 2.25/2.43 right_branch(5),
% 2.25/2.43 right_branch(4),
% 2.25/2.43 left_branch(0, 7, 2, 5),
% 2.25/2.43 left_branch(0, 0, 0, 6),
% 2.25/2.43 right_branch(6),
% 2.25/2.43 left_branch(0, 0, 0, 7),
% 2.25/2.43 right_branch(7),
% 2.25/2.43 right_branch(5),
% 2.25/2.43 right_branch(3),
% 2.25/2.43 left_branch(0, 18, 4, 4),
% 2.25/2.43 left_branch(0, 37, 0, 5),
% 2.25/2.43 right_branch(5),
% 2.25/2.43 left_branch(0, 25, 2, 6),
% 2.25/2.43 left_branch(0, 38, 0, 7),
% 2.25/2.43 right_branch(7),
% 2.25/2.43 left_branch(0, 24, 1, 8),
% 2.25/2.43 left_branch(0, 39, 0, 9),
% 2.25/2.43 right_branch(9),
% 2.25/2.43 right_branch(8),
% 2.25/2.43 right_branch(6),
% 2.25/2.43 left_branch(0, 26, 3, 7),
% 2.25/2.43 lemmata(0, 1),
% 2.25/2.43 left_branch(0, 24, 1, 9),
% 2.25/2.43 left_branch(0, 39, 0, 10),
% 2.25/2.43 right_branch(10),
% 2.25/2.43 right_branch(9),
% 2.25/2.43 left_branch(0, 38, 0, 10),
% 2.25/2.43 right_branch(10),
% 2.25/2.43 right_branch(7),
% 2.25/2.43 left_branch(0, 38, 0, 8),
% 2.25/2.43 right_branch(8),
% 2.25/2.43 right_branch(4),
% 2.25/2.43 left_branch(0, 0, 0, 5),
% 2.25/2.43 right_branch(5),
% 2.25/2.43 right_branch(2)
% 2.25/2.43 )).
% 2.25/2.43 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------