TSTP Solution File: SEU319+1 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SEU319+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 : n009.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 14:33:58 EDT 2024
% Result : Theorem 6.06s 6.25s
% Output : Proof 6.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU319+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.12 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Mar 20 15:02:59 EDT 2024
% 0.12/0.33 % CPUTime :
% 6.06/6.25 % SZS status Theorem for theBenchmark
% 6.06/6.25 % SZS output start Proof for theBenchmark
% 6.06/6.25
% 6.06/6.25 % Formula: d6_pre_topc ( axiom ) converted to clauses:
% 6.06/6.25 cnf(d6_pre_topc-1, axiom, ( ~top_str(_u1) | ~element(_u0, powerset(the_carrier(_u1))) | ~closed_subset(_u0, _u1) | open_subset(subset_difference(the_carrier(_u1), cast_as_carrier_subset(_u1), _u0), _u1) )).
% 6.06/6.25 cnf(d6_pre_topc-2, axiom, ( ~top_str(_u1) | ~element(_u0, powerset(the_carrier(_u1))) | ~open_subset(subset_difference(the_carrier(_u1), cast_as_carrier_subset(_u1), _u0), _u1) | closed_subset(_u0, _u1) )).
% 6.06/6.25
% 6.06/6.25 % Formula: dt_k1_zfmisc_1 ( axiom ) converted to clauses:
% 6.06/6.25 cnf(dt_k1_zfmisc_1, axiom, $true).
% 6.06/6.25
% 6.06/6.25 % Formula: dt_k2_pre_topc ( axiom ) converted to clauses:
% 6.06/6.25 cnf(dt_k2_pre_topc-1, axiom, ( ~one_sorted_str(_u2) | element(cast_as_carrier_subset(_u2), powerset(the_carrier(_u2))) )).
% 6.06/6.25
% 6.06/6.25 % Formula: dt_k3_subset_1 ( axiom ) converted to clauses:
% 6.06/6.25 cnf(dt_k3_subset_1-1, axiom, ( ~element(_u3, powerset(_u4)) | element(subset_complement(_u4, _u3), powerset(_u4)) )).
% 6.06/6.25
% 6.06/6.25 % Formula: dt_k4_xboole_0 ( axiom ) converted to clauses:
% 6.06/6.25 cnf(dt_k4_xboole_0, axiom, $true).
% 6.06/6.25
% 6.06/6.25 % Formula: dt_k6_subset_1 ( axiom ) converted to clauses:
% 6.06/6.25 cnf(dt_k6_subset_1-1, axiom, ( ~element(_u6, powerset(_u7)) | ~element(_u5, powerset(_u7)) | element(subset_difference(_u7, _u6, _u5), powerset(_u7)) )).
% 6.06/6.25
% 6.06/6.25 % Formula: dt_l1_pre_topc ( axiom ) converted to clauses:
% 6.06/6.25 cnf(dt_l1_pre_topc-1, axiom, ( ~top_str(_u8) | one_sorted_str(_u8) )).
% 6.06/6.25
% 6.06/6.25 % Formula: dt_l1_struct_0 ( axiom ) converted to clauses:
% 6.06/6.25 cnf(dt_l1_struct_0, axiom, $true).
% 6.06/6.25
% 6.06/6.25 % Formula: dt_m1_subset_1 ( axiom ) converted to clauses:
% 6.06/6.25 cnf(dt_m1_subset_1, axiom, $true).
% 6.06/6.25
% 6.06/6.25 % Formula: dt_u1_struct_0 ( axiom ) converted to clauses:
% 6.06/6.25 cnf(dt_u1_struct_0, axiom, $true).
% 6.06/6.25
% 6.06/6.25 % Formula: existence_l1_pre_topc ( axiom ) converted to clauses:
% 6.06/6.25 cnf(existence_l1_pre_topc-1, axiom, ( top_str(skolem1) )).
% 6.06/6.25
% 6.06/6.25 % Formula: existence_l1_struct_0 ( axiom ) converted to clauses:
% 6.06/6.25 cnf(existence_l1_struct_0-1, axiom, ( one_sorted_str(skolem2) )).
% 6.06/6.25
% 6.06/6.25 % Formula: existence_m1_subset_1 ( axiom ) converted to clauses:
% 6.06/6.25 cnf(existence_m1_subset_1-1, axiom, ( element(skolem3(_u12), _u12) )).
% 6.06/6.25
% 6.06/6.25 % Formula: involutiveness_k3_subset_1 ( axiom ) converted to clauses:
% 6.06/6.25 cnf(involutiveness_k3_subset_1-1, axiom, ( ~element(_u13, powerset(_u14)) | ( subset_complement(_u14, subset_complement(_u14, _u13)) = _u13) )).
% 6.06/6.25
% 6.06/6.25 % Formula: redefinition_k6_subset_1 ( axiom ) converted to clauses:
% 6.06/6.25 cnf(redefinition_k6_subset_1-1, axiom, ( ~element(_u16, powerset(_u17)) | ~element(_u15, powerset(_u17)) | ( subset_difference(_u17, _u16, _u15) = set_difference(_u16, _u15)) )).
% 6.06/6.25
% 6.06/6.25 % Formula: reflexivity_r1_tarski ( axiom ) converted to clauses:
% 6.06/6.25 cnf(reflexivity_r1_tarski-1, axiom, ( subset(_u19, _u19) )).
% 6.06/6.25
% 6.06/6.25 % Formula: t17_pre_topc ( axiom ) converted to clauses:
% 6.06/6.25 cnf(t17_pre_topc-1, axiom, ( ~one_sorted_str(_u21) | ~element(_u20, powerset(the_carrier(_u21))) | ( subset_complement(the_carrier(_u21), _u20) = subset_difference(the_carrier(_u21), cast_as_carrier_subset(_u21), _u20)) )).
% 6.06/6.25
% 6.06/6.25 % Formula: t29_tops_1 ( conjecture ) (definitionally) converted to clauses:
% 6.06/6.25 cnf(t29_tops_1-1, negated_conjecture, ( top_str(skolem4) )).
% 6.06/6.25 cnf(t29_tops_1-2, negated_conjecture, ( element(skolem5, powerset(the_carrier(skolem4))) )).
% 6.06/6.25 cnf(t29_tops_1-3, negated_conjecture, ( ~_def0 | ~_def1 )).
% 6.06/6.25 cnf(t29_tops_1-4, negated_conjecture, ( _def0 | closed_subset(skolem5, skolem4) )).
% 6.06/6.25 cnf(t29_tops_1-5, negated_conjecture, ( _def0 | ~open_subset(subset_complement(the_carrier(skolem4), skolem5), skolem4) )).
% 6.06/6.25 cnf(t29_tops_1-6, negated_conjecture, ( _def1 | open_subset(subset_complement(the_carrier(skolem4), skolem5), skolem4) )).
% 6.06/6.25 cnf(t29_tops_1-7, negated_conjecture, ( _def1 | ~closed_subset(skolem5, skolem4) )).
% 6.06/6.25
% 6.06/6.25 % Formula: t3_subset ( axiom ) converted to clauses:
% 6.06/6.25 cnf(t3_subset-1, axiom, ( ~element(_u28, powerset(_u26)) | subset(_u28, _u26) )).
% 6.06/6.25 cnf(t3_subset-2, axiom, ( ~subset(_u29, _u27) | element(_u29, powerset(_u27)) )).
% 6.06/6.25
% 6.06/6.25 % Problem matrix:
% 6.06/6.25 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 6.06/6.25 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 6.06/6.25 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 6.06/6.25 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( the_carrier(__eqx_0) = the_carrier(__eqy_0)) )).
% 6.06/6.25 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( powerset(__eqx_0) = powerset(__eqy_0)) )).
% 6.06/6.25 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( cast_as_carrier_subset(__eqx_0) = cast_as_carrier_subset(__eqy_0)) )).
% 6.06/6.25 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( subset_difference(__eqx_0, __eqx_1, __eqx_2) = subset_difference(__eqy_0, __eqy_1, __eqy_2)) )).
% 6.06/6.25 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( subset_complement(__eqx_0, __eqx_1) = subset_complement(__eqy_0, __eqy_1)) )).
% 6.06/6.25 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_difference(__eqx_0, __eqx_1) = set_difference(__eqy_0, __eqy_1)) )).
% 6.06/6.25 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( skolem3(__eqx_0) = skolem3(__eqy_0)) )).
% 6.06/6.25 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ~top_str(__eqx_0) | top_str(__eqy_0) )).
% 6.06/6.25 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~element(__eqx_0, __eqx_1) | element(__eqy_0, __eqy_1) )).
% 6.06/6.25 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~closed_subset(__eqx_0, __eqx_1) | closed_subset(__eqy_0, __eqy_1) )).
% 6.06/6.25 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~open_subset(__eqx_0, __eqx_1) | open_subset(__eqy_0, __eqy_1) )).
% 6.06/6.25 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ~one_sorted_str(__eqx_0) | one_sorted_str(__eqy_0) )).
% 6.06/6.25 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 6.06/6.25 cnf(matrix-16, plain, ( ~top_str(_u1) | ~element(_u0, powerset(the_carrier(_u1))) | ~closed_subset(_u0, _u1) | open_subset(subset_difference(the_carrier(_u1), cast_as_carrier_subset(_u1), _u0), _u1) )).
% 6.06/6.25 cnf(matrix-17, plain, ( ~top_str(_u1) | ~element(_u0, powerset(the_carrier(_u1))) | ~open_subset(subset_difference(the_carrier(_u1), cast_as_carrier_subset(_u1), _u0), _u1) | closed_subset(_u0, _u1) )).
% 6.06/6.25 cnf(matrix-18, plain, ( ~one_sorted_str(_u2) | element(cast_as_carrier_subset(_u2), powerset(the_carrier(_u2))) )).
% 6.06/6.25 cnf(matrix-19, plain, ( ~element(_u3, powerset(_u4)) | element(subset_complement(_u4, _u3), powerset(_u4)) )).
% 6.06/6.25 cnf(matrix-20, plain, ( ~element(_u6, powerset(_u7)) | ~element(_u5, powerset(_u7)) | element(subset_difference(_u7, _u6, _u5), powerset(_u7)) )).
% 6.06/6.25 cnf(matrix-21, plain, ( ~top_str(_u8) | one_sorted_str(_u8) )).
% 6.06/6.25 cnf(matrix-22, plain, ( top_str(skolem1) )).
% 6.06/6.25 cnf(matrix-23, plain, ( one_sorted_str(skolem2) )).
% 6.06/6.25 cnf(matrix-24, plain, ( element(skolem3(_u12), _u12) )).
% 6.06/6.25 cnf(matrix-25, plain, ( ~element(_u13, powerset(_u14)) | ( subset_complement(_u14, subset_complement(_u14, _u13)) = _u13) )).
% 6.06/6.25 cnf(matrix-26, plain, ( ~element(_u16, powerset(_u17)) | ~element(_u15, powerset(_u17)) | ( subset_difference(_u17, _u16, _u15) = set_difference(_u16, _u15)) )).
% 6.06/6.25 cnf(matrix-27, plain, ( subset(_u19, _u19) )).
% 6.06/6.25 cnf(matrix-28, plain, ( ~one_sorted_str(_u21) | ~element(_u20, powerset(the_carrier(_u21))) | ( subset_complement(the_carrier(_u21), _u20) = subset_difference(the_carrier(_u21), cast_as_carrier_subset(_u21), _u20)) )).
% 6.06/6.25 cnf(matrix-29, plain, ( top_str(skolem4) )).
% 6.06/6.25 cnf(matrix-30, plain, ( element(skolem5, powerset(the_carrier(skolem4))) )).
% 6.06/6.25 cnf(matrix-31, plain, ( ~_def0 | ~_def1 )).
% 6.06/6.25 cnf(matrix-32, plain, ( _def0 | closed_subset(skolem5, skolem4) )).
% 6.06/6.25 cnf(matrix-33, plain, ( _def0 | ~open_subset(subset_complement(the_carrier(skolem4), skolem5), skolem4) )).
% 6.06/6.25 cnf(matrix-34, plain, ( _def1 | open_subset(subset_complement(the_carrier(skolem4), skolem5), skolem4) )).
% 6.06/6.25 cnf(matrix-35, plain, ( _def1 | ~closed_subset(skolem5, skolem4) )).
% 6.06/6.25 cnf(matrix-36, plain, ( ~element(_u28, powerset(_u26)) | subset(_u28, _u26) )).
% 6.06/6.25 cnf(matrix-37, plain, ( ~subset(_u29, _u27) | element(_u29, powerset(_u27)) )).
% 6.06/6.25
% 6.06/6.25 % Proof stack:
% 6.06/6.25 cnf(proof-stack, plain,
% 6.06/6.25 proof_stack(
% 6.06/6.25 start(31),
% 6.06/6.25 left_branch(0, 33, 0, 2),
% 6.06/6.25 left_branch(0, 13, 3, 3),
% 6.06/6.25 left_branch(0, 1, 1, 4),
% 6.06/6.25 left_branch(0, 28, 2, 5),
% 6.06/6.25 left_branch(0, 21, 1, 6),
% 6.06/6.25 left_branch(0, 29, 0, 7),
% 6.06/6.25 right_branch(7),
% 6.06/6.25 right_branch(6),
% 6.06/6.25 left_branch(0, 30, 0, 7),
% 6.06/6.25 right_branch(7),
% 6.06/6.25 right_branch(5),
% 6.06/6.25 right_branch(4),
% 6.06/6.25 left_branch(0, 16, 3, 5),
% 6.06/6.25 left_branch(0, 29, 0, 6),
% 6.06/6.25 right_branch(6),
% 6.06/6.25 left_branch(0, 32, 1, 7),
% 6.06/6.25 reduction(0, 0),
% 6.06/6.25 right_branch(7),
% 6.06/6.25 left_branch(0, 30, 0, 8),
% 6.06/6.25 right_branch(8),
% 6.06/6.25 right_branch(5),
% 6.06/6.25 left_branch(0, 0, 0, 6),
% 6.06/6.25 right_branch(6),
% 6.06/6.25 right_branch(3),
% 6.06/6.25 right_branch(2),
% 6.06/6.25 left_branch(0, 35, 0, 3),
% 6.06/6.25 left_branch(0, 17, 3, 4),
% 6.06/6.25 left_branch(0, 29, 0, 5),
% 6.06/6.25 right_branch(5),
% 6.06/6.25 left_branch(0, 13, 3, 6),
% 6.06/6.25 left_branch(0, 28, 2, 7),
% 6.06/6.25 left_branch(0, 21, 1, 8),
% 6.06/6.25 lemmata(0, 1),
% 6.06/6.25 right_branch(8),
% 6.06/6.25 left_branch(0, 30, 0, 9),
% 6.06/6.25 right_branch(9),
% 6.06/6.25 right_branch(7),
% 6.06/6.25 left_branch(0, 34, 1, 8),
% 6.06/6.25 reduction(0, 0),
% 6.06/6.25 right_branch(8),
% 6.06/6.25 left_branch(0, 0, 0, 9),
% 6.06/6.25 right_branch(9),
% 6.06/6.25 right_branch(6),
% 6.06/6.25 left_branch(0, 37, 1, 7),
% 6.06/6.25 left_branch(0, 15, 3, 8),
% 6.06/6.25 left_branch(0, 1, 1, 9),
% 6.06/6.25 left_branch(0, 0, 0, 10),
% 6.06/6.25 right_branch(10),
% 6.06/6.25 right_branch(9),
% 6.06/6.25 left_branch(0, 36, 1, 10),
% 6.06/6.25 left_branch(0, 30, 0, 11),
% 6.06/6.25 right_branch(11),
% 6.06/6.25 right_branch(10),
% 6.06/6.25 left_branch(0, 3, 1, 11),
% 6.06/6.25 left_branch(0, 0, 0, 12),
% 6.06/6.25 right_branch(12),
% 6.06/6.25 right_branch(11),
% 6.06/6.25 right_branch(8),
% 6.06/6.25 right_branch(7),
% 6.06/6.25 right_branch(4),
% 6.06/6.25 right_branch(3)
% 6.06/6.25 )).
% 6.06/6.25 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------