TSTP Solution File: SEU199+1 by ConnectPP---0.3.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SEU199+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 : n023.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 14:33:32 EDT 2024
% Result : Theorem 0.77s 0.95s
% Output : Proof 0.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU199+1 : TPTP v8.1.2. Released v3.3.0.
% 0.04/0.12 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.33 % Computer : n023.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 14:29:42 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.77/0.95 % SZS status Theorem for theBenchmark
% 0.77/0.95 % SZS output start Proof for theBenchmark
% 0.77/0.95
% 0.77/0.95 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 0.77/0.95 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 0.77/0.95
% 0.77/0.95 % Formula: cc1_relat_1 ( axiom ) converted to clauses:
% 0.77/0.95 cnf(cc1_relat_1-1, axiom, ( ~empty(_u2) | relation(_u2) )).
% 0.77/0.95
% 0.77/0.95 % Formula: commutativity_k2_tarski ( axiom ) converted to clauses:
% 0.77/0.95 cnf(commutativity_k2_tarski-1, axiom, ( ( unordered_pair(_u4, _u3) = unordered_pair(_u3, _u4)) )).
% 0.77/0.95
% 0.77/0.95 % Formula: d12_relat_1 ( axiom ) converted to clauses:
% 0.77/0.95 cnf(d12_relat_1-1, axiom, ( ~relation(_u10) | ~relation(_u9) | ( _u9 != relation_rng_restriction(_u11, _u10)) | ~in(ordered_pair(_u14, _u12), _u9) | in(_u12, _u11) )).
% 0.77/0.95 cnf(d12_relat_1-2, axiom, ( ~relation(_u10) | ~relation(_u9) | ( _u9 != relation_rng_restriction(_u11, _u10)) | ~in(ordered_pair(_u14, _u12), _u9) | in(ordered_pair(_u14, _u12), _u10) )).
% 0.77/0.95 cnf(d12_relat_1-3, axiom, ( ~relation(_u10) | ~relation(_u9) | ( _u9 != relation_rng_restriction(_u11, _u10)) | ~in(_u13, _u11) | ~in(ordered_pair(_u15, _u13), _u10) | in(ordered_pair(_u15, _u13), _u9) )).
% 0.77/0.95 cnf(d12_relat_1-4, axiom, ( ~relation(_u10) | ~relation(_u9) | ( _u9 = relation_rng_restriction(_u11, _u10)) | in(ordered_pair(skolem1(_u11, _u10, _u9), skolem2(_u11, _u10, _u9)), _u9) | in(skolem4(_u11, _u10, _u9), _u11) )).
% 0.77/0.95 cnf(d12_relat_1-5, axiom, ( ~relation(_u10) | ~relation(_u9) | ( _u9 = relation_rng_restriction(_u11, _u10)) | in(ordered_pair(skolem1(_u11, _u10, _u9), skolem2(_u11, _u10, _u9)), _u9) | in(ordered_pair(skolem3(_u11, _u10, _u9), skolem4(_u11, _u10, _u9)), _u10) )).
% 0.77/0.95 cnf(d12_relat_1-6, axiom, ( ~relation(_u10) | ~relation(_u9) | ( _u9 = relation_rng_restriction(_u11, _u10)) | in(ordered_pair(skolem1(_u11, _u10, _u9), skolem2(_u11, _u10, _u9)), _u9) | ~in(ordered_pair(skolem3(_u11, _u10, _u9), skolem4(_u11, _u10, _u9)), _u9) )).
% 0.77/0.95 cnf(d12_relat_1-7, axiom, ( ~relation(_u10) | ~relation(_u9) | ( _u9 = relation_rng_restriction(_u11, _u10)) | ~in(skolem2(_u11, _u10, _u9), _u11) | ~in(ordered_pair(skolem1(_u11, _u10, _u9), skolem2(_u11, _u10, _u9)), _u10) | in(skolem4(_u11, _u10, _u9), _u11) )).
% 0.77/0.95 cnf(d12_relat_1-8, axiom, ( ~relation(_u10) | ~relation(_u9) | ( _u9 = relation_rng_restriction(_u11, _u10)) | ~in(skolem2(_u11, _u10, _u9), _u11) | ~in(ordered_pair(skolem1(_u11, _u10, _u9), skolem2(_u11, _u10, _u9)), _u10) | in(ordered_pair(skolem3(_u11, _u10, _u9), skolem4(_u11, _u10, _u9)), _u10) )).
% 0.77/0.95 cnf(d12_relat_1-9, axiom, ( ~relation(_u10) | ~relation(_u9) | ( _u9 = relation_rng_restriction(_u11, _u10)) | ~in(skolem2(_u11, _u10, _u9), _u11) | ~in(ordered_pair(skolem1(_u11, _u10, _u9), skolem2(_u11, _u10, _u9)), _u10) | ~in(ordered_pair(skolem3(_u11, _u10, _u9), skolem4(_u11, _u10, _u9)), _u9) )).
% 0.77/0.95
% 0.77/0.95 % Formula: d3_relat_1 ( axiom ) converted to clauses:
% 0.77/0.95 cnf(d3_relat_1-1, axiom, ( ~relation(_u25) | ~relation(_u24) | ~subset(_u25, _u24) | ~in(ordered_pair(_u21, _u20), _u25) | in(ordered_pair(_u21, _u20), _u24) )).
% 0.77/0.95 cnf(d3_relat_1-2, axiom, ( ~relation(_u25) | ~relation(_u24) | subset(_u25, _u24) | in(ordered_pair(skolem5(_u25, _u24), skolem6(_u25, _u24)), _u25) )).
% 0.77/0.95 cnf(d3_relat_1-3, axiom, ( ~relation(_u25) | ~relation(_u24) | subset(_u25, _u24) | ~in(ordered_pair(skolem5(_u25, _u24), skolem6(_u25, _u24)), _u24) )).
% 0.77/0.95
% 0.77/0.95 % Formula: d5_tarski ( axiom ) converted to clauses:
% 0.77/0.95 cnf(d5_tarski-1, axiom, ( ( ordered_pair(_u27, _u26) = unordered_pair(unordered_pair(_u27, _u26), singleton(_u27))) )).
% 0.77/0.95
% 0.77/0.95 % Formula: dt_k1_tarski ( axiom ) converted to clauses:
% 0.77/0.95 cnf(dt_k1_tarski, axiom, $true).
% 0.77/0.95
% 0.77/0.95 % Formula: dt_k1_xboole_0 ( axiom ) converted to clauses:
% 0.77/0.95 cnf(dt_k1_xboole_0, axiom, $true).
% 0.77/0.95
% 0.77/0.95 % Formula: dt_k1_zfmisc_1 ( axiom ) converted to clauses:
% 0.77/0.95 cnf(dt_k1_zfmisc_1, axiom, $true).
% 0.77/0.95
% 0.77/0.95 % Formula: dt_k2_tarski ( axiom ) converted to clauses:
% 0.77/0.95 cnf(dt_k2_tarski, axiom, $true).
% 0.77/0.95
% 0.77/0.95 % Formula: dt_k4_tarski ( axiom ) converted to clauses:
% 0.77/0.95 cnf(dt_k4_tarski, axiom, $true).
% 0.77/0.95
% 0.77/0.95 % Formula: dt_k8_relat_1 ( axiom ) converted to clauses:
% 0.77/0.95 cnf(dt_k8_relat_1-1, axiom, ( ~relation(_u28) | relation(relation_rng_restriction(_u29, _u28)) )).
% 0.77/0.95
% 0.77/0.95 % Formula: dt_m1_subset_1 ( axiom ) converted to clauses:
% 0.77/0.95 cnf(dt_m1_subset_1, axiom, $true).
% 0.77/0.95
% 0.77/0.95 % Formula: existence_m1_subset_1 ( axiom ) converted to clauses:
% 0.77/0.95 cnf(existence_m1_subset_1-1, axiom, ( element(skolem7(_u31), _u31) )).
% 0.77/0.95
% 0.77/0.95 % Formula: fc1_subset_1 ( axiom ) converted to clauses:
% 0.77/0.95 cnf(fc1_subset_1-1, axiom, ( ~empty(powerset(_u32)) )).
% 0.77/0.95
% 0.77/0.95 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 0.77/0.95 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 0.77/0.95
% 0.77/0.95 % Formula: fc1_zfmisc_1 ( axiom ) converted to clauses:
% 0.77/0.95 cnf(fc1_zfmisc_1-1, axiom, ( ~empty(ordered_pair(_u34, _u33)) )).
% 0.77/0.95
% 0.77/0.95 % Formula: fc2_subset_1 ( axiom ) converted to clauses:
% 0.77/0.95 cnf(fc2_subset_1-1, axiom, ( ~empty(singleton(_u35)) )).
% 0.77/0.95
% 0.77/0.95 % Formula: fc3_subset_1 ( axiom ) converted to clauses:
% 0.77/0.95 cnf(fc3_subset_1-1, axiom, ( ~empty(unordered_pair(_u37, _u36)) )).
% 0.77/0.95
% 0.77/0.95 % Formula: fc4_relat_1 ( axiom ) converted to clauses:
% 0.77/0.95 cnf(fc4_relat_1-1, axiom, ( empty(empty_set) )).
% 0.77/0.95 cnf(fc4_relat_1-2, axiom, ( relation(empty_set) )).
% 0.77/0.95
% 0.77/0.95 % Formula: rc1_relat_1 ( axiom ) converted to clauses:
% 0.77/0.95 cnf(rc1_relat_1-1, axiom, ( empty(skolem8) )).
% 0.77/0.95 cnf(rc1_relat_1-2, axiom, ( relation(skolem8) )).
% 0.77/0.95
% 0.77/0.95 % Formula: rc1_subset_1 ( axiom ) converted to clauses:
% 0.77/0.95 cnf(rc1_subset_1-1, axiom, ( empty(_u40) | element(skolem9(_u40), powerset(_u40)) )).
% 0.77/0.95 cnf(rc1_subset_1-2, axiom, ( empty(_u40) | ~empty(skolem9(_u40)) )).
% 0.77/0.95
% 0.77/0.95 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 0.77/0.95 cnf(rc1_xboole_0-1, axiom, ( empty(skolem10) )).
% 0.77/0.95
% 0.77/0.95 % Formula: rc2_relat_1 ( axiom ) converted to clauses:
% 0.77/0.95 cnf(rc2_relat_1-1, axiom, ( ~empty(skolem11) )).
% 0.77/0.95 cnf(rc2_relat_1-2, axiom, ( relation(skolem11) )).
% 0.77/0.95
% 0.77/0.95 % Formula: rc2_subset_1 ( axiom ) converted to clauses:
% 0.77/0.95 cnf(rc2_subset_1-1, axiom, ( element(skolem12(_u44), powerset(_u44)) )).
% 0.77/0.95 cnf(rc2_subset_1-2, axiom, ( empty(skolem12(_u44)) )).
% 0.77/0.95
% 0.77/0.95 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 0.77/0.95 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem13) )).
% 0.77/0.95
% 0.77/0.95 % Formula: reflexivity_r1_tarski ( axiom ) converted to clauses:
% 0.77/0.95 cnf(reflexivity_r1_tarski-1, axiom, ( subset(_u47, _u47) )).
% 0.77/0.95
% 0.77/0.95 % Formula: t117_relat_1 ( conjecture ) (definitionally) converted to clauses:
% 0.77/0.95 cnf(t117_relat_1-1, negated_conjecture, ( relation(skolem15) )).
% 0.77/0.95 cnf(t117_relat_1-2, negated_conjecture, ( ~subset(relation_rng_restriction(skolem14, skolem15), skolem15) )).
% 0.77/0.95
% 0.77/0.95 % Formula: t1_subset ( axiom ) converted to clauses:
% 0.77/0.95 cnf(t1_subset-1, axiom, ( ~in(_u51, _u50) | element(_u51, _u50) )).
% 0.77/0.95
% 0.77/0.95 % Formula: t2_subset ( axiom ) converted to clauses:
% 0.77/0.95 cnf(t2_subset-1, axiom, ( ~element(_u53, _u52) | empty(_u52) | in(_u53, _u52) )).
% 0.77/0.95
% 0.77/0.95 % Formula: t3_subset ( axiom ) converted to clauses:
% 0.77/0.95 cnf(t3_subset-1, axiom, ( ~element(_u58, powerset(_u56)) | subset(_u58, _u56) )).
% 0.77/0.95 cnf(t3_subset-2, axiom, ( ~subset(_u59, _u57) | element(_u59, powerset(_u57)) )).
% 0.77/0.95
% 0.77/0.95 % Formula: t4_subset ( axiom ) converted to clauses:
% 0.77/0.95 cnf(t4_subset-1, axiom, ( ~in(_u62, _u61) | ~element(_u61, powerset(_u60)) | element(_u62, _u60) )).
% 0.77/0.95
% 0.77/0.95 % Formula: t5_subset ( axiom ) converted to clauses:
% 0.77/0.95 cnf(t5_subset-1, axiom, ( ~in(_u65, _u64) | ~element(_u64, powerset(_u63)) | ~empty(_u63) )).
% 0.77/0.95
% 0.77/0.95 % Formula: t6_boole ( axiom ) converted to clauses:
% 0.77/0.95 cnf(t6_boole-1, axiom, ( ~empty(_u66) | ( _u66 = empty_set) )).
% 0.77/0.95
% 0.77/0.95 % Formula: t7_boole ( axiom ) converted to clauses:
% 0.77/0.95 cnf(t7_boole-1, axiom, ( ~in(_u68, _u67) | ~empty(_u67) )).
% 0.77/0.95
% 0.77/0.95 % Formula: t8_boole ( axiom ) converted to clauses:
% 0.77/0.95 cnf(t8_boole-1, axiom, ( ~empty(_u70) | ( _u70 = _u69) | ~empty(_u69) )).
% 0.77/0.95
% 0.77/0.95 % Problem matrix:
% 0.77/0.95 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 0.77/0.95 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 0.77/0.95 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 0.77/0.95 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( unordered_pair(__eqx_0, __eqx_1) = unordered_pair(__eqy_0, __eqy_1)) )).
% 0.77/0.95 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( relation_rng_restriction(__eqx_0, __eqx_1) = relation_rng_restriction(__eqy_0, __eqy_1)) )).
% 0.77/0.95 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( ordered_pair(__eqx_0, __eqx_1) = ordered_pair(__eqy_0, __eqy_1)) )).
% 0.77/0.95 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( singleton(__eqx_0) = singleton(__eqy_0)) )).
% 0.77/0.95 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( powerset(__eqx_0) = powerset(__eqy_0)) )).
% 0.77/0.95 cnf(matrix-8, 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)) )).
% 0.77/0.95 cnf(matrix-9, 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)) )).
% 0.77/0.95 cnf(matrix-10, 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)) )).
% 0.77/0.95 cnf(matrix-11, 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)) )).
% 0.77/0.95 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem5(__eqx_0, __eqx_1) = skolem5(__eqy_0, __eqy_1)) )).
% 0.77/0.95 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem6(__eqx_0, __eqx_1) = skolem6(__eqy_0, __eqy_1)) )).
% 0.77/0.95 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( skolem7(__eqx_0) = skolem7(__eqy_0)) )).
% 0.77/0.95 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( skolem9(__eqx_0) = skolem9(__eqy_0)) )).
% 0.77/0.95 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( skolem12(__eqx_0) = skolem12(__eqy_0)) )).
% 0.77/0.95 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 0.77/0.95 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 0.77/0.95 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ~relation(__eqx_0) | relation(__eqy_0) )).
% 0.77/0.95 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 0.77/0.95 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~element(__eqx_0, __eqx_1) | element(__eqy_0, __eqy_1) )).
% 0.77/0.95 cnf(matrix-22, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 0.77/0.95 cnf(matrix-23, plain, ( ~empty(_u2) | relation(_u2) )).
% 0.77/0.95 cnf(matrix-24, plain, ( ( unordered_pair(_u4, _u3) = unordered_pair(_u3, _u4)) )).
% 0.77/0.95 cnf(matrix-25, plain, ( ~relation(_u10) | ~relation(_u9) | ( _u9 != relation_rng_restriction(_u11, _u10)) | ~in(ordered_pair(_u14, _u12), _u9) | in(_u12, _u11) )).
% 0.77/0.95 cnf(matrix-26, plain, ( ~relation(_u10) | ~relation(_u9) | ( _u9 != relation_rng_restriction(_u11, _u10)) | ~in(ordered_pair(_u14, _u12), _u9) | in(ordered_pair(_u14, _u12), _u10) )).
% 0.77/0.95 cnf(matrix-27, plain, ( ~relation(_u10) | ~relation(_u9) | ( _u9 != relation_rng_restriction(_u11, _u10)) | ~in(_u13, _u11) | ~in(ordered_pair(_u15, _u13), _u10) | in(ordered_pair(_u15, _u13), _u9) )).
% 0.77/0.95 cnf(matrix-28, plain, ( ~relation(_u10) | ~relation(_u9) | ( _u9 = relation_rng_restriction(_u11, _u10)) | in(ordered_pair(skolem1(_u11, _u10, _u9), skolem2(_u11, _u10, _u9)), _u9) | in(skolem4(_u11, _u10, _u9), _u11) )).
% 0.77/0.95 cnf(matrix-29, plain, ( ~relation(_u10) | ~relation(_u9) | ( _u9 = relation_rng_restriction(_u11, _u10)) | in(ordered_pair(skolem1(_u11, _u10, _u9), skolem2(_u11, _u10, _u9)), _u9) | in(ordered_pair(skolem3(_u11, _u10, _u9), skolem4(_u11, _u10, _u9)), _u10) )).
% 0.77/0.95 cnf(matrix-30, plain, ( ~relation(_u10) | ~relation(_u9) | ( _u9 = relation_rng_restriction(_u11, _u10)) | in(ordered_pair(skolem1(_u11, _u10, _u9), skolem2(_u11, _u10, _u9)), _u9) | ~in(ordered_pair(skolem3(_u11, _u10, _u9), skolem4(_u11, _u10, _u9)), _u9) )).
% 0.77/0.95 cnf(matrix-31, plain, ( ~relation(_u10) | ~relation(_u9) | ( _u9 = relation_rng_restriction(_u11, _u10)) | ~in(skolem2(_u11, _u10, _u9), _u11) | ~in(ordered_pair(skolem1(_u11, _u10, _u9), skolem2(_u11, _u10, _u9)), _u10) | in(skolem4(_u11, _u10, _u9), _u11) )).
% 0.77/0.95 cnf(matrix-32, plain, ( ~relation(_u10) | ~relation(_u9) | ( _u9 = relation_rng_restriction(_u11, _u10)) | ~in(skolem2(_u11, _u10, _u9), _u11) | ~in(ordered_pair(skolem1(_u11, _u10, _u9), skolem2(_u11, _u10, _u9)), _u10) | in(ordered_pair(skolem3(_u11, _u10, _u9), skolem4(_u11, _u10, _u9)), _u10) )).
% 0.77/0.95 cnf(matrix-33, plain, ( ~relation(_u10) | ~relation(_u9) | ( _u9 = relation_rng_restriction(_u11, _u10)) | ~in(skolem2(_u11, _u10, _u9), _u11) | ~in(ordered_pair(skolem1(_u11, _u10, _u9), skolem2(_u11, _u10, _u9)), _u10) | ~in(ordered_pair(skolem3(_u11, _u10, _u9), skolem4(_u11, _u10, _u9)), _u9) )).
% 0.77/0.95 cnf(matrix-34, plain, ( ~relation(_u25) | ~relation(_u24) | ~subset(_u25, _u24) | ~in(ordered_pair(_u21, _u20), _u25) | in(ordered_pair(_u21, _u20), _u24) )).
% 0.77/0.95 cnf(matrix-35, plain, ( ~relation(_u25) | ~relation(_u24) | subset(_u25, _u24) | in(ordered_pair(skolem5(_u25, _u24), skolem6(_u25, _u24)), _u25) )).
% 0.77/0.95 cnf(matrix-36, plain, ( ~relation(_u25) | ~relation(_u24) | subset(_u25, _u24) | ~in(ordered_pair(skolem5(_u25, _u24), skolem6(_u25, _u24)), _u24) )).
% 0.77/0.95 cnf(matrix-37, plain, ( ( ordered_pair(_u27, _u26) = unordered_pair(unordered_pair(_u27, _u26), singleton(_u27))) )).
% 0.77/0.95 cnf(matrix-38, plain, ( ~relation(_u28) | relation(relation_rng_restriction(_u29, _u28)) )).
% 0.77/0.95 cnf(matrix-39, plain, ( element(skolem7(_u31), _u31) )).
% 0.77/0.95 cnf(matrix-40, plain, ( ~empty(powerset(_u32)) )).
% 0.77/0.95 cnf(matrix-41, plain, ( empty(empty_set) )).
% 0.77/0.95 cnf(matrix-42, plain, ( ~empty(ordered_pair(_u34, _u33)) )).
% 0.77/0.95 cnf(matrix-43, plain, ( ~empty(singleton(_u35)) )).
% 0.77/0.95 cnf(matrix-44, plain, ( ~empty(unordered_pair(_u37, _u36)) )).
% 0.77/0.95 cnf(matrix-45, plain, ( empty(empty_set) )).
% 0.77/0.95 cnf(matrix-46, plain, ( relation(empty_set) )).
% 0.77/0.95 cnf(matrix-47, plain, ( empty(skolem8) )).
% 0.77/0.95 cnf(matrix-48, plain, ( relation(skolem8) )).
% 0.77/0.95 cnf(matrix-49, plain, ( empty(_u40) | element(skolem9(_u40), powerset(_u40)) )).
% 0.77/0.95 cnf(matrix-50, plain, ( empty(_u40) | ~empty(skolem9(_u40)) )).
% 0.77/0.95 cnf(matrix-51, plain, ( empty(skolem10) )).
% 0.77/0.95 cnf(matrix-52, plain, ( ~empty(skolem11) )).
% 0.77/0.95 cnf(matrix-53, plain, ( relation(skolem11) )).
% 0.77/0.95 cnf(matrix-54, plain, ( element(skolem12(_u44), powerset(_u44)) )).
% 0.77/0.95 cnf(matrix-55, plain, ( empty(skolem12(_u44)) )).
% 0.77/0.95 cnf(matrix-56, plain, ( ~empty(skolem13) )).
% 0.77/0.95 cnf(matrix-57, plain, ( subset(_u47, _u47) )).
% 0.77/0.95 cnf(matrix-58, plain, ( relation(skolem15) )).
% 0.77/0.95 cnf(matrix-59, plain, ( ~subset(relation_rng_restriction(skolem14, skolem15), skolem15) )).
% 0.77/0.95 cnf(matrix-60, plain, ( ~in(_u51, _u50) | element(_u51, _u50) )).
% 0.77/0.95 cnf(matrix-61, plain, ( ~element(_u53, _u52) | empty(_u52) | in(_u53, _u52) )).
% 0.77/0.95 cnf(matrix-62, plain, ( ~element(_u58, powerset(_u56)) | subset(_u58, _u56) )).
% 0.77/0.95 cnf(matrix-63, plain, ( ~subset(_u59, _u57) | element(_u59, powerset(_u57)) )).
% 0.77/0.95 cnf(matrix-64, plain, ( ~in(_u62, _u61) | ~element(_u61, powerset(_u60)) | element(_u62, _u60) )).
% 0.77/0.95 cnf(matrix-65, plain, ( ~in(_u65, _u64) | ~element(_u64, powerset(_u63)) | ~empty(_u63) )).
% 0.77/0.95 cnf(matrix-66, plain, ( ~empty(_u66) | ( _u66 = empty_set) )).
% 0.77/0.95 cnf(matrix-67, plain, ( ~in(_u68, _u67) | ~empty(_u67) )).
% 0.77/0.95 cnf(matrix-68, plain, ( ~empty(_u70) | ( _u70 = _u69) | ~empty(_u69) )).
% 0.77/0.95
% 0.77/0.95 % Proof stack:
% 0.77/0.95 cnf(proof-stack, plain,
% 0.77/0.95 proof_stack(
% 0.77/0.95 start(59),
% 0.77/0.95 left_branch(0, 36, 2, 2),
% 0.77/0.95 left_branch(0, 38, 1, 3),
% 0.77/0.95 left_branch(0, 58, 0, 4),
% 0.77/0.95 right_branch(4),
% 0.77/0.95 right_branch(3),
% 0.77/0.95 left_branch(0, 26, 4, 4),
% 0.77/0.95 left_branch(0, 58, 0, 5),
% 0.77/0.95 right_branch(5),
% 0.77/0.95 left_branch(0, 35, 3, 6),
% 0.77/0.95 lemmata(0, 0),
% 0.77/0.95 reduction(0, 0),
% 0.77/0.95 lemmata(0, 1),
% 0.77/0.95 right_branch(6),
% 0.77/0.95 left_branch(0, 4, 2, 7),
% 0.77/0.95 left_branch(0, 0, 0, 8),
% 0.77/0.95 right_branch(8),
% 0.77/0.95 left_branch(0, 0, 0, 9),
% 0.77/0.95 right_branch(9),
% 0.77/0.95 right_branch(7),
% 0.77/0.95 lemmata(0, 0),
% 0.77/0.95 right_branch(4),
% 0.77/0.95 left_branch(0, 58, 0, 5),
% 0.77/0.95 right_branch(5),
% 0.77/0.95 right_branch(2)
% 0.77/0.95 )).
% 0.77/0.95 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------