TSTP Solution File: SEU137+2 by ConnectPP---0.3.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SEU137+2 : 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 : n020.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 14:33:16 EDT 2024
% Result : Theorem 68.41s 68.57s
% Output : Proof 68.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU137+2 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.34 % Computer : n020.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 : Wed Mar 20 15:02:58 EDT 2024
% 0.13/0.34 % CPUTime :
% 68.41/68.57 % SZS status Theorem for theBenchmark
% 68.41/68.57 % SZS output start Proof for theBenchmark
% 68.41/68.57
% 68.41/68.57 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 68.41/68.57 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 68.41/68.57
% 68.41/68.57 % Formula: commutativity_k2_xboole_0 ( axiom ) converted to clauses:
% 68.41/68.57 cnf(commutativity_k2_xboole_0-1, axiom, ( ( set_union2(_u3, _u2) = set_union2(_u2, _u3)) )).
% 68.41/68.57
% 68.41/68.57 % Formula: commutativity_k3_xboole_0 ( axiom ) converted to clauses:
% 68.41/68.57 cnf(commutativity_k3_xboole_0-1, axiom, ( ( set_intersection2(_u5, _u4) = set_intersection2(_u4, _u5)) )).
% 68.41/68.57
% 68.41/68.57 % Formula: d10_xboole_0 ( axiom ) converted to clauses:
% 68.41/68.57 cnf(d10_xboole_0-1, axiom, ( ( _u10 != _u8) | subset(_u10, _u8) )).
% 68.41/68.57 cnf(d10_xboole_0-2, axiom, ( ( _u10 != _u8) | subset(_u8, _u10) )).
% 68.41/68.57 cnf(d10_xboole_0-3, axiom, ( ~subset(_u11, _u9) | ~subset(_u9, _u11) | ( _u11 = _u9) )).
% 68.41/68.57
% 68.41/68.57 % Formula: d1_xboole_0 ( axiom ) converted to clauses:
% 68.41/68.57 cnf(d1_xboole_0-1, axiom, ( ( _u15 != empty_set) | ~in(_u12, _u15) )).
% 68.41/68.57 cnf(d1_xboole_0-2, axiom, ( in(skolem1(_u16), _u16) | ( _u16 = empty_set) )).
% 68.41/68.57
% 68.41/68.57 % Formula: d2_xboole_0 ( axiom ) converted to clauses:
% 68.41/68.57 cnf(d2_xboole_0-1, axiom, ( ( _u26 != set_union2(_u30, _u28)) | ~in(_u22, _u26) | in(_u22, _u30) | in(_u22, _u28) )).
% 68.41/68.57 cnf(d2_xboole_0-2, axiom, ( ( _u26 != set_union2(_u30, _u28)) | in(_u23, _u26) | ~in(_u23, _u30) )).
% 68.41/68.57 cnf(d2_xboole_0-3, axiom, ( ( _u26 != set_union2(_u30, _u28)) | in(_u23, _u26) | ~in(_u23, _u28) )).
% 68.41/68.57 cnf(d2_xboole_0-4, axiom, ( ( _u27 = set_union2(_u31, _u29)) | in(skolem2(_u31, _u29, _u27), _u27) | in(skolem3(_u31, _u29, _u27), _u31) | in(skolem3(_u31, _u29, _u27), _u29) )).
% 68.41/68.57 cnf(d2_xboole_0-5, axiom, ( ( _u27 = set_union2(_u31, _u29)) | in(skolem2(_u31, _u29, _u27), _u27) | ~in(skolem3(_u31, _u29, _u27), _u27) )).
% 68.41/68.57 cnf(d2_xboole_0-6, axiom, ( ( _u27 = set_union2(_u31, _u29)) | in(skolem3(_u31, _u29, _u27), _u31) | in(skolem3(_u31, _u29, _u27), _u29) | ~in(skolem2(_u31, _u29, _u27), _u31) )).
% 68.41/68.57 cnf(d2_xboole_0-7, axiom, ( ( _u27 = set_union2(_u31, _u29)) | in(skolem3(_u31, _u29, _u27), _u31) | in(skolem3(_u31, _u29, _u27), _u29) | ~in(skolem2(_u31, _u29, _u27), _u29) )).
% 68.41/68.57 cnf(d2_xboole_0-8, axiom, ( ( _u27 = set_union2(_u31, _u29)) | ~in(skolem3(_u31, _u29, _u27), _u27) | ~in(skolem2(_u31, _u29, _u27), _u31) )).
% 68.41/68.57 cnf(d2_xboole_0-9, axiom, ( ( _u27 = set_union2(_u31, _u29)) | ~in(skolem3(_u31, _u29, _u27), _u27) | ~in(skolem2(_u31, _u29, _u27), _u29) )).
% 68.41/68.57
% 68.41/68.57 % Formula: d3_tarski ( axiom ) converted to clauses:
% 68.41/68.57 cnf(d3_tarski-1, axiom, ( ~subset(_u38, _u36) | ~in(_u32, _u38) | in(_u32, _u36) )).
% 68.41/68.57 cnf(d3_tarski-2, axiom, ( subset(_u39, _u37) | in(skolem4(_u39, _u37), _u39) )).
% 68.41/68.57 cnf(d3_tarski-3, axiom, ( subset(_u39, _u37) | ~in(skolem4(_u39, _u37), _u37) )).
% 68.41/68.57
% 68.41/68.57 % Formula: d3_xboole_0 ( axiom ) converted to clauses:
% 68.41/68.57 cnf(d3_xboole_0-1, axiom, ( ( _u49 != set_intersection2(_u53, _u51)) | ~in(_u45, _u49) | in(_u45, _u53) )).
% 68.41/68.57 cnf(d3_xboole_0-2, axiom, ( ( _u49 != set_intersection2(_u53, _u51)) | ~in(_u45, _u49) | in(_u45, _u51) )).
% 68.41/68.57 cnf(d3_xboole_0-3, axiom, ( ( _u49 != set_intersection2(_u53, _u51)) | ~in(_u46, _u53) | ~in(_u46, _u51) | in(_u46, _u49) )).
% 68.41/68.57 cnf(d3_xboole_0-4, axiom, ( ( _u50 = set_intersection2(_u54, _u52)) | in(skolem5(_u54, _u52, _u50), _u50) | in(skolem6(_u54, _u52, _u50), _u54) )).
% 68.41/68.57 cnf(d3_xboole_0-5, axiom, ( ( _u50 = set_intersection2(_u54, _u52)) | in(skolem5(_u54, _u52, _u50), _u50) | in(skolem6(_u54, _u52, _u50), _u52) )).
% 68.41/68.57 cnf(d3_xboole_0-6, axiom, ( ( _u50 = set_intersection2(_u54, _u52)) | in(skolem5(_u54, _u52, _u50), _u50) | ~in(skolem6(_u54, _u52, _u50), _u50) )).
% 68.41/68.57 cnf(d3_xboole_0-7, axiom, ( ( _u50 = set_intersection2(_u54, _u52)) | ~in(skolem5(_u54, _u52, _u50), _u54) | ~in(skolem5(_u54, _u52, _u50), _u52) | in(skolem6(_u54, _u52, _u50), _u54) )).
% 68.41/68.57 cnf(d3_xboole_0-8, axiom, ( ( _u50 = set_intersection2(_u54, _u52)) | ~in(skolem5(_u54, _u52, _u50), _u54) | ~in(skolem5(_u54, _u52, _u50), _u52) | in(skolem6(_u54, _u52, _u50), _u52) )).
% 68.41/68.57 cnf(d3_xboole_0-9, axiom, ( ( _u50 = set_intersection2(_u54, _u52)) | ~in(skolem5(_u54, _u52, _u50), _u54) | ~in(skolem5(_u54, _u52, _u50), _u52) | ~in(skolem6(_u54, _u52, _u50), _u50) )).
% 68.41/68.57
% 68.41/68.57 % Formula: d4_xboole_0 ( axiom ) converted to clauses:
% 68.41/68.57 cnf(d4_xboole_0-1, axiom, ( ( _u64 != set_difference(_u68, _u66)) | ~in(_u60, _u64) | in(_u60, _u68) )).
% 68.41/68.57 cnf(d4_xboole_0-2, axiom, ( ( _u64 != set_difference(_u68, _u66)) | ~in(_u60, _u64) | ~in(_u60, _u66) )).
% 68.41/68.57 cnf(d4_xboole_0-3, axiom, ( ( _u64 != set_difference(_u68, _u66)) | ~in(_u61, _u68) | in(_u61, _u66) | in(_u61, _u64) )).
% 68.41/68.57 cnf(d4_xboole_0-4, axiom, ( ( _u65 = set_difference(_u69, _u67)) | in(skolem7(_u69, _u67, _u65), _u65) | in(skolem8(_u69, _u67, _u65), _u69) )).
% 68.41/68.57 cnf(d4_xboole_0-5, axiom, ( ( _u65 = set_difference(_u69, _u67)) | in(skolem7(_u69, _u67, _u65), _u65) | ~in(skolem8(_u69, _u67, _u65), _u67) )).
% 68.41/68.57 cnf(d4_xboole_0-6, axiom, ( ( _u65 = set_difference(_u69, _u67)) | in(skolem7(_u69, _u67, _u65), _u65) | ~in(skolem8(_u69, _u67, _u65), _u65) )).
% 68.41/68.57 cnf(d4_xboole_0-7, axiom, ( ( _u65 = set_difference(_u69, _u67)) | ~in(skolem7(_u69, _u67, _u65), _u69) | in(skolem7(_u69, _u67, _u65), _u67) | in(skolem8(_u69, _u67, _u65), _u69) )).
% 68.41/68.57 cnf(d4_xboole_0-8, axiom, ( ( _u65 = set_difference(_u69, _u67)) | ~in(skolem7(_u69, _u67, _u65), _u69) | in(skolem7(_u69, _u67, _u65), _u67) | ~in(skolem8(_u69, _u67, _u65), _u67) )).
% 68.41/68.57 cnf(d4_xboole_0-9, axiom, ( ( _u65 = set_difference(_u69, _u67)) | ~in(skolem7(_u69, _u67, _u65), _u69) | in(skolem7(_u69, _u67, _u65), _u67) | ~in(skolem8(_u69, _u67, _u65), _u65) )).
% 68.41/68.57
% 68.41/68.57 % Formula: d7_xboole_0 ( axiom ) converted to clauses:
% 68.41/68.57 cnf(d7_xboole_0-1, axiom, ( ~disjoint(_u74, _u72) | ( set_intersection2(_u74, _u72) = empty_set) )).
% 68.41/68.57 cnf(d7_xboole_0-2, axiom, ( ( set_intersection2(_u75, _u73) != empty_set) | disjoint(_u75, _u73) )).
% 68.41/68.57
% 68.41/68.57 % Formula: dt_k1_xboole_0 ( axiom ) converted to clauses:
% 68.41/68.57 cnf(dt_k1_xboole_0, axiom, $true).
% 68.41/68.57
% 68.41/68.57 % Formula: dt_k2_xboole_0 ( axiom ) converted to clauses:
% 68.41/68.57 cnf(dt_k2_xboole_0, axiom, $true).
% 68.41/68.57
% 68.41/68.57 % Formula: dt_k3_xboole_0 ( axiom ) converted to clauses:
% 68.41/68.57 cnf(dt_k3_xboole_0, axiom, $true).
% 68.41/68.57
% 68.41/68.57 % Formula: dt_k4_xboole_0 ( axiom ) converted to clauses:
% 68.41/68.57 cnf(dt_k4_xboole_0, axiom, $true).
% 68.41/68.57
% 68.41/68.57 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 68.41/68.57 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 68.41/68.57
% 68.41/68.57 % Formula: fc2_xboole_0 ( axiom ) converted to clauses:
% 68.41/68.57 cnf(fc2_xboole_0-1, axiom, ( empty(_u77) | ~empty(set_union2(_u77, _u76)) )).
% 68.41/68.57
% 68.41/68.57 % Formula: fc3_xboole_0 ( axiom ) converted to clauses:
% 68.41/68.57 cnf(fc3_xboole_0-1, axiom, ( empty(_u79) | ~empty(set_union2(_u78, _u79)) )).
% 68.41/68.57
% 68.41/68.57 % Formula: idempotence_k2_xboole_0 ( axiom ) converted to clauses:
% 68.41/68.57 cnf(idempotence_k2_xboole_0-1, axiom, ( ( set_union2(_u81, _u81) = _u81) )).
% 68.41/68.57
% 68.41/68.57 % Formula: idempotence_k3_xboole_0 ( axiom ) converted to clauses:
% 68.41/68.57 cnf(idempotence_k3_xboole_0-1, axiom, ( ( set_intersection2(_u83, _u83) = _u83) )).
% 68.41/68.57
% 68.41/68.57 % Formula: l32_xboole_1 ( lemma ) converted to clauses:
% 68.41/68.57 cnf(l32_xboole_1-1, lemma, ( ( set_difference(_u88, _u86) != empty_set) | subset(_u88, _u86) )).
% 68.41/68.57 cnf(l32_xboole_1-2, lemma, ( ~subset(_u89, _u87) | ( set_difference(_u89, _u87) = empty_set) )).
% 68.41/68.57
% 68.41/68.57 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 68.41/68.57 cnf(rc1_xboole_0-1, axiom, ( empty(skolem9) )).
% 68.41/68.57
% 68.41/68.57 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 68.41/68.57 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem10) )).
% 68.41/68.57
% 68.41/68.57 % Formula: reflexivity_r1_tarski ( axiom ) converted to clauses:
% 68.41/68.57 cnf(reflexivity_r1_tarski-1, axiom, ( subset(_u93, _u93) )).
% 68.41/68.57
% 68.41/68.57 % Formula: symmetry_r1_xboole_0 ( axiom ) converted to clauses:
% 68.41/68.57 cnf(symmetry_r1_xboole_0-1, axiom, ( ~disjoint(_u95, _u94) | disjoint(_u94, _u95) )).
% 68.41/68.57
% 68.41/68.57 % Formula: t12_xboole_1 ( lemma ) converted to clauses:
% 68.41/68.57 cnf(t12_xboole_1-1, lemma, ( ~subset(_u97, _u96) | ( set_union2(_u97, _u96) = _u96) )).
% 68.41/68.57
% 68.41/68.57 % Formula: t17_xboole_1 ( lemma ) converted to clauses:
% 68.41/68.57 cnf(t17_xboole_1-1, lemma, ( subset(set_intersection2(_u99, _u98), _u99) )).
% 68.41/68.57
% 68.41/68.57 % Formula: t19_xboole_1 ( lemma ) converted to clauses:
% 68.41/68.57 cnf(t19_xboole_1-1, lemma, ( ~subset(_u102, _u101) | ~subset(_u102, _u100) | subset(_u102, set_intersection2(_u101, _u100)) )).
% 68.41/68.57
% 68.41/68.57 % Formula: t1_boole ( axiom ) converted to clauses:
% 68.41/68.57 cnf(t1_boole-1, axiom, ( ( set_union2(_u103, empty_set) = _u103) )).
% 68.41/68.57
% 68.41/68.57 % Formula: t1_xboole_1 ( lemma ) converted to clauses:
% 68.41/68.57 cnf(t1_xboole_1-1, lemma, ( ~subset(_u106, _u105) | ~subset(_u105, _u104) | subset(_u106, _u104) )).
% 68.41/68.57
% 68.41/68.57 % Formula: t26_xboole_1 ( lemma ) converted to clauses:
% 68.41/68.57 cnf(t26_xboole_1-1, lemma, ( ~subset(_u109, _u108) | subset(set_intersection2(_u109, _u107), set_intersection2(_u108, _u107)) )).
% 68.41/68.57
% 68.41/68.57 % Formula: t28_xboole_1 ( lemma ) converted to clauses:
% 68.41/68.57 cnf(t28_xboole_1-1, lemma, ( ~subset(_u111, _u110) | ( set_intersection2(_u111, _u110) = _u111) )).
% 68.41/68.57
% 68.41/68.57 % Formula: t2_boole ( axiom ) converted to clauses:
% 68.41/68.57 cnf(t2_boole-1, axiom, ( ( set_intersection2(_u112, empty_set) = empty_set) )).
% 68.41/68.57
% 68.41/68.57 % Formula: t2_tarski ( axiom ) converted to clauses:
% 68.41/68.57 cnf(t2_tarski-1, axiom, ( ( _u115 = _u114) | in(skolem11(_u115, _u114), _u115) | in(skolem12(_u115, _u114), _u114) )).
% 68.41/68.57 cnf(t2_tarski-2, axiom, ( ( _u115 = _u114) | in(skolem11(_u115, _u114), _u115) | ~in(skolem12(_u115, _u114), _u115) )).
% 68.41/68.57 cnf(t2_tarski-3, axiom, ( ( _u115 = _u114) | ~in(skolem11(_u115, _u114), _u114) | in(skolem12(_u115, _u114), _u114) )).
% 68.41/68.57 cnf(t2_tarski-4, axiom, ( ( _u115 = _u114) | ~in(skolem11(_u115, _u114), _u114) | ~in(skolem12(_u115, _u114), _u115) )).
% 68.41/68.57
% 68.41/68.57 % Formula: t2_xboole_1 ( lemma ) converted to clauses:
% 68.41/68.57 cnf(t2_xboole_1-1, lemma, ( subset(empty_set, _u118) )).
% 68.41/68.57
% 68.41/68.57 % Formula: t33_xboole_1 ( lemma ) converted to clauses:
% 68.41/68.57 cnf(t33_xboole_1-1, lemma, ( ~subset(_u121, _u120) | subset(set_difference(_u121, _u119), set_difference(_u120, _u119)) )).
% 68.41/68.57
% 68.41/68.57 % Formula: t36_xboole_1 ( lemma ) converted to clauses:
% 68.41/68.57 cnf(t36_xboole_1-1, lemma, ( subset(set_difference(_u123, _u122), _u123) )).
% 68.41/68.57
% 68.41/68.57 % Formula: t37_xboole_1 ( lemma ) converted to clauses:
% 68.41/68.57 cnf(t37_xboole_1-1, lemma, ( ( set_difference(_u128, _u126) != empty_set) | subset(_u128, _u126) )).
% 68.41/68.57 cnf(t37_xboole_1-2, lemma, ( ~subset(_u129, _u127) | ( set_difference(_u129, _u127) = empty_set) )).
% 68.41/68.57
% 68.41/68.57 % Formula: t39_xboole_1 ( lemma ) converted to clauses:
% 68.41/68.57 cnf(t39_xboole_1-1, lemma, ( ( set_union2(_u131, set_difference(_u130, _u131)) = set_union2(_u131, _u130)) )).
% 68.41/68.57
% 68.41/68.57 % Formula: t3_boole ( axiom ) converted to clauses:
% 68.41/68.57 cnf(t3_boole-1, axiom, ( ( set_difference(_u132, empty_set) = _u132) )).
% 68.41/68.57
% 68.41/68.57 % Formula: t3_xboole_0 ( lemma ) converted to clauses:
% 68.41/68.57 cnf(t3_xboole_0-1, lemma, ( disjoint(_u139, _u137) | in(skolem13(_u139, _u137), _u139) )).
% 68.41/68.57 cnf(t3_xboole_0-2, lemma, ( disjoint(_u139, _u137) | in(skolem13(_u139, _u137), _u137) )).
% 68.41/68.57 cnf(t3_xboole_0-3, lemma, ( ~in(_u134, _u140) | ~in(_u134, _u138) | ~disjoint(_u140, _u138) )).
% 68.41/68.57
% 68.41/68.57 % Formula: t3_xboole_1 ( lemma ) converted to clauses:
% 68.41/68.57 cnf(t3_xboole_1-1, lemma, ( ~subset(_u141, empty_set) | ( _u141 = empty_set) )).
% 68.41/68.57
% 68.41/68.57 % Formula: t40_xboole_1 ( lemma ) converted to clauses:
% 68.41/68.57 cnf(t40_xboole_1-1, lemma, ( ( set_difference(set_union2(_u143, _u142), _u142) = set_difference(_u143, _u142)) )).
% 68.41/68.57
% 68.41/68.57 % Formula: t45_xboole_1 ( conjecture ) (definitionally) converted to clauses:
% 68.41/68.57 cnf(t45_xboole_1-1, negated_conjecture, ( subset(skolem14, skolem15) )).
% 68.41/68.57 cnf(t45_xboole_1-2, negated_conjecture, ( ( skolem15 != set_union2(skolem14, set_difference(skolem15, skolem14))) )).
% 68.41/68.57
% 68.41/68.57 % Formula: t4_boole ( axiom ) converted to clauses:
% 68.41/68.57 cnf(t4_boole-1, axiom, ( ( set_difference(empty_set, _u146) = empty_set) )).
% 68.41/68.57
% 68.41/68.57 % Formula: t4_xboole_0 ( lemma ) converted to clauses:
% 68.41/68.57 cnf(t4_xboole_0-1, lemma, ( disjoint(_u153, _u151) | in(skolem16(_u153, _u151), set_intersection2(_u153, _u151)) )).
% 68.41/68.57 cnf(t4_xboole_0-2, lemma, ( ~in(_u148, set_intersection2(_u154, _u152)) | ~disjoint(_u154, _u152) )).
% 68.41/68.57
% 68.41/68.57 % Formula: t6_boole ( axiom ) converted to clauses:
% 68.41/68.57 cnf(t6_boole-1, axiom, ( ~empty(_u155) | ( _u155 = empty_set) )).
% 68.41/68.57
% 68.41/68.57 % Formula: t7_boole ( axiom ) converted to clauses:
% 68.41/68.57 cnf(t7_boole-1, axiom, ( ~in(_u157, _u156) | ~empty(_u156) )).
% 68.41/68.57
% 68.41/68.57 % Formula: t7_xboole_1 ( lemma ) converted to clauses:
% 68.41/68.57 cnf(t7_xboole_1-1, lemma, ( subset(_u159, set_union2(_u159, _u158)) )).
% 68.41/68.57
% 68.41/68.57 % Formula: t8_boole ( axiom ) converted to clauses:
% 68.41/68.57 cnf(t8_boole-1, axiom, ( ~empty(_u161) | ( _u161 = _u160) | ~empty(_u160) )).
% 68.41/68.57
% 68.41/68.57 % Formula: t8_xboole_1 ( lemma ) converted to clauses:
% 68.41/68.57 cnf(t8_xboole_1-1, lemma, ( ~subset(_u164, _u163) | ~subset(_u162, _u163) | subset(set_union2(_u164, _u162), _u163) )).
% 68.41/68.57
% 68.41/68.57 % Problem matrix:
% 68.41/68.57 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 68.41/68.57 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 68.41/68.57 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 68.41/68.57 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_union2(__eqx_0, __eqx_1) = set_union2(__eqy_0, __eqy_1)) )).
% 68.41/68.57 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_intersection2(__eqx_0, __eqx_1) = set_intersection2(__eqy_0, __eqy_1)) )).
% 68.41/68.57 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_difference(__eqx_0, __eqx_1) = set_difference(__eqy_0, __eqy_1)) )).
% 68.41/68.57 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( skolem1(__eqx_0) = skolem1(__eqy_0)) )).
% 68.41/68.57 cnf(matrix-7, 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)) )).
% 68.41/68.57 cnf(matrix-8, 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)) )).
% 68.41/68.57 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem4(__eqx_0, __eqx_1) = skolem4(__eqy_0, __eqy_1)) )).
% 68.41/68.57 cnf(matrix-10, 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)) )).
% 68.41/68.57 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem6(__eqx_0, __eqx_1, __eqx_2) = skolem6(__eqy_0, __eqy_1, __eqy_2)) )).
% 68.41/68.57 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem7(__eqx_0, __eqx_1, __eqx_2) = skolem7(__eqy_0, __eqy_1, __eqy_2)) )).
% 68.41/68.57 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem8(__eqx_0, __eqx_1, __eqx_2) = skolem8(__eqy_0, __eqy_1, __eqy_2)) )).
% 68.41/68.57 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem11(__eqx_0, __eqx_1) = skolem11(__eqy_0, __eqy_1)) )).
% 68.41/68.57 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem12(__eqx_0, __eqx_1) = skolem12(__eqy_0, __eqy_1)) )).
% 68.41/68.57 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem13(__eqx_0, __eqx_1) = skolem13(__eqy_0, __eqy_1)) )).
% 68.41/68.57 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem16(__eqx_0, __eqx_1) = skolem16(__eqy_0, __eqy_1)) )).
% 68.41/68.57 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 68.41/68.57 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 68.41/68.57 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~disjoint(__eqx_0, __eqx_1) | disjoint(__eqy_0, __eqy_1) )).
% 68.41/68.57 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 68.41/68.57 cnf(matrix-22, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 68.41/68.57 cnf(matrix-23, plain, ( ( set_union2(_u3, _u2) = set_union2(_u2, _u3)) )).
% 68.41/68.57 cnf(matrix-24, plain, ( ( set_intersection2(_u5, _u4) = set_intersection2(_u4, _u5)) )).
% 68.41/68.57 cnf(matrix-25, plain, ( ( _u10 != _u8) | subset(_u10, _u8) )).
% 68.41/68.57 cnf(matrix-26, plain, ( ( _u10 != _u8) | subset(_u8, _u10) )).
% 68.41/68.57 cnf(matrix-27, plain, ( ~subset(_u11, _u9) | ~subset(_u9, _u11) | ( _u11 = _u9) )).
% 68.41/68.57 cnf(matrix-28, plain, ( ( _u15 != empty_set) | ~in(_u12, _u15) )).
% 68.41/68.57 cnf(matrix-29, plain, ( in(skolem1(_u16), _u16) | ( _u16 = empty_set) )).
% 68.41/68.57 cnf(matrix-30, plain, ( ( _u26 != set_union2(_u30, _u28)) | ~in(_u22, _u26) | in(_u22, _u30) | in(_u22, _u28) )).
% 68.41/68.57 cnf(matrix-31, plain, ( ( _u26 != set_union2(_u30, _u28)) | in(_u23, _u26) | ~in(_u23, _u30) )).
% 68.41/68.57 cnf(matrix-32, plain, ( ( _u26 != set_union2(_u30, _u28)) | in(_u23, _u26) | ~in(_u23, _u28) )).
% 68.41/68.57 cnf(matrix-33, plain, ( ( _u27 = set_union2(_u31, _u29)) | in(skolem2(_u31, _u29, _u27), _u27) | in(skolem3(_u31, _u29, _u27), _u31) | in(skolem3(_u31, _u29, _u27), _u29) )).
% 68.41/68.57 cnf(matrix-34, plain, ( ( _u27 = set_union2(_u31, _u29)) | in(skolem2(_u31, _u29, _u27), _u27) | ~in(skolem3(_u31, _u29, _u27), _u27) )).
% 68.41/68.57 cnf(matrix-35, plain, ( ( _u27 = set_union2(_u31, _u29)) | in(skolem3(_u31, _u29, _u27), _u31) | in(skolem3(_u31, _u29, _u27), _u29) | ~in(skolem2(_u31, _u29, _u27), _u31) )).
% 68.41/68.57 cnf(matrix-36, plain, ( ( _u27 = set_union2(_u31, _u29)) | in(skolem3(_u31, _u29, _u27), _u31) | in(skolem3(_u31, _u29, _u27), _u29) | ~in(skolem2(_u31, _u29, _u27), _u29) )).
% 68.41/68.57 cnf(matrix-37, plain, ( ( _u27 = set_union2(_u31, _u29)) | ~in(skolem3(_u31, _u29, _u27), _u27) | ~in(skolem2(_u31, _u29, _u27), _u31) )).
% 68.41/68.57 cnf(matrix-38, plain, ( ( _u27 = set_union2(_u31, _u29)) | ~in(skolem3(_u31, _u29, _u27), _u27) | ~in(skolem2(_u31, _u29, _u27), _u29) )).
% 68.41/68.57 cnf(matrix-39, plain, ( ~subset(_u38, _u36) | ~in(_u32, _u38) | in(_u32, _u36) )).
% 68.41/68.57 cnf(matrix-40, plain, ( subset(_u39, _u37) | in(skolem4(_u39, _u37), _u39) )).
% 68.41/68.57 cnf(matrix-41, plain, ( subset(_u39, _u37) | ~in(skolem4(_u39, _u37), _u37) )).
% 68.41/68.57 cnf(matrix-42, plain, ( ( _u49 != set_intersection2(_u53, _u51)) | ~in(_u45, _u49) | in(_u45, _u53) )).
% 68.41/68.57 cnf(matrix-43, plain, ( ( _u49 != set_intersection2(_u53, _u51)) | ~in(_u45, _u49) | in(_u45, _u51) )).
% 68.41/68.57 cnf(matrix-44, plain, ( ( _u49 != set_intersection2(_u53, _u51)) | ~in(_u46, _u53) | ~in(_u46, _u51) | in(_u46, _u49) )).
% 68.41/68.57 cnf(matrix-45, plain, ( ( _u50 = set_intersection2(_u54, _u52)) | in(skolem5(_u54, _u52, _u50), _u50) | in(skolem6(_u54, _u52, _u50), _u54) )).
% 68.41/68.57 cnf(matrix-46, plain, ( ( _u50 = set_intersection2(_u54, _u52)) | in(skolem5(_u54, _u52, _u50), _u50) | in(skolem6(_u54, _u52, _u50), _u52) )).
% 68.41/68.57 cnf(matrix-47, plain, ( ( _u50 = set_intersection2(_u54, _u52)) | in(skolem5(_u54, _u52, _u50), _u50) | ~in(skolem6(_u54, _u52, _u50), _u50) )).
% 68.41/68.57 cnf(matrix-48, plain, ( ( _u50 = set_intersection2(_u54, _u52)) | ~in(skolem5(_u54, _u52, _u50), _u54) | ~in(skolem5(_u54, _u52, _u50), _u52) | in(skolem6(_u54, _u52, _u50), _u54) )).
% 68.41/68.57 cnf(matrix-49, plain, ( ( _u50 = set_intersection2(_u54, _u52)) | ~in(skolem5(_u54, _u52, _u50), _u54) | ~in(skolem5(_u54, _u52, _u50), _u52) | in(skolem6(_u54, _u52, _u50), _u52) )).
% 68.41/68.57 cnf(matrix-50, plain, ( ( _u50 = set_intersection2(_u54, _u52)) | ~in(skolem5(_u54, _u52, _u50), _u54) | ~in(skolem5(_u54, _u52, _u50), _u52) | ~in(skolem6(_u54, _u52, _u50), _u50) )).
% 68.41/68.57 cnf(matrix-51, plain, ( ( _u64 != set_difference(_u68, _u66)) | ~in(_u60, _u64) | in(_u60, _u68) )).
% 68.41/68.57 cnf(matrix-52, plain, ( ( _u64 != set_difference(_u68, _u66)) | ~in(_u60, _u64) | ~in(_u60, _u66) )).
% 68.41/68.57 cnf(matrix-53, plain, ( ( _u64 != set_difference(_u68, _u66)) | ~in(_u61, _u68) | in(_u61, _u66) | in(_u61, _u64) )).
% 68.41/68.57 cnf(matrix-54, plain, ( ( _u65 = set_difference(_u69, _u67)) | in(skolem7(_u69, _u67, _u65), _u65) | in(skolem8(_u69, _u67, _u65), _u69) )).
% 68.41/68.57 cnf(matrix-55, plain, ( ( _u65 = set_difference(_u69, _u67)) | in(skolem7(_u69, _u67, _u65), _u65) | ~in(skolem8(_u69, _u67, _u65), _u67) )).
% 68.41/68.57 cnf(matrix-56, plain, ( ( _u65 = set_difference(_u69, _u67)) | in(skolem7(_u69, _u67, _u65), _u65) | ~in(skolem8(_u69, _u67, _u65), _u65) )).
% 68.41/68.57 cnf(matrix-57, plain, ( ( _u65 = set_difference(_u69, _u67)) | ~in(skolem7(_u69, _u67, _u65), _u69) | in(skolem7(_u69, _u67, _u65), _u67) | in(skolem8(_u69, _u67, _u65), _u69) )).
% 68.41/68.57 cnf(matrix-58, plain, ( ( _u65 = set_difference(_u69, _u67)) | ~in(skolem7(_u69, _u67, _u65), _u69) | in(skolem7(_u69, _u67, _u65), _u67) | ~in(skolem8(_u69, _u67, _u65), _u67) )).
% 68.41/68.57 cnf(matrix-59, plain, ( ( _u65 = set_difference(_u69, _u67)) | ~in(skolem7(_u69, _u67, _u65), _u69) | in(skolem7(_u69, _u67, _u65), _u67) | ~in(skolem8(_u69, _u67, _u65), _u65) )).
% 68.41/68.57 cnf(matrix-60, plain, ( ~disjoint(_u74, _u72) | ( set_intersection2(_u74, _u72) = empty_set) )).
% 68.41/68.57 cnf(matrix-61, plain, ( ( set_intersection2(_u75, _u73) != empty_set) | disjoint(_u75, _u73) )).
% 68.41/68.57 cnf(matrix-62, plain, ( empty(empty_set) )).
% 68.41/68.57 cnf(matrix-63, plain, ( empty(_u77) | ~empty(set_union2(_u77, _u76)) )).
% 68.41/68.57 cnf(matrix-64, plain, ( empty(_u79) | ~empty(set_union2(_u78, _u79)) )).
% 68.41/68.57 cnf(matrix-65, plain, ( ( set_union2(_u81, _u81) = _u81) )).
% 68.41/68.57 cnf(matrix-66, plain, ( ( set_intersection2(_u83, _u83) = _u83) )).
% 68.41/68.57 cnf(matrix-67, plain, ( ( set_difference(_u88, _u86) != empty_set) | subset(_u88, _u86) )).
% 68.41/68.57 cnf(matrix-68, plain, ( ~subset(_u89, _u87) | ( set_difference(_u89, _u87) = empty_set) )).
% 68.41/68.57 cnf(matrix-69, plain, ( empty(skolem9) )).
% 68.41/68.57 cnf(matrix-70, plain, ( ~empty(skolem10) )).
% 68.41/68.57 cnf(matrix-71, plain, ( subset(_u93, _u93) )).
% 68.41/68.57 cnf(matrix-72, plain, ( ~disjoint(_u95, _u94) | disjoint(_u94, _u95) )).
% 68.41/68.57 cnf(matrix-73, plain, ( ~subset(_u97, _u96) | ( set_union2(_u97, _u96) = _u96) )).
% 68.41/68.57 cnf(matrix-74, plain, ( subset(set_intersection2(_u99, _u98), _u99) )).
% 68.41/68.57 cnf(matrix-75, plain, ( ~subset(_u102, _u101) | ~subset(_u102, _u100) | subset(_u102, set_intersection2(_u101, _u100)) )).
% 68.41/68.57 cnf(matrix-76, plain, ( ( set_union2(_u103, empty_set) = _u103) )).
% 68.41/68.57 cnf(matrix-77, plain, ( ~subset(_u106, _u105) | ~subset(_u105, _u104) | subset(_u106, _u104) )).
% 68.41/68.57 cnf(matrix-78, plain, ( ~subset(_u109, _u108) | subset(set_intersection2(_u109, _u107), set_intersection2(_u108, _u107)) )).
% 68.41/68.57 cnf(matrix-79, plain, ( ~subset(_u111, _u110) | ( set_intersection2(_u111, _u110) = _u111) )).
% 68.41/68.57 cnf(matrix-80, plain, ( ( set_intersection2(_u112, empty_set) = empty_set) )).
% 68.41/68.57 cnf(matrix-81, plain, ( ( _u115 = _u114) | in(skolem11(_u115, _u114), _u115) | in(skolem12(_u115, _u114), _u114) )).
% 68.41/68.57 cnf(matrix-82, plain, ( ( _u115 = _u114) | in(skolem11(_u115, _u114), _u115) | ~in(skolem12(_u115, _u114), _u115) )).
% 68.41/68.57 cnf(matrix-83, plain, ( ( _u115 = _u114) | ~in(skolem11(_u115, _u114), _u114) | in(skolem12(_u115, _u114), _u114) )).
% 68.41/68.57 cnf(matrix-84, plain, ( ( _u115 = _u114) | ~in(skolem11(_u115, _u114), _u114) | ~in(skolem12(_u115, _u114), _u115) )).
% 68.41/68.57 cnf(matrix-85, plain, ( subset(empty_set, _u118) )).
% 68.41/68.57 cnf(matrix-86, plain, ( ~subset(_u121, _u120) | subset(set_difference(_u121, _u119), set_difference(_u120, _u119)) )).
% 68.41/68.57 cnf(matrix-87, plain, ( subset(set_difference(_u123, _u122), _u123) )).
% 68.41/68.57 cnf(matrix-88, plain, ( ( set_difference(_u128, _u126) != empty_set) | subset(_u128, _u126) )).
% 68.41/68.57 cnf(matrix-89, plain, ( ~subset(_u129, _u127) | ( set_difference(_u129, _u127) = empty_set) )).
% 68.41/68.57 cnf(matrix-90, plain, ( ( set_union2(_u131, set_difference(_u130, _u131)) = set_union2(_u131, _u130)) )).
% 68.41/68.57 cnf(matrix-91, plain, ( ( set_difference(_u132, empty_set) = _u132) )).
% 68.41/68.57 cnf(matrix-92, plain, ( disjoint(_u139, _u137) | in(skolem13(_u139, _u137), _u139) )).
% 68.41/68.57 cnf(matrix-93, plain, ( disjoint(_u139, _u137) | in(skolem13(_u139, _u137), _u137) )).
% 68.41/68.57 cnf(matrix-94, plain, ( ~in(_u134, _u140) | ~in(_u134, _u138) | ~disjoint(_u140, _u138) )).
% 68.41/68.57 cnf(matrix-95, plain, ( ~subset(_u141, empty_set) | ( _u141 = empty_set) )).
% 68.41/68.57 cnf(matrix-96, plain, ( ( set_difference(set_union2(_u143, _u142), _u142) = set_difference(_u143, _u142)) )).
% 68.41/68.57 cnf(matrix-97, plain, ( subset(skolem14, skolem15) )).
% 68.41/68.57 cnf(matrix-98, plain, ( ( skolem15 != set_union2(skolem14, set_difference(skolem15, skolem14))) )).
% 68.41/68.57 cnf(matrix-99, plain, ( ( set_difference(empty_set, _u146) = empty_set) )).
% 68.41/68.57 cnf(matrix-100, plain, ( disjoint(_u153, _u151) | in(skolem16(_u153, _u151), set_intersection2(_u153, _u151)) )).
% 68.41/68.57 cnf(matrix-101, plain, ( ~in(_u148, set_intersection2(_u154, _u152)) | ~disjoint(_u154, _u152) )).
% 68.41/68.57 cnf(matrix-102, plain, ( ~empty(_u155) | ( _u155 = empty_set) )).
% 68.41/68.57 cnf(matrix-103, plain, ( ~in(_u157, _u156) | ~empty(_u156) )).
% 68.41/68.57 cnf(matrix-104, plain, ( subset(_u159, set_union2(_u159, _u158)) )).
% 68.41/68.57 cnf(matrix-105, plain, ( ~empty(_u161) | ( _u161 = _u160) | ~empty(_u160) )).
% 68.41/68.57 cnf(matrix-106, plain, ( ~subset(_u164, _u163) | ~subset(_u162, _u163) | subset(set_union2(_u164, _u162), _u163) )).
% 68.41/68.57
% 68.41/68.57 % Proof stack:
% 68.41/68.57 cnf(proof-stack, plain,
% 68.41/68.57 proof_stack(
% 68.41/68.57 start(98),
% 68.41/68.57 left_branch(0, 2, 2, 2),
% 68.41/68.57 left_branch(0, 27, 2, 3),
% 68.41/68.57 left_branch(0, 104, 0, 4),
% 68.41/68.57 right_branch(4),
% 68.41/68.57 left_branch(0, 106, 2, 5),
% 68.41/68.57 left_branch(0, 71, 0, 6),
% 68.41/68.57 right_branch(6),
% 68.41/68.57 left_branch(0, 97, 0, 7),
% 68.41/68.57 right_branch(7),
% 68.41/68.57 right_branch(5),
% 68.41/68.57 right_branch(3),
% 68.41/68.57 left_branch(0, 2, 2, 4),
% 68.41/68.57 left_branch(0, 23, 0, 5),
% 68.41/68.57 right_branch(5),
% 68.41/68.57 left_branch(0, 1, 1, 6),
% 68.41/68.57 left_branch(0, 90, 0, 7),
% 68.41/68.57 right_branch(7),
% 68.41/68.57 right_branch(6),
% 68.41/68.57 right_branch(4),
% 68.41/68.57 right_branch(2)
% 68.41/68.57 )).
% 68.41/68.57 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------