TSTP Solution File: SEU140+2 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SEU140+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 : n027.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 45.12s 45.36s
% Output : Proof 45.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU140+2 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.34 % Computer : n027.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 15:33:45 EDT 2024
% 0.13/0.34 % CPUTime :
% 45.12/45.36 % SZS status Theorem for theBenchmark
% 45.12/45.36 % SZS output start Proof for theBenchmark
% 45.12/45.36
% 45.12/45.36 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 45.12/45.36 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 45.12/45.36
% 45.12/45.36 % Formula: antisymmetry_r2_xboole_0 ( axiom ) converted to clauses:
% 45.12/45.36 cnf(antisymmetry_r2_xboole_0-1, axiom, ( ~proper_subset(_u3, _u2) | ~proper_subset(_u2, _u3) )).
% 45.12/45.36
% 45.12/45.36 % Formula: commutativity_k2_xboole_0 ( axiom ) converted to clauses:
% 45.12/45.36 cnf(commutativity_k2_xboole_0-1, axiom, ( ( set_union2(_u5, _u4) = set_union2(_u4, _u5)) )).
% 45.12/45.36
% 45.12/45.36 % Formula: commutativity_k3_xboole_0 ( axiom ) converted to clauses:
% 45.12/45.36 cnf(commutativity_k3_xboole_0-1, axiom, ( ( set_intersection2(_u7, _u6) = set_intersection2(_u6, _u7)) )).
% 45.12/45.36
% 45.12/45.36 % Formula: d10_xboole_0 ( axiom ) converted to clauses:
% 45.12/45.36 cnf(d10_xboole_0-1, axiom, ( ( _u12 != _u10) | subset(_u12, _u10) )).
% 45.12/45.36 cnf(d10_xboole_0-2, axiom, ( ( _u12 != _u10) | subset(_u10, _u12) )).
% 45.12/45.36 cnf(d10_xboole_0-3, axiom, ( ~subset(_u13, _u11) | ~subset(_u11, _u13) | ( _u13 = _u11) )).
% 45.12/45.36
% 45.12/45.36 % Formula: d1_xboole_0 ( axiom ) converted to clauses:
% 45.12/45.36 cnf(d1_xboole_0-1, axiom, ( ( _u17 != empty_set) | ~in(_u14, _u17) )).
% 45.12/45.36 cnf(d1_xboole_0-2, axiom, ( in(skolem1(_u18), _u18) | ( _u18 = empty_set) )).
% 45.12/45.36
% 45.12/45.36 % Formula: d2_xboole_0 ( axiom ) converted to clauses:
% 45.12/45.36 cnf(d2_xboole_0-1, axiom, ( ( _u28 != set_union2(_u32, _u30)) | ~in(_u24, _u28) | in(_u24, _u32) | in(_u24, _u30) )).
% 45.12/45.36 cnf(d2_xboole_0-2, axiom, ( ( _u28 != set_union2(_u32, _u30)) | in(_u25, _u28) | ~in(_u25, _u32) )).
% 45.12/45.36 cnf(d2_xboole_0-3, axiom, ( ( _u28 != set_union2(_u32, _u30)) | in(_u25, _u28) | ~in(_u25, _u30) )).
% 45.12/45.36 cnf(d2_xboole_0-4, axiom, ( ( _u29 = set_union2(_u33, _u31)) | in(skolem2(_u33, _u31, _u29), _u29) | in(skolem3(_u33, _u31, _u29), _u33) | in(skolem3(_u33, _u31, _u29), _u31) )).
% 45.12/45.36 cnf(d2_xboole_0-5, axiom, ( ( _u29 = set_union2(_u33, _u31)) | in(skolem2(_u33, _u31, _u29), _u29) | ~in(skolem3(_u33, _u31, _u29), _u29) )).
% 45.12/45.36 cnf(d2_xboole_0-6, axiom, ( ( _u29 = set_union2(_u33, _u31)) | in(skolem3(_u33, _u31, _u29), _u33) | in(skolem3(_u33, _u31, _u29), _u31) | ~in(skolem2(_u33, _u31, _u29), _u33) )).
% 45.12/45.36 cnf(d2_xboole_0-7, axiom, ( ( _u29 = set_union2(_u33, _u31)) | in(skolem3(_u33, _u31, _u29), _u33) | in(skolem3(_u33, _u31, _u29), _u31) | ~in(skolem2(_u33, _u31, _u29), _u31) )).
% 45.12/45.36 cnf(d2_xboole_0-8, axiom, ( ( _u29 = set_union2(_u33, _u31)) | ~in(skolem3(_u33, _u31, _u29), _u29) | ~in(skolem2(_u33, _u31, _u29), _u33) )).
% 45.12/45.36 cnf(d2_xboole_0-9, axiom, ( ( _u29 = set_union2(_u33, _u31)) | ~in(skolem3(_u33, _u31, _u29), _u29) | ~in(skolem2(_u33, _u31, _u29), _u31) )).
% 45.12/45.36
% 45.12/45.36 % Formula: d3_tarski ( axiom ) converted to clauses:
% 45.12/45.36 cnf(d3_tarski-1, axiom, ( ~subset(_u40, _u38) | ~in(_u34, _u40) | in(_u34, _u38) )).
% 45.12/45.36 cnf(d3_tarski-2, axiom, ( subset(_u41, _u39) | in(skolem4(_u41, _u39), _u41) )).
% 45.12/45.36 cnf(d3_tarski-3, axiom, ( subset(_u41, _u39) | ~in(skolem4(_u41, _u39), _u39) )).
% 45.12/45.36
% 45.12/45.36 % Formula: d3_xboole_0 ( axiom ) converted to clauses:
% 45.12/45.36 cnf(d3_xboole_0-1, axiom, ( ( _u51 != set_intersection2(_u55, _u53)) | ~in(_u47, _u51) | in(_u47, _u55) )).
% 45.12/45.36 cnf(d3_xboole_0-2, axiom, ( ( _u51 != set_intersection2(_u55, _u53)) | ~in(_u47, _u51) | in(_u47, _u53) )).
% 45.12/45.36 cnf(d3_xboole_0-3, axiom, ( ( _u51 != set_intersection2(_u55, _u53)) | ~in(_u48, _u55) | ~in(_u48, _u53) | in(_u48, _u51) )).
% 45.12/45.36 cnf(d3_xboole_0-4, axiom, ( ( _u52 = set_intersection2(_u56, _u54)) | in(skolem5(_u56, _u54, _u52), _u52) | in(skolem6(_u56, _u54, _u52), _u56) )).
% 45.12/45.36 cnf(d3_xboole_0-5, axiom, ( ( _u52 = set_intersection2(_u56, _u54)) | in(skolem5(_u56, _u54, _u52), _u52) | in(skolem6(_u56, _u54, _u52), _u54) )).
% 45.12/45.36 cnf(d3_xboole_0-6, axiom, ( ( _u52 = set_intersection2(_u56, _u54)) | in(skolem5(_u56, _u54, _u52), _u52) | ~in(skolem6(_u56, _u54, _u52), _u52) )).
% 45.12/45.36 cnf(d3_xboole_0-7, axiom, ( ( _u52 = set_intersection2(_u56, _u54)) | ~in(skolem5(_u56, _u54, _u52), _u56) | ~in(skolem5(_u56, _u54, _u52), _u54) | in(skolem6(_u56, _u54, _u52), _u56) )).
% 45.12/45.36 cnf(d3_xboole_0-8, axiom, ( ( _u52 = set_intersection2(_u56, _u54)) | ~in(skolem5(_u56, _u54, _u52), _u56) | ~in(skolem5(_u56, _u54, _u52), _u54) | in(skolem6(_u56, _u54, _u52), _u54) )).
% 45.12/45.36 cnf(d3_xboole_0-9, axiom, ( ( _u52 = set_intersection2(_u56, _u54)) | ~in(skolem5(_u56, _u54, _u52), _u56) | ~in(skolem5(_u56, _u54, _u52), _u54) | ~in(skolem6(_u56, _u54, _u52), _u52) )).
% 45.12/45.36
% 45.12/45.36 % Formula: d4_xboole_0 ( axiom ) converted to clauses:
% 45.12/45.36 cnf(d4_xboole_0-1, axiom, ( ( _u66 != set_difference(_u70, _u68)) | ~in(_u62, _u66) | in(_u62, _u70) )).
% 45.12/45.36 cnf(d4_xboole_0-2, axiom, ( ( _u66 != set_difference(_u70, _u68)) | ~in(_u62, _u66) | ~in(_u62, _u68) )).
% 45.12/45.36 cnf(d4_xboole_0-3, axiom, ( ( _u66 != set_difference(_u70, _u68)) | ~in(_u63, _u70) | in(_u63, _u68) | in(_u63, _u66) )).
% 45.12/45.36 cnf(d4_xboole_0-4, axiom, ( ( _u67 = set_difference(_u71, _u69)) | in(skolem7(_u71, _u69, _u67), _u67) | in(skolem8(_u71, _u69, _u67), _u71) )).
% 45.12/45.36 cnf(d4_xboole_0-5, axiom, ( ( _u67 = set_difference(_u71, _u69)) | in(skolem7(_u71, _u69, _u67), _u67) | ~in(skolem8(_u71, _u69, _u67), _u69) )).
% 45.12/45.36 cnf(d4_xboole_0-6, axiom, ( ( _u67 = set_difference(_u71, _u69)) | in(skolem7(_u71, _u69, _u67), _u67) | ~in(skolem8(_u71, _u69, _u67), _u67) )).
% 45.12/45.36 cnf(d4_xboole_0-7, axiom, ( ( _u67 = set_difference(_u71, _u69)) | ~in(skolem7(_u71, _u69, _u67), _u71) | in(skolem7(_u71, _u69, _u67), _u69) | in(skolem8(_u71, _u69, _u67), _u71) )).
% 45.12/45.36 cnf(d4_xboole_0-8, axiom, ( ( _u67 = set_difference(_u71, _u69)) | ~in(skolem7(_u71, _u69, _u67), _u71) | in(skolem7(_u71, _u69, _u67), _u69) | ~in(skolem8(_u71, _u69, _u67), _u69) )).
% 45.12/45.36 cnf(d4_xboole_0-9, axiom, ( ( _u67 = set_difference(_u71, _u69)) | ~in(skolem7(_u71, _u69, _u67), _u71) | in(skolem7(_u71, _u69, _u67), _u69) | ~in(skolem8(_u71, _u69, _u67), _u67) )).
% 45.12/45.36
% 45.12/45.36 % Formula: d7_xboole_0 ( axiom ) converted to clauses:
% 45.12/45.36 cnf(d7_xboole_0-1, axiom, ( ~disjoint(_u76, _u74) | ( set_intersection2(_u76, _u74) = empty_set) )).
% 45.12/45.36 cnf(d7_xboole_0-2, axiom, ( ( set_intersection2(_u77, _u75) != empty_set) | disjoint(_u77, _u75) )).
% 45.12/45.36
% 45.12/45.36 % Formula: d8_xboole_0 ( axiom ) converted to clauses:
% 45.12/45.36 cnf(d8_xboole_0-1, axiom, ( ~proper_subset(_u82, _u80) | subset(_u82, _u80) )).
% 45.12/45.36 cnf(d8_xboole_0-2, axiom, ( ~proper_subset(_u82, _u80) | ( _u82 != _u80) )).
% 45.12/45.36 cnf(d8_xboole_0-3, axiom, ( ~subset(_u83, _u81) | ( _u83 = _u81) | proper_subset(_u83, _u81) )).
% 45.12/45.36
% 45.12/45.36 % Formula: dt_k1_xboole_0 ( axiom ) converted to clauses:
% 45.12/45.36 cnf(dt_k1_xboole_0, axiom, $true).
% 45.12/45.36
% 45.12/45.36 % Formula: dt_k2_xboole_0 ( axiom ) converted to clauses:
% 45.12/45.36 cnf(dt_k2_xboole_0, axiom, $true).
% 45.12/45.36
% 45.12/45.36 % Formula: dt_k3_xboole_0 ( axiom ) converted to clauses:
% 45.12/45.36 cnf(dt_k3_xboole_0, axiom, $true).
% 45.12/45.36
% 45.12/45.36 % Formula: dt_k4_xboole_0 ( axiom ) converted to clauses:
% 45.12/45.36 cnf(dt_k4_xboole_0, axiom, $true).
% 45.12/45.36
% 45.12/45.36 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 45.12/45.36 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 45.12/45.36
% 45.12/45.36 % Formula: fc2_xboole_0 ( axiom ) converted to clauses:
% 45.12/45.36 cnf(fc2_xboole_0-1, axiom, ( empty(_u85) | ~empty(set_union2(_u85, _u84)) )).
% 45.12/45.36
% 45.12/45.36 % Formula: fc3_xboole_0 ( axiom ) converted to clauses:
% 45.12/45.36 cnf(fc3_xboole_0-1, axiom, ( empty(_u87) | ~empty(set_union2(_u86, _u87)) )).
% 45.12/45.36
% 45.12/45.36 % Formula: idempotence_k2_xboole_0 ( axiom ) converted to clauses:
% 45.12/45.36 cnf(idempotence_k2_xboole_0-1, axiom, ( ( set_union2(_u89, _u89) = _u89) )).
% 45.12/45.36
% 45.12/45.36 % Formula: idempotence_k3_xboole_0 ( axiom ) converted to clauses:
% 45.12/45.36 cnf(idempotence_k3_xboole_0-1, axiom, ( ( set_intersection2(_u91, _u91) = _u91) )).
% 45.12/45.36
% 45.12/45.36 % Formula: irreflexivity_r2_xboole_0 ( axiom ) converted to clauses:
% 45.12/45.36 cnf(irreflexivity_r2_xboole_0-1, axiom, ( ~proper_subset(_u93, _u93) )).
% 45.12/45.36
% 45.12/45.36 % Formula: l32_xboole_1 ( lemma ) converted to clauses:
% 45.12/45.36 cnf(l32_xboole_1-1, lemma, ( ( set_difference(_u98, _u96) != empty_set) | subset(_u98, _u96) )).
% 45.12/45.36 cnf(l32_xboole_1-2, lemma, ( ~subset(_u99, _u97) | ( set_difference(_u99, _u97) = empty_set) )).
% 45.12/45.36
% 45.12/45.36 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 45.12/45.36 cnf(rc1_xboole_0-1, axiom, ( empty(skolem9) )).
% 45.12/45.36
% 45.12/45.36 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 45.12/45.36 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem10) )).
% 45.12/45.36
% 45.12/45.36 % Formula: reflexivity_r1_tarski ( axiom ) converted to clauses:
% 45.12/45.36 cnf(reflexivity_r1_tarski-1, axiom, ( subset(_u103, _u103) )).
% 45.12/45.36
% 45.12/45.36 % Formula: symmetry_r1_xboole_0 ( axiom ) converted to clauses:
% 45.12/45.36 cnf(symmetry_r1_xboole_0-1, axiom, ( ~disjoint(_u105, _u104) | disjoint(_u104, _u105) )).
% 45.12/45.36
% 45.12/45.36 % Formula: t12_xboole_1 ( lemma ) converted to clauses:
% 45.12/45.36 cnf(t12_xboole_1-1, lemma, ( ~subset(_u107, _u106) | ( set_union2(_u107, _u106) = _u106) )).
% 45.12/45.36
% 45.12/45.36 % Formula: t17_xboole_1 ( lemma ) converted to clauses:
% 45.12/45.36 cnf(t17_xboole_1-1, lemma, ( subset(set_intersection2(_u109, _u108), _u109) )).
% 45.12/45.36
% 45.12/45.36 % Formula: t19_xboole_1 ( lemma ) converted to clauses:
% 45.12/45.36 cnf(t19_xboole_1-1, lemma, ( ~subset(_u112, _u111) | ~subset(_u112, _u110) | subset(_u112, set_intersection2(_u111, _u110)) )).
% 45.12/45.36
% 45.12/45.36 % Formula: t1_boole ( axiom ) converted to clauses:
% 45.12/45.36 cnf(t1_boole-1, axiom, ( ( set_union2(_u113, empty_set) = _u113) )).
% 45.12/45.36
% 45.12/45.36 % Formula: t1_xboole_1 ( lemma ) converted to clauses:
% 45.12/45.36 cnf(t1_xboole_1-1, lemma, ( ~subset(_u116, _u115) | ~subset(_u115, _u114) | subset(_u116, _u114) )).
% 45.12/45.36
% 45.12/45.36 % Formula: t26_xboole_1 ( lemma ) converted to clauses:
% 45.12/45.36 cnf(t26_xboole_1-1, lemma, ( ~subset(_u119, _u118) | subset(set_intersection2(_u119, _u117), set_intersection2(_u118, _u117)) )).
% 45.12/45.36
% 45.12/45.36 % Formula: t28_xboole_1 ( lemma ) converted to clauses:
% 45.12/45.36 cnf(t28_xboole_1-1, lemma, ( ~subset(_u121, _u120) | ( set_intersection2(_u121, _u120) = _u121) )).
% 45.12/45.36
% 45.12/45.36 % Formula: t2_boole ( axiom ) converted to clauses:
% 45.12/45.36 cnf(t2_boole-1, axiom, ( ( set_intersection2(_u122, empty_set) = empty_set) )).
% 45.12/45.36
% 45.12/45.36 % Formula: t2_tarski ( axiom ) converted to clauses:
% 45.12/45.36 cnf(t2_tarski-1, axiom, ( ( _u125 = _u124) | in(skolem11(_u125, _u124), _u125) | in(skolem12(_u125, _u124), _u124) )).
% 45.12/45.36 cnf(t2_tarski-2, axiom, ( ( _u125 = _u124) | in(skolem11(_u125, _u124), _u125) | ~in(skolem12(_u125, _u124), _u125) )).
% 45.12/45.36 cnf(t2_tarski-3, axiom, ( ( _u125 = _u124) | ~in(skolem11(_u125, _u124), _u124) | in(skolem12(_u125, _u124), _u124) )).
% 45.12/45.36 cnf(t2_tarski-4, axiom, ( ( _u125 = _u124) | ~in(skolem11(_u125, _u124), _u124) | ~in(skolem12(_u125, _u124), _u125) )).
% 45.12/45.36
% 45.12/45.36 % Formula: t2_xboole_1 ( lemma ) converted to clauses:
% 45.12/45.36 cnf(t2_xboole_1-1, lemma, ( subset(empty_set, _u128) )).
% 45.12/45.36
% 45.12/45.36 % Formula: t33_xboole_1 ( lemma ) converted to clauses:
% 45.12/45.36 cnf(t33_xboole_1-1, lemma, ( ~subset(_u131, _u130) | subset(set_difference(_u131, _u129), set_difference(_u130, _u129)) )).
% 45.12/45.36
% 45.12/45.36 % Formula: t36_xboole_1 ( lemma ) converted to clauses:
% 45.12/45.36 cnf(t36_xboole_1-1, lemma, ( subset(set_difference(_u133, _u132), _u133) )).
% 45.12/45.36
% 45.12/45.36 % Formula: t37_xboole_1 ( lemma ) converted to clauses:
% 45.12/45.36 cnf(t37_xboole_1-1, lemma, ( ( set_difference(_u138, _u136) != empty_set) | subset(_u138, _u136) )).
% 45.12/45.36 cnf(t37_xboole_1-2, lemma, ( ~subset(_u139, _u137) | ( set_difference(_u139, _u137) = empty_set) )).
% 45.12/45.36
% 45.12/45.36 % Formula: t39_xboole_1 ( lemma ) converted to clauses:
% 45.12/45.36 cnf(t39_xboole_1-1, lemma, ( ( set_union2(_u141, set_difference(_u140, _u141)) = set_union2(_u141, _u140)) )).
% 45.12/45.36
% 45.12/45.36 % Formula: t3_boole ( axiom ) converted to clauses:
% 45.12/45.36 cnf(t3_boole-1, axiom, ( ( set_difference(_u142, empty_set) = _u142) )).
% 45.12/45.36
% 45.12/45.36 % Formula: t3_xboole_0 ( lemma ) converted to clauses:
% 45.12/45.36 cnf(t3_xboole_0-1, lemma, ( disjoint(_u149, _u147) | in(skolem13(_u149, _u147), _u149) )).
% 45.12/45.36 cnf(t3_xboole_0-2, lemma, ( disjoint(_u149, _u147) | in(skolem13(_u149, _u147), _u147) )).
% 45.12/45.36 cnf(t3_xboole_0-3, lemma, ( ~in(_u144, _u150) | ~in(_u144, _u148) | ~disjoint(_u150, _u148) )).
% 45.12/45.36
% 45.12/45.36 % Formula: t3_xboole_1 ( lemma ) converted to clauses:
% 45.12/45.37 cnf(t3_xboole_1-1, lemma, ( ~subset(_u151, empty_set) | ( _u151 = empty_set) )).
% 45.12/45.37
% 45.12/45.37 % Formula: t40_xboole_1 ( lemma ) converted to clauses:
% 45.12/45.37 cnf(t40_xboole_1-1, lemma, ( ( set_difference(set_union2(_u153, _u152), _u152) = set_difference(_u153, _u152)) )).
% 45.12/45.37
% 45.12/45.37 % Formula: t45_xboole_1 ( lemma ) converted to clauses:
% 45.12/45.37 cnf(t45_xboole_1-1, lemma, ( ~subset(_u155, _u154) | ( _u154 = set_union2(_u155, set_difference(_u154, _u155))) )).
% 45.12/45.37
% 45.12/45.37 % Formula: t48_xboole_1 ( lemma ) converted to clauses:
% 45.12/45.37 cnf(t48_xboole_1-1, lemma, ( ( set_difference(_u157, set_difference(_u157, _u156)) = set_intersection2(_u157, _u156)) )).
% 45.12/45.37
% 45.12/45.37 % Formula: t4_boole ( axiom ) converted to clauses:
% 45.12/45.37 cnf(t4_boole-1, axiom, ( ( set_difference(empty_set, _u158) = empty_set) )).
% 45.12/45.37
% 45.12/45.37 % Formula: t4_xboole_0 ( lemma ) converted to clauses:
% 45.12/45.37 cnf(t4_xboole_0-1, lemma, ( disjoint(_u165, _u163) | in(skolem14(_u165, _u163), set_intersection2(_u165, _u163)) )).
% 45.12/45.37 cnf(t4_xboole_0-2, lemma, ( ~in(_u160, set_intersection2(_u166, _u164)) | ~disjoint(_u166, _u164) )).
% 45.12/45.37
% 45.12/45.37 % Formula: t60_xboole_1 ( lemma ) converted to clauses:
% 45.12/45.37 cnf(t60_xboole_1-1, lemma, ( ~subset(_u168, _u167) | ~proper_subset(_u167, _u168) )).
% 45.12/45.37
% 45.12/45.37 % Formula: t63_xboole_1 ( conjecture ) (definitionally) converted to clauses:
% 45.12/45.37 cnf(t63_xboole_1-1, negated_conjecture, ( subset(skolem15, skolem16) )).
% 45.12/45.37 cnf(t63_xboole_1-2, negated_conjecture, ( disjoint(skolem16, skolem17) )).
% 45.12/45.37 cnf(t63_xboole_1-3, negated_conjecture, ( ~disjoint(skolem15, skolem17) )).
% 45.12/45.37
% 45.12/45.37 % Formula: t6_boole ( axiom ) converted to clauses:
% 45.12/45.37 cnf(t6_boole-1, axiom, ( ~empty(_u172) | ( _u172 = empty_set) )).
% 45.12/45.37
% 45.12/45.37 % Formula: t7_boole ( axiom ) converted to clauses:
% 45.12/45.37 cnf(t7_boole-1, axiom, ( ~in(_u174, _u173) | ~empty(_u173) )).
% 45.12/45.37
% 45.12/45.37 % Formula: t7_xboole_1 ( lemma ) converted to clauses:
% 45.12/45.37 cnf(t7_xboole_1-1, lemma, ( subset(_u176, set_union2(_u176, _u175)) )).
% 45.12/45.37
% 45.12/45.37 % Formula: t8_boole ( axiom ) converted to clauses:
% 45.12/45.37 cnf(t8_boole-1, axiom, ( ~empty(_u178) | ( _u178 = _u177) | ~empty(_u177) )).
% 45.12/45.37
% 45.12/45.37 % Formula: t8_xboole_1 ( lemma ) converted to clauses:
% 45.12/45.37 cnf(t8_xboole_1-1, lemma, ( ~subset(_u181, _u180) | ~subset(_u179, _u180) | subset(set_union2(_u181, _u179), _u180) )).
% 45.12/45.37
% 45.12/45.37 % Problem matrix:
% 45.12/45.37 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 45.12/45.37 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 45.12/45.37 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 45.12/45.37 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_union2(__eqx_0, __eqx_1) = set_union2(__eqy_0, __eqy_1)) )).
% 45.12/45.37 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_intersection2(__eqx_0, __eqx_1) = set_intersection2(__eqy_0, __eqy_1)) )).
% 45.12/45.37 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_difference(__eqx_0, __eqx_1) = set_difference(__eqy_0, __eqy_1)) )).
% 45.12/45.37 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( skolem1(__eqx_0) = skolem1(__eqy_0)) )).
% 45.12/45.37 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)) )).
% 45.12/45.37 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)) )).
% 45.12/45.37 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem4(__eqx_0, __eqx_1) = skolem4(__eqy_0, __eqy_1)) )).
% 45.12/45.37 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)) )).
% 45.12/45.37 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)) )).
% 45.12/45.37 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)) )).
% 45.12/45.37 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)) )).
% 45.12/45.37 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem11(__eqx_0, __eqx_1) = skolem11(__eqy_0, __eqy_1)) )).
% 45.12/45.37 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem12(__eqx_0, __eqx_1) = skolem12(__eqy_0, __eqy_1)) )).
% 45.12/45.37 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem13(__eqx_0, __eqx_1) = skolem13(__eqy_0, __eqy_1)) )).
% 45.12/45.37 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem14(__eqx_0, __eqx_1) = skolem14(__eqy_0, __eqy_1)) )).
% 45.12/45.37 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 45.12/45.37 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~proper_subset(__eqx_0, __eqx_1) | proper_subset(__eqy_0, __eqy_1) )).
% 45.12/45.37 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 45.12/45.37 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~disjoint(__eqx_0, __eqx_1) | disjoint(__eqy_0, __eqy_1) )).
% 45.12/45.37 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 45.12/45.37 cnf(matrix-23, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 45.12/45.37 cnf(matrix-24, plain, ( ~proper_subset(_u3, _u2) | ~proper_subset(_u2, _u3) )).
% 45.12/45.37 cnf(matrix-25, plain, ( ( set_union2(_u5, _u4) = set_union2(_u4, _u5)) )).
% 45.12/45.37 cnf(matrix-26, plain, ( ( set_intersection2(_u7, _u6) = set_intersection2(_u6, _u7)) )).
% 45.12/45.37 cnf(matrix-27, plain, ( ( _u12 != _u10) | subset(_u12, _u10) )).
% 45.12/45.37 cnf(matrix-28, plain, ( ( _u12 != _u10) | subset(_u10, _u12) )).
% 45.12/45.37 cnf(matrix-29, plain, ( ~subset(_u13, _u11) | ~subset(_u11, _u13) | ( _u13 = _u11) )).
% 45.12/45.37 cnf(matrix-30, plain, ( ( _u17 != empty_set) | ~in(_u14, _u17) )).
% 45.12/45.37 cnf(matrix-31, plain, ( in(skolem1(_u18), _u18) | ( _u18 = empty_set) )).
% 45.12/45.37 cnf(matrix-32, plain, ( ( _u28 != set_union2(_u32, _u30)) | ~in(_u24, _u28) | in(_u24, _u32) | in(_u24, _u30) )).
% 45.12/45.37 cnf(matrix-33, plain, ( ( _u28 != set_union2(_u32, _u30)) | in(_u25, _u28) | ~in(_u25, _u32) )).
% 45.12/45.37 cnf(matrix-34, plain, ( ( _u28 != set_union2(_u32, _u30)) | in(_u25, _u28) | ~in(_u25, _u30) )).
% 45.12/45.37 cnf(matrix-35, plain, ( ( _u29 = set_union2(_u33, _u31)) | in(skolem2(_u33, _u31, _u29), _u29) | in(skolem3(_u33, _u31, _u29), _u33) | in(skolem3(_u33, _u31, _u29), _u31) )).
% 45.12/45.37 cnf(matrix-36, plain, ( ( _u29 = set_union2(_u33, _u31)) | in(skolem2(_u33, _u31, _u29), _u29) | ~in(skolem3(_u33, _u31, _u29), _u29) )).
% 45.12/45.37 cnf(matrix-37, plain, ( ( _u29 = set_union2(_u33, _u31)) | in(skolem3(_u33, _u31, _u29), _u33) | in(skolem3(_u33, _u31, _u29), _u31) | ~in(skolem2(_u33, _u31, _u29), _u33) )).
% 45.12/45.37 cnf(matrix-38, plain, ( ( _u29 = set_union2(_u33, _u31)) | in(skolem3(_u33, _u31, _u29), _u33) | in(skolem3(_u33, _u31, _u29), _u31) | ~in(skolem2(_u33, _u31, _u29), _u31) )).
% 45.12/45.37 cnf(matrix-39, plain, ( ( _u29 = set_union2(_u33, _u31)) | ~in(skolem3(_u33, _u31, _u29), _u29) | ~in(skolem2(_u33, _u31, _u29), _u33) )).
% 45.12/45.37 cnf(matrix-40, plain, ( ( _u29 = set_union2(_u33, _u31)) | ~in(skolem3(_u33, _u31, _u29), _u29) | ~in(skolem2(_u33, _u31, _u29), _u31) )).
% 45.12/45.37 cnf(matrix-41, plain, ( ~subset(_u40, _u38) | ~in(_u34, _u40) | in(_u34, _u38) )).
% 45.12/45.37 cnf(matrix-42, plain, ( subset(_u41, _u39) | in(skolem4(_u41, _u39), _u41) )).
% 45.12/45.37 cnf(matrix-43, plain, ( subset(_u41, _u39) | ~in(skolem4(_u41, _u39), _u39) )).
% 45.12/45.37 cnf(matrix-44, plain, ( ( _u51 != set_intersection2(_u55, _u53)) | ~in(_u47, _u51) | in(_u47, _u55) )).
% 45.12/45.37 cnf(matrix-45, plain, ( ( _u51 != set_intersection2(_u55, _u53)) | ~in(_u47, _u51) | in(_u47, _u53) )).
% 45.12/45.37 cnf(matrix-46, plain, ( ( _u51 != set_intersection2(_u55, _u53)) | ~in(_u48, _u55) | ~in(_u48, _u53) | in(_u48, _u51) )).
% 45.12/45.37 cnf(matrix-47, plain, ( ( _u52 = set_intersection2(_u56, _u54)) | in(skolem5(_u56, _u54, _u52), _u52) | in(skolem6(_u56, _u54, _u52), _u56) )).
% 45.12/45.37 cnf(matrix-48, plain, ( ( _u52 = set_intersection2(_u56, _u54)) | in(skolem5(_u56, _u54, _u52), _u52) | in(skolem6(_u56, _u54, _u52), _u54) )).
% 45.12/45.37 cnf(matrix-49, plain, ( ( _u52 = set_intersection2(_u56, _u54)) | in(skolem5(_u56, _u54, _u52), _u52) | ~in(skolem6(_u56, _u54, _u52), _u52) )).
% 45.12/45.37 cnf(matrix-50, plain, ( ( _u52 = set_intersection2(_u56, _u54)) | ~in(skolem5(_u56, _u54, _u52), _u56) | ~in(skolem5(_u56, _u54, _u52), _u54) | in(skolem6(_u56, _u54, _u52), _u56) )).
% 45.12/45.37 cnf(matrix-51, plain, ( ( _u52 = set_intersection2(_u56, _u54)) | ~in(skolem5(_u56, _u54, _u52), _u56) | ~in(skolem5(_u56, _u54, _u52), _u54) | in(skolem6(_u56, _u54, _u52), _u54) )).
% 45.12/45.37 cnf(matrix-52, plain, ( ( _u52 = set_intersection2(_u56, _u54)) | ~in(skolem5(_u56, _u54, _u52), _u56) | ~in(skolem5(_u56, _u54, _u52), _u54) | ~in(skolem6(_u56, _u54, _u52), _u52) )).
% 45.12/45.37 cnf(matrix-53, plain, ( ( _u66 != set_difference(_u70, _u68)) | ~in(_u62, _u66) | in(_u62, _u70) )).
% 45.12/45.37 cnf(matrix-54, plain, ( ( _u66 != set_difference(_u70, _u68)) | ~in(_u62, _u66) | ~in(_u62, _u68) )).
% 45.12/45.37 cnf(matrix-55, plain, ( ( _u66 != set_difference(_u70, _u68)) | ~in(_u63, _u70) | in(_u63, _u68) | in(_u63, _u66) )).
% 45.12/45.37 cnf(matrix-56, plain, ( ( _u67 = set_difference(_u71, _u69)) | in(skolem7(_u71, _u69, _u67), _u67) | in(skolem8(_u71, _u69, _u67), _u71) )).
% 45.12/45.37 cnf(matrix-57, plain, ( ( _u67 = set_difference(_u71, _u69)) | in(skolem7(_u71, _u69, _u67), _u67) | ~in(skolem8(_u71, _u69, _u67), _u69) )).
% 45.12/45.37 cnf(matrix-58, plain, ( ( _u67 = set_difference(_u71, _u69)) | in(skolem7(_u71, _u69, _u67), _u67) | ~in(skolem8(_u71, _u69, _u67), _u67) )).
% 45.12/45.37 cnf(matrix-59, plain, ( ( _u67 = set_difference(_u71, _u69)) | ~in(skolem7(_u71, _u69, _u67), _u71) | in(skolem7(_u71, _u69, _u67), _u69) | in(skolem8(_u71, _u69, _u67), _u71) )).
% 45.12/45.37 cnf(matrix-60, plain, ( ( _u67 = set_difference(_u71, _u69)) | ~in(skolem7(_u71, _u69, _u67), _u71) | in(skolem7(_u71, _u69, _u67), _u69) | ~in(skolem8(_u71, _u69, _u67), _u69) )).
% 45.12/45.37 cnf(matrix-61, plain, ( ( _u67 = set_difference(_u71, _u69)) | ~in(skolem7(_u71, _u69, _u67), _u71) | in(skolem7(_u71, _u69, _u67), _u69) | ~in(skolem8(_u71, _u69, _u67), _u67) )).
% 45.12/45.37 cnf(matrix-62, plain, ( ~disjoint(_u76, _u74) | ( set_intersection2(_u76, _u74) = empty_set) )).
% 45.12/45.37 cnf(matrix-63, plain, ( ( set_intersection2(_u77, _u75) != empty_set) | disjoint(_u77, _u75) )).
% 45.12/45.37 cnf(matrix-64, plain, ( ~proper_subset(_u82, _u80) | subset(_u82, _u80) )).
% 45.12/45.37 cnf(matrix-65, plain, ( ~proper_subset(_u82, _u80) | ( _u82 != _u80) )).
% 45.12/45.37 cnf(matrix-66, plain, ( ~subset(_u83, _u81) | ( _u83 = _u81) | proper_subset(_u83, _u81) )).
% 45.12/45.37 cnf(matrix-67, plain, ( empty(empty_set) )).
% 45.12/45.37 cnf(matrix-68, plain, ( empty(_u85) | ~empty(set_union2(_u85, _u84)) )).
% 45.12/45.37 cnf(matrix-69, plain, ( empty(_u87) | ~empty(set_union2(_u86, _u87)) )).
% 45.12/45.37 cnf(matrix-70, plain, ( ( set_union2(_u89, _u89) = _u89) )).
% 45.12/45.37 cnf(matrix-71, plain, ( ( set_intersection2(_u91, _u91) = _u91) )).
% 45.12/45.37 cnf(matrix-72, plain, ( ~proper_subset(_u93, _u93) )).
% 45.12/45.37 cnf(matrix-73, plain, ( ( set_difference(_u98, _u96) != empty_set) | subset(_u98, _u96) )).
% 45.12/45.37 cnf(matrix-74, plain, ( ~subset(_u99, _u97) | ( set_difference(_u99, _u97) = empty_set) )).
% 45.12/45.37 cnf(matrix-75, plain, ( empty(skolem9) )).
% 45.12/45.37 cnf(matrix-76, plain, ( ~empty(skolem10) )).
% 45.12/45.37 cnf(matrix-77, plain, ( subset(_u103, _u103) )).
% 45.12/45.37 cnf(matrix-78, plain, ( ~disjoint(_u105, _u104) | disjoint(_u104, _u105) )).
% 45.12/45.37 cnf(matrix-79, plain, ( ~subset(_u107, _u106) | ( set_union2(_u107, _u106) = _u106) )).
% 45.12/45.37 cnf(matrix-80, plain, ( subset(set_intersection2(_u109, _u108), _u109) )).
% 45.12/45.37 cnf(matrix-81, plain, ( ~subset(_u112, _u111) | ~subset(_u112, _u110) | subset(_u112, set_intersection2(_u111, _u110)) )).
% 45.12/45.37 cnf(matrix-82, plain, ( ( set_union2(_u113, empty_set) = _u113) )).
% 45.12/45.37 cnf(matrix-83, plain, ( ~subset(_u116, _u115) | ~subset(_u115, _u114) | subset(_u116, _u114) )).
% 45.12/45.37 cnf(matrix-84, plain, ( ~subset(_u119, _u118) | subset(set_intersection2(_u119, _u117), set_intersection2(_u118, _u117)) )).
% 45.12/45.37 cnf(matrix-85, plain, ( ~subset(_u121, _u120) | ( set_intersection2(_u121, _u120) = _u121) )).
% 45.12/45.37 cnf(matrix-86, plain, ( ( set_intersection2(_u122, empty_set) = empty_set) )).
% 45.12/45.37 cnf(matrix-87, plain, ( ( _u125 = _u124) | in(skolem11(_u125, _u124), _u125) | in(skolem12(_u125, _u124), _u124) )).
% 45.12/45.37 cnf(matrix-88, plain, ( ( _u125 = _u124) | in(skolem11(_u125, _u124), _u125) | ~in(skolem12(_u125, _u124), _u125) )).
% 45.12/45.37 cnf(matrix-89, plain, ( ( _u125 = _u124) | ~in(skolem11(_u125, _u124), _u124) | in(skolem12(_u125, _u124), _u124) )).
% 45.12/45.37 cnf(matrix-90, plain, ( ( _u125 = _u124) | ~in(skolem11(_u125, _u124), _u124) | ~in(skolem12(_u125, _u124), _u125) )).
% 45.12/45.37 cnf(matrix-91, plain, ( subset(empty_set, _u128) )).
% 45.12/45.37 cnf(matrix-92, plain, ( ~subset(_u131, _u130) | subset(set_difference(_u131, _u129), set_difference(_u130, _u129)) )).
% 45.12/45.37 cnf(matrix-93, plain, ( subset(set_difference(_u133, _u132), _u133) )).
% 45.12/45.37 cnf(matrix-94, plain, ( ( set_difference(_u138, _u136) != empty_set) | subset(_u138, _u136) )).
% 45.12/45.37 cnf(matrix-95, plain, ( ~subset(_u139, _u137) | ( set_difference(_u139, _u137) = empty_set) )).
% 45.12/45.37 cnf(matrix-96, plain, ( ( set_union2(_u141, set_difference(_u140, _u141)) = set_union2(_u141, _u140)) )).
% 45.12/45.37 cnf(matrix-97, plain, ( ( set_difference(_u142, empty_set) = _u142) )).
% 45.12/45.37 cnf(matrix-98, plain, ( disjoint(_u149, _u147) | in(skolem13(_u149, _u147), _u149) )).
% 45.12/45.37 cnf(matrix-99, plain, ( disjoint(_u149, _u147) | in(skolem13(_u149, _u147), _u147) )).
% 45.12/45.37 cnf(matrix-100, plain, ( ~in(_u144, _u150) | ~in(_u144, _u148) | ~disjoint(_u150, _u148) )).
% 45.12/45.37 cnf(matrix-101, plain, ( ~subset(_u151, empty_set) | ( _u151 = empty_set) )).
% 45.12/45.37 cnf(matrix-102, plain, ( ( set_difference(set_union2(_u153, _u152), _u152) = set_difference(_u153, _u152)) )).
% 45.12/45.37 cnf(matrix-103, plain, ( ~subset(_u155, _u154) | ( _u154 = set_union2(_u155, set_difference(_u154, _u155))) )).
% 45.12/45.37 cnf(matrix-104, plain, ( ( set_difference(_u157, set_difference(_u157, _u156)) = set_intersection2(_u157, _u156)) )).
% 45.12/45.37 cnf(matrix-105, plain, ( ( set_difference(empty_set, _u158) = empty_set) )).
% 45.12/45.37 cnf(matrix-106, plain, ( disjoint(_u165, _u163) | in(skolem14(_u165, _u163), set_intersection2(_u165, _u163)) )).
% 45.12/45.37 cnf(matrix-107, plain, ( ~in(_u160, set_intersection2(_u166, _u164)) | ~disjoint(_u166, _u164) )).
% 45.12/45.37 cnf(matrix-108, plain, ( ~subset(_u168, _u167) | ~proper_subset(_u167, _u168) )).
% 45.12/45.37 cnf(matrix-109, plain, ( subset(skolem15, skolem16) )).
% 45.12/45.37 cnf(matrix-110, plain, ( disjoint(skolem16, skolem17) )).
% 45.12/45.37 cnf(matrix-111, plain, ( ~disjoint(skolem15, skolem17) )).
% 45.12/45.37 cnf(matrix-112, plain, ( ~empty(_u172) | ( _u172 = empty_set) )).
% 45.12/45.37 cnf(matrix-113, plain, ( ~in(_u174, _u173) | ~empty(_u173) )).
% 45.12/45.37 cnf(matrix-114, plain, ( subset(_u176, set_union2(_u176, _u175)) )).
% 45.12/45.37 cnf(matrix-115, plain, ( ~empty(_u178) | ( _u178 = _u177) | ~empty(_u177) )).
% 45.12/45.37 cnf(matrix-116, plain, ( ~subset(_u181, _u180) | ~subset(_u179, _u180) | subset(set_union2(_u181, _u179), _u180) )).
% 45.12/45.37
% 45.12/45.37 % Proof stack:
% 45.12/45.37 cnf(proof-stack, plain,
% 45.12/45.37 proof_stack(
% 45.12/45.37 start(109),
% 45.12/45.37 left_branch(0, 84, 0, 2),
% 45.12/45.37 left_branch(0, 41, 0, 3),
% 45.12/45.37 left_branch(0, 107, 0, 4),
% 45.12/45.37 left_branch(0, 110, 0, 5),
% 45.12/45.37 right_branch(5),
% 45.12/45.37 right_branch(4),
% 45.12/45.37 left_branch(0, 106, 1, 5),
% 45.12/45.37 left_branch(0, 111, 0, 6),
% 45.12/45.37 right_branch(6),
% 45.12/45.37 right_branch(5),
% 45.12/45.37 right_branch(3),
% 45.12/45.37 right_branch(2)
% 45.12/45.37 )).
% 45.12/45.37 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------