TSTP Solution File: LAT223-10 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT223-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n022.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 : Thu Aug 31 06:00:05 EDT 2023
% Result : Unsatisfiable 12.32s 12.50s
% Output : CNFRefutation 12.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 22
% Syntax : Number of formulae : 120 ( 112 unt; 8 typ; 0 def)
% Number of atoms : 112 ( 111 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 9 ( 4 >; 5 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 192 ( 42 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(decl_23,type,
meet: ( $i * $i ) > $i ).
tff(decl_24,type,
join: ( $i * $i ) > $i ).
tff(decl_25,type,
complement: $i > $i ).
tff(decl_26,type,
one: $i ).
tff(decl_27,type,
zero: $i ).
tff(decl_28,type,
b: $i ).
tff(decl_29,type,
a: $i ).
cnf(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption1) ).
cnf(complement_join,axiom,
join(X1,complement(X1)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_join) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet) ).
cnf(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption2) ).
cnf(prove_distributivity_hypothesis,hypothesis,
meet(b,a) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity_hypothesis) ).
cnf(associativity_of_join,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_join) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_join) ).
cnf(complement_meet,axiom,
meet(X1,complement(X1)) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_meet) ).
cnf(associativity_of_meet,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_meet) ).
cnf(equation_H7,axiom,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,meet(X1,join(meet(X1,X2),meet(X3,join(X1,X2)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H7) ).
cnf(meet_join_complement,axiom,
ifeq(join(X1,X2),one,ifeq(meet(X1,X2),zero,complement(X1),X2),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meet_join_complement) ).
cnf(ifeq_axiom,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_meet) ).
cnf(prove_distributivity,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity) ).
cnf(c_0_14,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_15,axiom,
join(X1,complement(X1)) = one,
complement_join ).
cnf(c_0_16,plain,
meet(X1,one) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_18,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_19,plain,
meet(one,X1) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,hypothesis,
meet(b,a) = a,
prove_distributivity_hypothesis ).
cnf(c_0_21,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_22,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_23,plain,
join(one,X1) = one,
inference(spm,[status(thm)],[c_0_14,c_0_19]) ).
cnf(c_0_24,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_25,axiom,
meet(X1,complement(X1)) = zero,
complement_meet ).
cnf(c_0_26,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_27,hypothesis,
meet(a,b) = a,
inference(rw,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_28,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_14]),c_0_22]) ).
cnf(c_0_29,plain,
join(X1,join(complement(X1),X2)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_15]),c_0_23]) ).
cnf(c_0_30,plain,
join(X1,one) = one,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_25]) ).
cnf(c_0_32,hypothesis,
meet(a,meet(b,X1)) = meet(a,X1),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
join(complement(X1),join(X2,X1)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_22]) ).
cnf(c_0_34,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_24]) ).
cnf(c_0_35,hypothesis,
meet(a,join(b,X1)) = a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_14]),c_0_27]) ).
cnf(c_0_36,plain,
join(X1,complement(meet(X1,X2))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_18]),c_0_24]) ).
cnf(c_0_37,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(spm,[status(thm)],[c_0_17,c_0_26]) ).
cnf(c_0_38,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_26,c_0_14]) ).
cnf(c_0_39,plain,
meet(X1,zero) = zero,
inference(spm,[status(thm)],[c_0_21,c_0_34]) ).
cnf(c_0_40,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_24]) ).
cnf(c_0_41,plain,
meet(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_18,c_0_34]) ).
cnf(c_0_42,hypothesis,
join(b,join(X1,a)) = join(b,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_35]),c_0_22]) ).
cnf(c_0_43,plain,
join(X1,complement(meet(X2,meet(X3,X1)))) = one,
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,plain,
meet(X1,complement(join(X1,X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_25]),c_0_39]) ).
cnf(c_0_45,plain,
meet(X1,meet(X2,X1)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_18]),c_0_26]) ).
cnf(c_0_46,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_25]),c_0_41]) ).
cnf(c_0_47,hypothesis,
join(b,join(a,X1)) = join(b,X1),
inference(spm,[status(thm)],[c_0_42,c_0_24]) ).
cnf(c_0_48,axiom,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,meet(X1,join(meet(X1,X2),meet(X3,join(X1,X2)))))),
equation_H7 ).
cnf(c_0_49,hypothesis,
join(meet(b,X1),complement(meet(X2,meet(a,X1)))) = one,
inference(spm,[status(thm)],[c_0_43,c_0_32]) ).
cnf(c_0_50,hypothesis,
join(b,a) = b,
inference(spm,[status(thm)],[c_0_21,c_0_27]) ).
cnf(c_0_51,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(spm,[status(thm)],[c_0_44,c_0_24]) ).
cnf(c_0_52,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_53,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_24]),c_0_22]) ).
cnf(c_0_54,hypothesis,
join(meet(a,X1),meet(b,X1)) = meet(b,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_32]),c_0_24]) ).
cnf(c_0_55,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_26]) ).
cnf(c_0_56,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_39]),c_0_26]) ).
cnf(c_0_57,hypothesis,
meet(join(a,X1),join(b,X1)) = join(a,X1),
inference(spm,[status(thm)],[c_0_40,c_0_47]) ).
cnf(c_0_58,axiom,
ifeq(join(X1,X2),one,ifeq(meet(X1,X2),zero,complement(X1),X2),X2) = X2,
meet_join_complement ).
cnf(c_0_59,plain,
meet(X1,join(complement(X1),join(X2,meet(X1,join(meet(X1,join(complement(X1),X2)),X3))))) = meet(X1,join(complement(X1),join(X2,meet(X1,X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_29]),c_0_16]),c_0_22]),c_0_22]) ).
cnf(c_0_60,hypothesis,
join(meet(b,join(X1,a)),complement(meet(X2,a))) = one,
inference(spm,[status(thm)],[c_0_49,c_0_40]) ).
cnf(c_0_61,hypothesis,
join(a,b) = b,
inference(rw,[status(thm)],[c_0_50,c_0_24]) ).
cnf(c_0_62,plain,
meet(complement(join(X1,X2)),join(meet(X3,X1),X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_17]) ).
cnf(c_0_63,hypothesis,
join(meet(a,X1),join(X2,meet(b,X1))) = join(X2,meet(b,X1)),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_64,plain,
join(X1,join(X2,meet(X3,X1))) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_14]),c_0_22]) ).
cnf(c_0_65,hypothesis,
meet(join(a,X1),complement(join(b,X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_17]) ).
cnf(c_0_66,plain,
ifeq(join(X1,X2),one,ifeq(meet(X2,X1),zero,complement(X1),X2),X2) = X2,
inference(spm,[status(thm)],[c_0_58,c_0_17]) ).
cnf(c_0_67,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_68,plain,
join(X1,complement(meet(X2,X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_21]),c_0_24]) ).
cnf(c_0_69,hypothesis,
meet(b,join(a,join(complement(b),meet(b,complement(meet(X1,a)))))) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_16]),c_0_61]),c_0_24]),c_0_15]),c_0_16]),c_0_53]) ).
cnf(c_0_70,hypothesis,
meet(complement(join(X1,X2)),join(X2,meet(b,X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]) ).
cnf(c_0_71,hypothesis,
meet(complement(b),join(a,meet(b,X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_18]),c_0_17]) ).
cnf(c_0_72,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_25]),c_0_24]),c_0_15]),c_0_67]),c_0_67]) ).
cnf(c_0_73,hypothesis,
join(a,join(complement(b),meet(b,complement(meet(X1,a))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_22]),c_0_22]),c_0_28]) ).
cnf(c_0_74,hypothesis,
meet(complement(join(X1,X2)),join(X1,meet(b,X2))) = zero,
inference(spm,[status(thm)],[c_0_70,c_0_24]) ).
cnf(c_0_75,hypothesis,
ifeq(join(a,join(complement(b),meet(b,X1))),one,b,join(a,meet(b,X1))) = join(a,meet(b,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_71]),c_0_67]),c_0_53]),c_0_72]) ).
cnf(c_0_76,hypothesis,
join(a,join(complement(b),meet(b,complement(a)))) = one,
inference(spm,[status(thm)],[c_0_73,c_0_19]) ).
cnf(c_0_77,plain,
join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_28]),c_0_22]),c_0_22]) ).
cnf(c_0_78,plain,
join(X1,join(X2,meet(X3,join(X1,X2)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_79,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_14,c_0_26]) ).
cnf(c_0_80,hypothesis,
meet(complement(join(X1,X2)),join(meet(b,X2),X1)) = zero,
inference(spm,[status(thm)],[c_0_74,c_0_24]) ).
cnf(c_0_81,plain,
join(X1,join(X2,complement(join(X1,X2)))) = one,
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_82,hypothesis,
join(a,meet(b,complement(a))) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_67]) ).
cnf(c_0_83,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_26,c_0_40]) ).
cnf(c_0_84,plain,
join(X1,join(X2,meet(X3,join(X2,X1)))) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_28]) ).
cnf(c_0_85,plain,
join(meet(X1,X2),meet(X2,join(meet(X1,X2),X3))) = meet(X2,join(meet(X1,X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_79]),c_0_24]) ).
cnf(c_0_86,hypothesis,
complement(join(X1,join(X2,complement(join(meet(b,X2),X1))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_22]),c_0_16]),c_0_24]) ).
cnf(c_0_87,hypothesis,
join(a,join(meet(b,complement(a)),X1)) = join(b,X1),
inference(spm,[status(thm)],[c_0_22,c_0_82]) ).
cnf(c_0_88,plain,
join(meet(X1,X2),meet(join(X3,X1),X2)) = meet(join(X3,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_83]),c_0_24]) ).
cnf(c_0_89,plain,
join(X1,meet(X2,join(meet(X3,X2),X1))) = join(X1,meet(X3,X2)),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_90,hypothesis,
join(X1,join(X2,complement(join(meet(b,X2),X1)))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_86]),c_0_31]) ).
cnf(c_0_91,plain,
join(X1,join(X2,complement(join(X2,X1)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_81]),c_0_30]),c_0_22]),c_0_24]) ).
cnf(c_0_92,plain,
complement(one) = zero,
inference(spm,[status(thm)],[c_0_25,c_0_19]) ).
cnf(c_0_93,hypothesis,
join(b,meet(complement(a),join(X1,b))) = join(a,meet(complement(a),join(X1,b))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_17]),c_0_17]) ).
cnf(c_0_94,plain,
join(X1,meet(X2,join(meet(X2,X3),X1))) = join(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_89,c_0_17]) ).
cnf(c_0_95,plain,
meet(join(X1,X2),join(X2,X1)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_40,c_0_28]) ).
cnf(c_0_96,hypothesis,
join(X1,join(X2,complement(join(X1,meet(b,X2))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]),c_0_31]),c_0_22]),c_0_24]) ).
cnf(c_0_97,hypothesis,
join(a,meet(complement(a),join(b,meet(complement(a),X1)))) = join(b,meet(complement(a),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_24]) ).
cnf(c_0_98,hypothesis,
join(b,complement(a)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_15]),c_0_30]) ).
cnf(c_0_99,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_22,c_0_18]) ).
cnf(c_0_100,hypothesis,
join(X1,join(X2,complement(join(X2,meet(b,X1))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_22]),c_0_24]),c_0_19]) ).
cnf(c_0_101,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_102,hypothesis,
join(b,meet(complement(a),join(meet(b,complement(a)),X1))) = join(b,meet(complement(a),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_48]),c_0_97]),c_0_17]),c_0_24]),c_0_98]),c_0_16]) ).
cnf(c_0_103,hypothesis,
join(X1,complement(join(meet(X1,X2),meet(b,X1)))) = one,
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_104,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_26,c_0_101]) ).
cnf(c_0_105,plain,
join(meet(X1,X2),meet(X1,meet(X2,X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_26]) ).
cnf(c_0_106,hypothesis,
join(b,meet(complement(a),complement(meet(b,complement(a))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_16]),c_0_98]),c_0_26]),c_0_104]),c_0_24]),c_0_105]) ).
cnf(c_0_107,plain,
meet(X1,meet(X2,complement(meet(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_108,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
prove_distributivity ).
cnf(c_0_109,hypothesis,
meet(complement(a),complement(meet(b,complement(a)))) = complement(b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_106]),c_0_107]),c_0_67]),c_0_67]) ).
cnf(c_0_110,negated_conjecture,
join(complement(a),complement(b)) != complement(a),
inference(rw,[status(thm)],[c_0_108,c_0_24]) ).
cnf(c_0_111,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_109]),c_0_110]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT223-10 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 09:14:56 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 12.32/12.50 % Version : CSE_E---1.5
% 12.32/12.50 % Problem : theBenchmark.p
% 12.32/12.50 % Proof found
% 12.32/12.50 % SZS status Theorem for theBenchmark.p
% 12.32/12.50 % SZS output start Proof
% See solution above
% 12.32/12.51 % Total time : 11.933000 s
% 12.32/12.51 % SZS output end Proof
% 12.32/12.51 % Total time : 11.937000 s
%------------------------------------------------------------------------------