TSTP Solution File: LAT255-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT255-1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n029.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 06:00:15 EDT 2023
% Result : Unsatisfiable 8.34s 8.40s
% Output : CNFRefutation 8.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 21
% Syntax : Number of formulae : 123 ( 111 unt; 7 typ; 0 def)
% Number of atoms : 125 ( 124 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 184 ( 43 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
meet: ( $i * $i ) > $i ).
tff(decl_23,type,
join: ( $i * $i ) > $i ).
tff(decl_24,type,
complement: $i > $i ).
tff(decl_25,type,
one: $i ).
tff(decl_26,type,
zero: $i ).
tff(decl_27,type,
b: $i ).
tff(decl_28,type,
a: $i ).
cnf(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption1) ).
cnf(complement_join,axiom,
join(X1,complement(X1)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',complement_join) ).
cnf(prove_distributivity_hypothesis,hypothesis,
meet(b,a) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity_hypothesis) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
cnf(associativity_of_meet,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',associativity_of_meet) ).
cnf(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).
cnf(associativity_of_join,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',associativity_of_join) ).
cnf(idempotence_of_join,axiom,
join(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',idempotence_of_join) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
cnf(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',idempotence_of_meet) ).
cnf(complement_meet,axiom,
meet(X1,complement(X1)) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',complement_meet) ).
cnf(equation_H80,axiom,
meet(X1,join(meet(X1,X2),meet(X3,join(X1,meet(X2,join(X1,X3)))))) = join(meet(X1,X2),meet(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H80) ).
cnf(meet_join_complement,axiom,
( complement(X1) = X2
| meet(X1,X2) != zero
| join(X1,X2) != one ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',meet_join_complement) ).
cnf(prove_distributivity,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
file('/export/starexec/sandbox/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,hypothesis,
meet(b,a) = a,
prove_distributivity_hypothesis ).
cnf(c_0_17,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_18,plain,
meet(X1,one) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_20,hypothesis,
meet(a,b) = a,
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_22,plain,
meet(one,X1) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_23,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_24,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_25,hypothesis,
meet(a,meet(b,X1)) = meet(a,X1),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_17]) ).
cnf(c_0_27,plain,
join(one,X1) = one,
inference(spm,[status(thm)],[c_0_14,c_0_22]) ).
cnf(c_0_28,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_30,hypothesis,
meet(a,join(b,X1)) = a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_14]),c_0_20]) ).
cnf(c_0_31,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_14]),c_0_23]) ).
cnf(c_0_32,plain,
join(X1,join(complement(X1),X2)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_15]),c_0_27]) ).
cnf(c_0_33,plain,
join(X1,one) = one,
inference(spm,[status(thm)],[c_0_28,c_0_15]) ).
cnf(c_0_34,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_29]) ).
cnf(c_0_35,hypothesis,
join(b,join(X1,a)) = join(b,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_30]),c_0_23]) ).
cnf(c_0_36,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_37,plain,
join(complement(X1),join(X2,X1)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_23]) ).
cnf(c_0_38,hypothesis,
meet(join(X1,a),join(b,X1)) = join(X1,a),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_36]) ).
cnf(c_0_40,plain,
join(X1,complement(meet(X2,X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_26]),c_0_29]) ).
cnf(c_0_41,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_42,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_17]),c_0_19]) ).
cnf(c_0_43,hypothesis,
meet(join(X1,a),join(X1,b)) = join(X1,a),
inference(spm,[status(thm)],[c_0_38,c_0_29]) ).
cnf(c_0_44,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_39,c_0_17]) ).
cnf(c_0_45,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X3,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_46,hypothesis,
join(b,a) = b,
inference(spm,[status(thm)],[c_0_26,c_0_20]) ).
cnf(c_0_47,plain,
join(complement(meet(X1,X2)),meet(join(X1,X3),X2)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_29]) ).
cnf(c_0_48,hypothesis,
meet(join(X1,a),meet(X2,join(X1,b))) = meet(X2,join(X1,a)),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_41]),c_0_19]),c_0_44]),c_0_45]) ).
cnf(c_0_50,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_19,c_0_34]) ).
cnf(c_0_51,plain,
meet(join(X1,X2),join(X2,X1)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_31]) ).
cnf(c_0_52,hypothesis,
meet(a,meet(X1,b)) = meet(a,X1),
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_53,axiom,
meet(X1,complement(X1)) = zero,
complement_meet ).
cnf(c_0_54,hypothesis,
join(b,join(a,X1)) = join(b,X1),
inference(spm,[status(thm)],[c_0_23,c_0_46]) ).
cnf(c_0_55,hypothesis,
join(complement(meet(X1,X2)),meet(X2,join(X1,a))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_56,plain,
meet(join(X1,X2),meet(join(X2,X1),X3)) = meet(join(X1,X2),X3),
inference(spm,[status(thm)],[c_0_50,c_0_31]) ).
cnf(c_0_57,plain,
meet(join(X1,X2),meet(X3,join(X2,X1))) = meet(X3,join(X1,X2)),
inference(spm,[status(thm)],[c_0_42,c_0_51]) ).
cnf(c_0_58,hypothesis,
join(meet(X1,b),meet(a,X1)) = meet(X1,b),
inference(spm,[status(thm)],[c_0_26,c_0_52]) ).
cnf(c_0_59,plain,
meet(X1,zero) = zero,
inference(spm,[status(thm)],[c_0_39,c_0_53]) ).
cnf(c_0_60,hypothesis,
join(b,meet(a,X1)) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_21]),c_0_46]) ).
cnf(c_0_61,hypothesis,
join(complement(X1),meet(join(X1,X2),join(X1,a))) = one,
inference(spm,[status(thm)],[c_0_55,c_0_14]) ).
cnf(c_0_62,plain,
meet(X1,join(X2,X3)) = meet(join(X3,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_56]),c_0_57]) ).
cnf(c_0_63,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_19]) ).
cnf(c_0_64,hypothesis,
join(meet(X1,b),join(meet(a,X1),X2)) = join(meet(X1,b),X2),
inference(spm,[status(thm)],[c_0_23,c_0_58]) ).
cnf(c_0_65,plain,
join(X1,complement(meet(X1,X2))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_21]),c_0_29]) ).
cnf(c_0_66,hypothesis,
meet(join(a,X1),join(b,X1)) = join(a,X1),
inference(spm,[status(thm)],[c_0_34,c_0_54]) ).
cnf(c_0_67,axiom,
meet(X1,join(meet(X1,X2),meet(X3,join(X1,meet(X2,join(X1,X3)))))) = join(meet(X1,X2),meet(X1,X3)),
equation_H80 ).
cnf(c_0_68,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_53]) ).
cnf(c_0_69,hypothesis,
join(b,complement(a)) = join(b,one),
inference(spm,[status(thm)],[c_0_54,c_0_15]) ).
cnf(c_0_70,plain,
meet(X1,complement(join(X1,X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_53]),c_0_59]) ).
cnf(c_0_71,hypothesis,
join(b,complement(meet(a,X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_60]),c_0_29]) ).
cnf(c_0_72,hypothesis,
join(complement(X1),meet(join(X1,a),join(X2,X1))) = one,
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_73,hypothesis,
join(b,join(X1,meet(X2,a))) = join(b,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_30]),c_0_23]) ).
cnf(c_0_74,hypothesis,
join(meet(X1,b),complement(meet(a,meet(X1,X2)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_33]),c_0_19]) ).
cnf(c_0_75,hypothesis,
meet(join(a,X1),meet(join(b,X1),X2)) = meet(join(a,X1),X2),
inference(spm,[status(thm)],[c_0_19,c_0_66]) ).
cnf(c_0_76,plain,
meet(X1,join(meet(X1,X2),meet(complement(X1),join(X1,X2)))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_15]),c_0_18]),c_0_53]),c_0_68]) ).
cnf(c_0_77,hypothesis,
join(b,complement(a)) = one,
inference(rw,[status(thm)],[c_0_69,c_0_33]) ).
cnf(c_0_78,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(spm,[status(thm)],[c_0_70,c_0_29]) ).
cnf(c_0_79,axiom,
( complement(X1) = X2
| meet(X1,X2) != zero
| join(X1,X2) != one ),
meet_join_complement ).
cnf(c_0_80,hypothesis,
meet(b,join(meet(b,X1),meet(complement(meet(a,X2)),join(b,X1)))) = join(meet(b,X1),meet(b,complement(meet(a,X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_71]),c_0_18]) ).
cnf(c_0_81,hypothesis,
join(X1,join(a,complement(join(X1,meet(X2,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_72,c_0_73]),c_0_23]),c_0_29]),c_0_26]),c_0_38]),c_0_29]),c_0_23]) ).
cnf(c_0_82,hypothesis,
join(b,meet(X1,a)) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_26]),c_0_46]) ).
cnf(c_0_83,hypothesis,
join(meet(b,join(a,X1)),complement(meet(a,X2))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_17]),c_0_41]) ).
cnf(c_0_84,hypothesis,
meet(b,join(complement(b),meet(b,complement(a)))) = meet(b,complement(a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_18]),c_0_29]) ).
cnf(c_0_85,hypothesis,
meet(join(a,X1),complement(join(b,X1))) = zero,
inference(spm,[status(thm)],[c_0_78,c_0_54]) ).
cnf(c_0_86,plain,
( complement(X1) = X2
| meet(X2,X1) != zero
| join(X1,X2) != one ),
inference(spm,[status(thm)],[c_0_79,c_0_17]) ).
cnf(c_0_87,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_23,c_0_26]) ).
cnf(c_0_88,hypothesis,
join(meet(b,join(a,complement(b))),meet(b,complement(meet(a,X1)))) = b,
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_80,c_0_81]),c_0_82]),c_0_18]),c_0_83]),c_0_18]),c_0_82]) ).
cnf(c_0_89,hypothesis,
meet(a,join(complement(b),meet(b,complement(a)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_84]),c_0_25]),c_0_53]) ).
cnf(c_0_90,plain,
meet(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_17,c_0_59]) ).
cnf(c_0_91,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_92,hypothesis,
meet(complement(b),join(a,meet(b,X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_21]),c_0_17]) ).
cnf(c_0_93,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_53]),c_0_29]),c_0_15])]) ).
cnf(c_0_94,plain,
join(X1,join(X2,X3)) = join(X2,join(X3,X1)),
inference(spm,[status(thm)],[c_0_23,c_0_29]) ).
cnf(c_0_95,hypothesis,
join(a,join(complement(b),meet(b,complement(meet(a,X1))))) = one,
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_87,c_0_88]),c_0_23]),c_0_29]),c_0_15]),c_0_33]),c_0_23]) ).
cnf(c_0_96,hypothesis,
join(a,b) = b,
inference(rw,[status(thm)],[c_0_46,c_0_29]) ).
cnf(c_0_97,hypothesis,
meet(a,meet(join(complement(b),meet(b,complement(a))),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_89]),c_0_90]) ).
cnf(c_0_98,plain,
meet(join(X1,X2),join(meet(X1,X3),X2)) = join(meet(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_91]),c_0_17]) ).
cnf(c_0_99,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_14,c_0_19]) ).
cnf(c_0_100,hypothesis,
( join(a,meet(b,X1)) = b
| join(a,join(complement(b),meet(b,X1))) != one ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_92]),c_0_93]),c_0_94]),c_0_29]) ).
cnf(c_0_101,hypothesis,
join(a,join(complement(b),meet(b,complement(a)))) = one,
inference(spm,[status(thm)],[c_0_95,c_0_18]) ).
cnf(c_0_102,hypothesis,
join(a,join(b,X1)) = join(b,X1),
inference(spm,[status(thm)],[c_0_23,c_0_96]) ).
cnf(c_0_103,hypothesis,
meet(a,join(meet(b,X1),meet(X2,join(b,meet(X1,join(b,X2)))))) = meet(a,join(meet(b,X1),meet(b,X2))),
inference(spm,[status(thm)],[c_0_25,c_0_67]) ).
cnf(c_0_104,hypothesis,
meet(a,join(meet(b,complement(a)),meet(complement(b),X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_29]) ).
cnf(c_0_105,plain,
meet(X1,meet(X2,join(meet(X2,X1),X3))) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_99,c_0_17]) ).
cnf(c_0_106,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_23,c_0_31]),c_0_23]),c_0_23]) ).
cnf(c_0_107,hypothesis,
join(a,meet(b,complement(a))) = b,
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_108,hypothesis,
join(a,join(X1,b)) = join(X1,b),
inference(spm,[status(thm)],[c_0_102,c_0_29]) ).
cnf(c_0_109,hypothesis,
( join(meet(b,X1),meet(X2,join(b,meet(X1,join(b,X2))))) = complement(a)
| join(a,join(meet(b,X1),meet(X2,join(b,meet(X1,join(b,X2)))))) != one
| meet(a,join(meet(b,X1),meet(b,X2))) != zero ),
inference(spm,[status(thm)],[c_0_79,c_0_103]) ).
cnf(c_0_110,hypothesis,
meet(a,join(meet(b,complement(a)),meet(X1,complement(b)))) = zero,
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_111,hypothesis,
join(a,join(X1,meet(b,complement(a)))) = join(X1,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108]) ).
cnf(c_0_112,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
prove_distributivity ).
cnf(c_0_113,hypothesis,
join(complement(b),meet(b,complement(a))) = complement(a),
inference(cn,[status(thm)],[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(rw,[status(thm)],[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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_15]),c_0_18]),c_0_69]),c_0_33]),c_0_18]),c_0_29]),c_0_15]),c_0_18]),c_0_69]),c_0_33]),c_0_18]),c_0_29]),c_0_111]),c_0_29]),c_0_15])]) ).
cnf(c_0_114,negated_conjecture,
join(complement(a),complement(b)) != complement(a),
inference(rw,[status(thm)],[c_0_112,c_0_29]) ).
cnf(c_0_115,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_113]),c_0_29]),c_0_114]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT255-1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n029.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 : Thu Aug 24 05:08:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 8.34/8.40 % Version : CSE_E---1.5
% 8.34/8.40 % Problem : theBenchmark.p
% 8.34/8.40 % Proof found
% 8.34/8.40 % SZS status Theorem for theBenchmark.p
% 8.34/8.40 % SZS output start Proof
% See solution above
% 8.34/8.41 % Total time : 7.829000 s
% 8.34/8.41 % SZS output end Proof
% 8.34/8.41 % Total time : 7.833000 s
%------------------------------------------------------------------------------