%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT231-1 : TPTP v9.2.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:37:43 PM UTC 2026
% Result : Unsatisfiable 62.75s 37.07s
% Output : CNFRefutation 63.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of clauses : 111 ( 107 unt; 0 nHn; 22 RR)
% Number of literals : 118 ( 117 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% 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 : 177 ( 34 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',idempotence_of_meet) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
cnf(prove_distributivity_hypothesis,hypothesis,
meet(b,a) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity_hypothesis) ).
cnf(complement_meet,axiom,
meet(X1,complement(X1)) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',complement_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(equation_H21,axiom,
join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(meet(X2,join(X1,meet(X2,X3))),meet(X3,join(X1,X2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H21) ).
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,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_17,axiom,
meet(X1,X1) = X1,
idempotence_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(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_20,hypothesis,
meet(b,a) = a,
prove_distributivity_hypothesis ).
cnf(c_0_21,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,axiom,
meet(X1,complement(X1)) = zero,
complement_meet ).
cnf(c_0_23,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_24,plain,
meet(one,X1) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_26,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_27,hypothesis,
meet(a,b) = a,
inference(rw,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_28,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_29,plain,
meet(X1,zero) = zero,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_30,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_19]) ).
cnf(c_0_31,plain,
join(one,X1) = one,
inference(spm,[status(thm)],[c_0_14,c_0_24]) ).
cnf(c_0_32,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,hypothesis,
meet(a,meet(b,X1)) = meet(a,X1),
inference(spm,[status(thm)],[c_0_16,c_0_27]) ).
cnf(c_0_34,plain,
meet(X1,complement(join(X1,X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_22]),c_0_29]) ).
cnf(c_0_35,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_36,hypothesis,
join(b,a) = b,
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
cnf(c_0_37,axiom,
join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(meet(X2,join(X1,meet(X2,X3))),meet(X3,join(X1,X2)))),
equation_H21 ).
cnf(c_0_38,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_14]),c_0_25]) ).
cnf(c_0_39,plain,
join(X1,join(complement(X1),X2)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_15]),c_0_31]) ).
cnf(c_0_40,plain,
join(X1,one) = one,
inference(spm,[status(thm)],[c_0_32,c_0_15]) ).
cnf(c_0_41,hypothesis,
meet(a,meet(X1,b)) = meet(a,X1),
inference(spm,[status(thm)],[c_0_33,c_0_19]) ).
cnf(c_0_42,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_43,hypothesis,
join(b,join(a,X1)) = join(b,X1),
inference(spm,[status(thm)],[c_0_25,c_0_36]) ).
cnf(c_0_44,plain,
meet(X1,join(meet(X2,join(X1,X3)),meet(X3,join(X1,meet(X3,X2))))) = join(meet(X1,X3),meet(X1,X2)),
inference(rw,[status(thm)],[c_0_37,c_0_35]) ).
cnf(c_0_45,plain,
join(complement(X1),join(X2,X1)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_25]),c_0_40]),c_0_40]),c_0_25]) ).
cnf(c_0_46,hypothesis,
join(meet(X1,b),meet(a,X1)) = meet(X1,b),
inference(spm,[status(thm)],[c_0_30,c_0_41]) ).
cnf(c_0_47,hypothesis,
meet(join(a,X1),complement(join(b,X1))) = zero,
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,plain,
meet(X1,join(X2,X1)) = X1,
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_44,c_0_40]),c_0_18]),c_0_24]),c_0_24]),c_0_38]),c_0_18]),c_0_23]) ).
cnf(c_0_49,hypothesis,
join(meet(X1,b),complement(meet(a,X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_35]) ).
cnf(c_0_50,hypothesis,
meet(complement(b),join(a,meet(b,X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_23]),c_0_19]) ).
cnf(c_0_51,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X3,X1)),
inference(spm,[status(thm)],[c_0_16,c_0_19]) ).
cnf(c_0_52,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_53,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_54,hypothesis,
meet(join(a,X1),join(b,X1)) = join(a,X1),
inference(spm,[status(thm)],[c_0_48,c_0_43]) ).
cnf(c_0_55,plain,
join(meet(X1,X2),meet(X1,meet(X2,X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_23,c_0_16]) ).
cnf(c_0_56,hypothesis,
join(complement(join(meet(a,X1),meet(a,X2))),meet(b,join(meet(X2,join(a,X1)),meet(X1,join(a,meet(X1,X2)))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_44]),c_0_19]),c_0_35]) ).
cnf(c_0_57,hypothesis,
meet(complement(b),join(a,meet(X1,meet(X2,b)))) = zero,
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_58,hypothesis,
meet(a,complement(b)) = meet(a,zero),
inference(spm,[status(thm)],[c_0_33,c_0_22]) ).
cnf(c_0_59,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_52,c_0_35]) ).
cnf(c_0_60,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_53]),c_0_16]),c_0_16]) ).
cnf(c_0_61,hypothesis,
meet(join(a,X1),join(X1,b)) = join(a,X1),
inference(spm,[status(thm)],[c_0_54,c_0_35]) ).
cnf(c_0_62,plain,
join(X1,join(X2,X3)) = join(X2,join(X3,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_35]) ).
cnf(c_0_63,hypothesis,
meet(a,join(b,X1)) = a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_14]),c_0_27]) ).
cnf(c_0_64,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_25,c_0_38]),c_0_25]),c_0_25]) ).
cnf(c_0_65,plain,
join(meet(X1,X2),meet(X2,X1)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_17]),c_0_16]),c_0_53]),c_0_16]),c_0_53]) ).
cnf(c_0_66,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_19]),c_0_16]) ).
cnf(c_0_67,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_16]) ).
cnf(c_0_68,hypothesis,
join(complement(meet(a,X1)),meet(X1,meet(b,join(a,complement(b))))) = 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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_29]),c_0_41]),c_0_59]),c_0_16]),c_0_52]),c_0_60]) ).
cnf(c_0_69,hypothesis,
meet(X1,join(a,join(X2,meet(join(X2,b),join(X1,join(a,X2)))))) = join(meet(X1,join(a,X2)),meet(X1,join(X2,b))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_61]),c_0_48]),c_0_62]) ).
cnf(c_0_70,hypothesis,
meet(a,join(X1,b)) = a,
inference(spm,[status(thm)],[c_0_63,c_0_35]) ).
cnf(c_0_71,hypothesis,
meet(join(X1,b),join(a,X1)) = join(a,X1),
inference(spm,[status(thm)],[c_0_19,c_0_61]) ).
cnf(c_0_72,plain,
join(meet(X1,X2),join(X3,meet(X2,X1))) = join(meet(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_38]) ).
cnf(c_0_73,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_66,c_0_48]) ).
cnf(c_0_74,plain,
meet(X1,join(meet(X2,X1),meet(X3,X1))) = join(meet(X1,X3),meet(X1,X2)),
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_44,c_0_23]),c_0_16]),c_0_23]),c_0_16]),c_0_21]),c_0_53]) ).
cnf(c_0_75,plain,
meet(X1,join(meet(X1,X2),meet(X1,X3))) = join(meet(X1,X2),meet(X1,X3)),
inference(spm,[status(thm)],[c_0_21,c_0_44]) ).
cnf(c_0_76,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_14,c_0_16]) ).
cnf(c_0_77,plain,
join(X1,join(X2,meet(X3,X1))) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_14]),c_0_25]) ).
cnf(c_0_78,hypothesis,
join(complement(a),meet(b,meet(join(a,complement(b)),join(a,X1)))) = 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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_14]),c_0_70]),c_0_26]),c_0_32]),c_0_71]),c_0_38]),c_0_38]),c_0_51]) ).
cnf(c_0_79,plain,
join(meet(X1,X2),X3) = join(X3,meet(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_65]),c_0_72]) ).
cnf(c_0_80,hypothesis,
join(a,b) = b,
inference(rw,[status(thm)],[c_0_36,c_0_35]) ).
cnf(c_0_81,plain,
meet(X1,join(meet(X2,X1),meet(X2,X3))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_16]),c_0_75]),c_0_53]) ).
cnf(c_0_82,plain,
meet(X1,meet(X2,join(meet(X2,X1),X3))) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_76,c_0_19]) ).
cnf(c_0_83,hypothesis,
join(b,complement(a)) = join(b,one),
inference(spm,[status(thm)],[c_0_43,c_0_15]) ).
cnf(c_0_84,axiom,
( complement(X1) = X2
| meet(X1,X2) != zero
| join(X1,X2) != one ),
meet_join_complement ).
cnf(c_0_85,plain,
join(X1,join(X2,complement(X1))) = one,
inference(spm,[status(thm)],[c_0_39,c_0_35]) ).
cnf(c_0_86,hypothesis,
join(complement(a),meet(join(a,X1),join(a,complement(b)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_40]),c_0_79]) ).
cnf(c_0_87,hypothesis,
join(a,join(b,X1)) = join(b,X1),
inference(spm,[status(thm)],[c_0_25,c_0_80]) ).
cnf(c_0_88,plain,
meet(X1,join(meet(X2,X1),meet(X3,X2))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_89,hypothesis,
join(b,complement(a)) = one,
inference(rw,[status(thm)],[c_0_83,c_0_40]) ).
cnf(c_0_90,plain,
( complement(X1) = X2
| meet(X2,X1) != zero
| join(X1,X2) != one ),
inference(spm,[status(thm)],[c_0_84,c_0_19]) ).
cnf(c_0_91,plain,
meet(X1,join(X2,meet(join(X3,complement(X1)),join(X1,meet(join(X3,complement(X1)),X2))))) = join(meet(X1,join(X3,complement(X1))),meet(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_85]),c_0_18]) ).
cnf(c_0_92,hypothesis,
join(complement(a),meet(join(a,complement(b)),join(b,X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_19]) ).
cnf(c_0_93,plain,
meet(X1,join(X2,meet(X1,join(X2,X3)))) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_14]),c_0_79]) ).
cnf(c_0_94,hypothesis,
meet(b,join(X1,meet(complement(a),join(b,meet(complement(a),X1))))) = join(meet(b,complement(a)),meet(b,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_89]),c_0_18]) ).
cnf(c_0_95,hypothesis,
meet(complement(b),join(a,meet(X1,b))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_30]),c_0_19]) ).
cnf(c_0_96,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_22]),c_0_35]),c_0_15])]) ).
cnf(c_0_97,hypothesis,
join(meet(b,complement(a)),meet(b,join(a,complement(b)))) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_18]),c_0_79]),c_0_19]) ).
cnf(c_0_98,hypothesis,
join(meet(b,complement(a)),meet(b,X1)) = meet(b,join(X1,meet(b,complement(a)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_77]) ).
cnf(c_0_99,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_25,c_0_30]) ).
cnf(c_0_100,hypothesis,
( join(a,meet(X1,b)) = 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_84,c_0_95]),c_0_96]),c_0_62]),c_0_79]) ).
cnf(c_0_101,hypothesis,
join(a,join(complement(b),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(spm,[status(thm)],[c_0_77,c_0_97]),c_0_25]),c_0_35]),c_0_15]),c_0_40]),c_0_25]) ).
cnf(c_0_102,hypothesis,
meet(b,join(complement(b),meet(b,complement(a)))) = meet(b,complement(a)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_22]),c_0_52]) ).
cnf(c_0_103,plain,
join(X1,join(X2,X3)) = join(X3,join(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_77]),c_0_25]),c_0_62]),c_0_99]) ).
cnf(c_0_104,hypothesis,
join(a,meet(b,complement(a))) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_19]) ).
cnf(c_0_105,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_33,c_0_102]),c_0_33]),c_0_22]) ).
cnf(c_0_106,hypothesis,
join(a,join(X1,meet(b,complement(a)))) = join(X1,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_62]) ).
cnf(c_0_107,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
prove_distributivity ).
cnf(c_0_108,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(spm,[status(thm)],[c_0_84,c_0_105]),c_0_106]),c_0_35]),c_0_15])]) ).
cnf(c_0_109,negated_conjecture,
join(complement(a),complement(b)) != complement(a),
inference(rw,[status(thm)],[c_0_107,c_0_35]) ).
cnf(c_0_110,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_108]),c_0_35]),c_0_109]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT231-1 : TPTP v9.2.1. Released v3.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n023.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 20:55:38 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 62.75/37.07 % Version : CSE_E---1.7
% 62.75/37.07 % Problem : theBenchmark.p
% 62.75/37.07 % SZS status Unsatisfiable for theBenchmark.p
% 62.75/37.07 % SZS output start CNFRefutation
% See solution above
% 63.03/37.32 % Total time : 27.429s
%------------------------------------------------------------------------------