%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT232-1 : TPTP v9.2.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n028.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 46.63s 27.25s
% Output : CNFRefutation 46.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of clauses : 101 ( 97 unt; 0 nHn; 20 RR)
% Number of literals : 108 ( 107 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 ( 28 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_of_join,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',associativity_of_join) ).
cnf(idempotence_of_join,axiom,
join(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',idempotence_of_join) ).
cnf(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption1) ).
cnf(complement_join,axiom,
join(X1,complement(X1)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',complement_join) ).
cnf(equation_H22,axiom,
join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(meet(X2,join(X3,meet(X1,X2))),meet(X3,join(X1,X2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H22) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
cnf(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption2) ).
cnf(prove_distributivity_hypothesis,hypothesis,
meet(b,a) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity_hypothesis) ).
cnf(associativity_of_meet,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',associativity_of_meet) ).
cnf(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',idempotence_of_meet) ).
cnf(complement_meet,axiom,
meet(X1,complement(X1)) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',complement_meet) ).
cnf(meet_join_complement,axiom,
( complement(X1) = X2
| meet(X1,X2) != zero
| join(X1,X2) != one ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',meet_join_complement) ).
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,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_15,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_16,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_17,axiom,
join(X1,complement(X1)) = one,
complement_join ).
cnf(c_0_18,axiom,
join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(meet(X2,join(X3,meet(X1,X2))),meet(X3,join(X1,X2)))),
equation_H22 ).
cnf(c_0_19,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_20,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
meet(X1,one) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_23,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_24,hypothesis,
meet(b,a) = a,
prove_distributivity_hypothesis ).
cnf(c_0_25,plain,
meet(X1,join(meet(X2,join(X1,X3)),meet(X3,join(X2,meet(X1,X3))))) = join(meet(X1,X3),meet(X1,X2)),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,plain,
join(X1,one) = one,
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_27,plain,
meet(one,X1) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_29,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_30,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_31,hypothesis,
meet(a,b) = a,
inference(rw,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_32,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_25,c_0_26]),c_0_21]),c_0_21]),c_0_27]),c_0_20]),c_0_21]),c_0_23]) ).
cnf(c_0_33,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_16]),c_0_14]) ).
cnf(c_0_34,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,axiom,
meet(X1,complement(X1)) = zero,
complement_meet ).
cnf(c_0_36,plain,
join(one,X1) = one,
inference(spm,[status(thm)],[c_0_16,c_0_27]) ).
cnf(c_0_37,hypothesis,
meet(a,meet(b,X1)) = meet(a,X1),
inference(spm,[status(thm)],[c_0_29,c_0_31]) ).
cnf(c_0_38,hypothesis,
join(b,a) = b,
inference(spm,[status(thm)],[c_0_28,c_0_31]) ).
cnf(c_0_39,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_29,c_0_32]) ).
cnf(c_0_40,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_22]),c_0_29]) ).
cnf(c_0_41,plain,
meet(join(X1,X2),join(X2,X1)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_42,plain,
join(meet(X1,X2),meet(X1,meet(X2,X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_23,c_0_29]) ).
cnf(c_0_43,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_34,c_0_22]) ).
cnf(c_0_44,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_29,c_0_16]) ).
cnf(c_0_45,plain,
meet(X1,zero) = zero,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_46,plain,
join(X1,join(complement(X1),X2)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_17]),c_0_36]) ).
cnf(c_0_47,hypothesis,
meet(a,meet(X1,b)) = meet(a,X1),
inference(spm,[status(thm)],[c_0_37,c_0_22]) ).
cnf(c_0_48,hypothesis,
join(b,join(a,X1)) = join(b,X1),
inference(spm,[status(thm)],[c_0_14,c_0_38]) ).
cnf(c_0_49,plain,
meet(X1,join(X2,join(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_14]) ).
cnf(c_0_50,plain,
join(X1,join(X2,join(X3,X1))) = join(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_33,c_0_14]) ).
cnf(c_0_51,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X3,X1)),
inference(spm,[status(thm)],[c_0_29,c_0_22]) ).
cnf(c_0_52,plain,
meet(join(X1,X2),meet(join(X2,X1),X3)) = meet(join(X1,X2),X3),
inference(spm,[status(thm)],[c_0_39,c_0_33]) ).
cnf(c_0_53,plain,
meet(join(X1,X2),meet(X3,join(X2,X1))) = meet(X3,join(X1,X2)),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_54,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_55,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_16,c_0_29]) ).
cnf(c_0_56,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_14,c_0_33]),c_0_14]),c_0_14]) ).
cnf(c_0_57,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_42,c_0_30]),c_0_29]),c_0_43]),c_0_29]),c_0_43]) ).
cnf(c_0_58,plain,
meet(X1,complement(join(X1,X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_35]),c_0_45]) ).
cnf(c_0_59,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_33,c_0_46]),c_0_14]),c_0_26]),c_0_26]),c_0_14]) ).
cnf(c_0_60,hypothesis,
join(meet(X1,b),meet(a,X1)) = meet(X1,b),
inference(spm,[status(thm)],[c_0_28,c_0_47]) ).
cnf(c_0_61,hypothesis,
join(b,complement(a)) = join(b,one),
inference(spm,[status(thm)],[c_0_48,c_0_17]) ).
cnf(c_0_62,plain,
meet(join(X1,X2),join(X2,join(X3,X1))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_63,plain,
meet(X1,join(X2,X3)) = meet(join(X3,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
cnf(c_0_64,plain,
join(X1,join(X2,meet(X3,join(X2,X1)))) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_41]),c_0_14]) ).
cnf(c_0_65,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_28,c_0_55]),c_0_19]) ).
cnf(c_0_66,plain,
join(X1,join(X2,X3)) = join(X2,join(X3,X1)),
inference(spm,[status(thm)],[c_0_14,c_0_19]) ).
cnf(c_0_67,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_56,c_0_57]),c_0_33]) ).
cnf(c_0_68,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(spm,[status(thm)],[c_0_58,c_0_19]) ).
cnf(c_0_69,axiom,
( complement(X1) = X2
| meet(X1,X2) != zero
| join(X1,X2) != one ),
meet_join_complement ).
cnf(c_0_70,hypothesis,
join(meet(X1,b),complement(meet(a,X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_19]) ).
cnf(c_0_71,hypothesis,
join(b,complement(a)) = one,
inference(rw,[status(thm)],[c_0_61,c_0_26]) ).
cnf(c_0_72,plain,
meet(join(X1,X2),join(X1,meet(X2,X3))) = join(meet(X2,X3),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_23]),c_0_63]) ).
cnf(c_0_73,plain,
join(X1,meet(X2,join(meet(X3,X2),X1))) = join(X1,meet(X3,X2)),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_74,plain,
meet(join(X1,X2),join(X1,meet(X3,X2))) = join(meet(X3,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_28]),c_0_63]) ).
cnf(c_0_75,plain,
join(meet(X1,X2),X3) = join(X3,meet(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_57]),c_0_67]) ).
cnf(c_0_76,hypothesis,
meet(join(a,X1),complement(join(b,X1))) = zero,
inference(spm,[status(thm)],[c_0_68,c_0_48]) ).
cnf(c_0_77,plain,
( complement(X1) = X2
| meet(X2,X1) != zero
| join(X1,X2) != one ),
inference(spm,[status(thm)],[c_0_69,c_0_22]) ).
cnf(c_0_78,plain,
meet(X1,join(X2,meet(join(complement(X1),X3),join(X2,meet(X1,join(complement(X1),X3)))))) = join(meet(X1,join(complement(X1),X3)),meet(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_46]),c_0_21]) ).
cnf(c_0_79,hypothesis,
join(complement(a),meet(b,join(X1,a))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_32]),c_0_22]),c_0_19]) ).
cnf(c_0_80,plain,
join(complement(X1),join(X1,X2)) = one,
inference(spm,[status(thm)],[c_0_59,c_0_19]) ).
cnf(c_0_81,hypothesis,
meet(b,join(X1,meet(complement(a),join(X1,meet(b,complement(a)))))) = join(meet(b,complement(a)),meet(b,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_71]),c_0_21]) ).
cnf(c_0_82,plain,
join(X1,meet(X2,join(X1,meet(X3,X2)))) = join(meet(X3,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]),c_0_75]),c_0_63]) ).
cnf(c_0_83,hypothesis,
meet(complement(b),join(a,meet(b,X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_23]),c_0_22]) ).
cnf(c_0_84,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_35]),c_0_19]),c_0_17])]) ).
cnf(c_0_85,plain,
join(X1,join(X2,meet(X3,X1))) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_16]),c_0_14]) ).
cnf(c_0_86,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_21]),c_0_19]),c_0_80]),c_0_21]),c_0_19]),c_0_19]) ).
cnf(c_0_87,hypothesis,
join(meet(b,complement(a)),meet(b,X1)) = meet(b,join(meet(b,complement(a)),X1)),
inference(rw,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_88,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_35]) ).
cnf(c_0_89,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_14,c_0_28]) ).
cnf(c_0_90,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_69,c_0_83]),c_0_84]),c_0_66]),c_0_19]) ).
cnf(c_0_91,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_85,c_0_86]),c_0_14]),c_0_19]),c_0_17]),c_0_26]),c_0_14]) ).
cnf(c_0_92,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_87,c_0_35]),c_0_88]),c_0_19]) ).
cnf(c_0_93,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_66,c_0_85]),c_0_14]),c_0_66]),c_0_89]) ).
cnf(c_0_94,hypothesis,
join(a,meet(b,complement(a))) = b,
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_95,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_37,c_0_92]),c_0_37]),c_0_35]) ).
cnf(c_0_96,hypothesis,
join(a,join(X1,meet(b,complement(a)))) = join(X1,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_66]) ).
cnf(c_0_97,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
prove_distributivity ).
cnf(c_0_98,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_69,c_0_95]),c_0_96]),c_0_19]),c_0_17])]) ).
cnf(c_0_99,negated_conjecture,
join(complement(a),complement(b)) != complement(a),
inference(rw,[status(thm)],[c_0_97,c_0_19]) ).
cnf(c_0_100,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_98]),c_0_19]),c_0_99]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT232-1 : TPTP v9.2.1. Released v3.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n028.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 20:55:01 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 46.63/27.25 % Version : CSE_E---1.7
% 46.63/27.25 % Problem : theBenchmark.p
% 46.63/27.25 % SZS status Unsatisfiable for theBenchmark.p
% 46.63/27.25 % SZS output start CNFRefutation
% See solution above
% 46.83/27.45 % Total time : 20.403s
%------------------------------------------------------------------------------