%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT228-1 : 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 : n011.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 04:37:42 PM UTC 2026
% Result : Unsatisfiable 68.14s 39.67s
% Output : CNFRefutation 68.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of clauses : 70 ( 65 unt; 0 nHn; 22 RR)
% Number of literals : 79 ( 78 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 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 : 107 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption2) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
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/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(complement_join,axiom,
join(X1,complement(X1)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',complement_join) ).
cnf(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption1) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
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(equation_H16,axiom,
meet(X1,join(meet(X1,X2),meet(X1,X3))) = meet(X1,join(meet(X1,X2),meet(X3,join(X2,meet(X3,join(X1,X2)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H16) ).
cnf(complement_meet,axiom,
meet(X1,complement(X1)) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',complement_meet) ).
cnf(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',idempotence_of_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(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_15,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_16,hypothesis,
meet(b,a) = a,
prove_distributivity_hypothesis ).
cnf(c_0_17,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,hypothesis,
meet(a,b) = a,
inference(rw,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_19,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_20,hypothesis,
join(b,a) = b,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_22,hypothesis,
join(b,join(a,X1)) = join(b,X1),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,axiom,
join(X1,complement(X1)) = one,
complement_join ).
cnf(c_0_24,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_21]) ).
cnf(c_0_25,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_26,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_27,hypothesis,
join(b,complement(a)) = join(b,one),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
join(X1,one) = one,
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_29,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_30,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_25]),c_0_19]) ).
cnf(c_0_32,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_33,axiom,
meet(X1,join(meet(X1,X2),meet(X1,X3))) = meet(X1,join(meet(X1,X2),meet(X3,join(X2,meet(X3,join(X1,X2)))))),
equation_H16 ).
cnf(c_0_34,hypothesis,
join(b,complement(a)) = one,
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,plain,
meet(X1,one) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_36,axiom,
meet(X1,complement(X1)) = zero,
complement_meet ).
cnf(c_0_37,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_38,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_39,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_15]),c_0_29]) ).
cnf(c_0_40,plain,
meet(join(X1,X2),join(X2,X1)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_41,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_30,c_0_32]),c_0_15]) ).
cnf(c_0_42,hypothesis,
meet(b,join(meet(b,complement(a)),meet(b,X1))) = meet(b,join(meet(b,complement(a)),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_30]) ).
cnf(c_0_43,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_36]) ).
cnf(c_0_44,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_29,c_0_37]) ).
cnf(c_0_45,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X3,X1)),
inference(spm,[status(thm)],[c_0_29,c_0_15]) ).
cnf(c_0_46,plain,
meet(join(X1,X2),meet(join(X2,X1),X3)) = meet(join(X1,X2),X3),
inference(spm,[status(thm)],[c_0_38,c_0_31]) ).
cnf(c_0_47,plain,
meet(join(X1,X2),meet(X3,join(X2,X1))) = meet(X3,join(X1,X2)),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,plain,
meet(X1,join(meet(X1,X2),meet(X1,X3))) = join(meet(X1,X2),meet(X1,X3)),
inference(spm,[status(thm)],[c_0_41,c_0_14]) ).
cnf(c_0_49,axiom,
( complement(X1) = X2
| meet(X1,X2) != zero
| join(X1,X2) != one ),
meet_join_complement ).
cnf(c_0_50,plain,
meet(X1,meet(X2,complement(meet(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_36,c_0_29]) ).
cnf(c_0_51,hypothesis,
meet(b,join(complement(b),meet(b,complement(a)))) = meet(b,complement(a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_36]),c_0_43]),c_0_44]),c_0_26]) ).
cnf(c_0_52,plain,
meet(X1,join(X2,X3)) = meet(join(X3,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_53,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_54,hypothesis,
join(meet(b,complement(a)),meet(b,X1)) = meet(b,join(meet(b,complement(a)),X1)),
inference(rw,[status(thm)],[c_0_42,c_0_48]) ).
cnf(c_0_55,plain,
( complement(X1) = X2
| meet(X2,X1) != zero
| join(X1,X2) != one ),
inference(spm,[status(thm)],[c_0_49,c_0_15]) ).
cnf(c_0_56,plain,
( complement(X1) = meet(X2,X3)
| meet(X2,meet(X3,X1)) != zero
| join(X1,meet(X2,X3)) != one ),
inference(spm,[status(thm)],[c_0_49,c_0_45]) ).
cnf(c_0_57,hypothesis,
meet(b,meet(complement(meet(b,complement(a))),join(complement(b),meet(b,complement(a))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_26]) ).
cnf(c_0_58,plain,
meet(X1,meet(X2,complement(meet(X2,X1)))) = zero,
inference(spm,[status(thm)],[c_0_50,c_0_15]) ).
cnf(c_0_59,hypothesis,
join(complement(a),meet(b,join(meet(b,complement(a)),X1))) = join(complement(a),meet(b,X1)),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_60,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_36]),c_0_26]),c_0_23])]) ).
cnf(c_0_61,hypothesis,
complement(join(complement(b),meet(b,complement(a)))) = meet(b,complement(meet(b,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(spm,[status(thm)],[c_0_56,c_0_57]),c_0_19]),c_0_54]),c_0_23]),c_0_35]),c_0_26]),c_0_23])]) ).
cnf(c_0_62,plain,
( meet(X1,complement(meet(X1,X2))) = complement(X2)
| join(X2,meet(X1,complement(meet(X1,X2)))) != one ),
inference(spm,[status(thm)],[c_0_49,c_0_58]) ).
cnf(c_0_63,hypothesis,
join(complement(a),meet(b,complement(meet(b,complement(a))))) = one,
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_23]),c_0_35]),c_0_26]),c_0_27]),c_0_28]) ).
cnf(c_0_64,hypothesis,
complement(meet(b,complement(meet(b,complement(a))))) = join(complement(b),meet(b,complement(a))),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_65,hypothesis,
meet(b,complement(meet(b,complement(a)))) = a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_60]) ).
cnf(c_0_66,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
prove_distributivity ).
cnf(c_0_67,hypothesis,
join(complement(b),meet(b,complement(a))) = complement(a),
inference(rw,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_68,negated_conjecture,
join(complement(a),complement(b)) != complement(a),
inference(rw,[status(thm)],[c_0_66,c_0_26]) ).
cnf(c_0_69,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_67]),c_0_26]),c_0_68]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT228-1 : 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 : n011.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 20:55:17 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 68.14/39.67 % Version : CSE_E---1.7
% 68.14/39.67 % Problem : theBenchmark.p
% 68.14/39.67 % SZS status Unsatisfiable for theBenchmark.p
% 68.14/39.67 % SZS output start CNFRefutation
% See solution above
% 68.44/39.96 % Total time : 29.431s
%------------------------------------------------------------------------------