%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT245-1 : 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 : 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 : Tue May 5 04:37:44 PM UTC 2026
% Result : Unsatisfiable 44.48s 26.13s
% Output : CNFRefutation 44.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of clauses : 59 ( 57 unt; 0 nHn; 13 RR)
% Number of literals : 63 ( 62 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 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 : 93 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_distributivity_hypothesis,hypothesis,
meet(b,a) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity_hypothesis) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LAT001-0.ax',associativity_of_meet) ).
cnf(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption2) ).
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(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',idempotence_of_meet) ).
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(complement_meet,axiom,
meet(X1,complement(X1)) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',complement_meet) ).
cnf(equation_H59,axiom,
meet(X1,meet(join(X2,X3),join(X2,X4))) = meet(X1,join(X2,meet(join(X2,X4),join(X3,meet(X1,X2))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H59) ).
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(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,hypothesis,
meet(b,a) = a,
prove_distributivity_hypothesis ).
cnf(c_0_15,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_16,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_17,hypothesis,
meet(a,b) = a,
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_19,hypothesis,
meet(a,meet(b,X1)) = meet(a,X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_21,hypothesis,
meet(a,meet(X1,b)) = meet(a,X1),
inference(spm,[status(thm)],[c_0_19,c_0_15]) ).
cnf(c_0_22,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_23,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_24,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_25,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_26,hypothesis,
join(meet(X1,b),meet(a,X1)) = meet(X1,b),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,axiom,
meet(X1,complement(X1)) = zero,
complement_meet ).
cnf(c_0_29,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_16,c_0_24]) ).
cnf(c_0_30,plain,
join(X1,join(X2,meet(X3,join(X1,X2)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_25]) ).
cnf(c_0_31,hypothesis,
join(a,meet(b,join(X1,a))) = meet(b,join(X1,a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_15]),c_0_23]),c_0_15]) ).
cnf(c_0_32,hypothesis,
meet(a,complement(b)) = meet(a,zero),
inference(spm,[status(thm)],[c_0_19,c_0_28]) ).
cnf(c_0_33,plain,
meet(X1,zero) = zero,
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_34,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_16,c_0_22]) ).
cnf(c_0_35,plain,
meet(X1,meet(X2,complement(meet(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_28,c_0_16]) ).
cnf(c_0_36,hypothesis,
join(X1,meet(b,join(X1,a))) = join(X1,a),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_15]),c_0_16]) ).
cnf(c_0_38,axiom,
meet(X1,meet(join(X2,X3),join(X2,X4))) = meet(X1,join(X2,meet(join(X2,X4),join(X3,meet(X1,X2))))),
equation_H59 ).
cnf(c_0_39,hypothesis,
meet(a,complement(b)) = zero,
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_28]) ).
cnf(c_0_41,plain,
meet(X1,meet(X2,complement(meet(join(X1,X3),X2)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_33]) ).
cnf(c_0_42,hypothesis,
join(X1,meet(b,join(a,X1))) = join(a,X1),
inference(spm,[status(thm)],[c_0_36,c_0_23]) ).
cnf(c_0_43,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_37,c_0_27]) ).
cnf(c_0_44,hypothesis,
meet(a,meet(join(complement(b),X1),join(complement(b),X2))) = meet(a,join(complement(b),meet(join(complement(b),X2),X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_45,hypothesis,
meet(X1,meet(X2,complement(meet(join(a,X1),X2)))) = zero,
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_47,hypothesis,
meet(a,join(complement(b),meet(join(a,complement(b)),X1))) = meet(a,join(complement(b),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_23]),c_0_15]) ).
cnf(c_0_48,hypothesis,
meet(X1,complement(meet(join(a,X1),join(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_34,c_0_45]) ).
cnf(c_0_49,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_25,c_0_46]) ).
cnf(c_0_50,plain,
meet(join(X1,X2),join(X1,join(X2,X3))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_25]) ).
cnf(c_0_51,axiom,
join(X1,complement(X1)) = one,
complement_join ).
cnf(c_0_52,axiom,
( complement(X1) = X2
| meet(X1,X2) != zero
| join(X1,X2) != one ),
meet_join_complement ).
cnf(c_0_53,hypothesis,
meet(a,join(complement(b),complement(join(a,complement(b))))) = zero,
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_47,c_0_48]),c_0_40]),c_0_32]),c_0_33]),c_0_49]),c_0_25]),c_0_50]) ).
cnf(c_0_54,plain,
join(X1,join(X2,complement(join(X1,X2)))) = one,
inference(spm,[status(thm)],[c_0_51,c_0_25]) ).
cnf(c_0_55,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
prove_distributivity ).
cnf(c_0_56,hypothesis,
join(complement(b),complement(join(a,complement(b)))) = complement(a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54])]) ).
cnf(c_0_57,negated_conjecture,
join(complement(a),complement(b)) != complement(a),
inference(rw,[status(thm)],[c_0_55,c_0_23]) ).
cnf(c_0_58,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_56]),c_0_23]),c_0_57]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT245-1 : 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
% 0.14/0.33 % Computer : n022.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 20:55:36 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.35 % start to proof: theBenchmark
% 44.48/26.13 % Version : CSE_E---1.7
% 44.48/26.13 % Problem : theBenchmark.p
% 44.48/26.13 % SZS status Unsatisfiable for theBenchmark.p
% 44.48/26.13 % SZS output start CNFRefutation
% See solution above
% 44.66/26.32 % Total time : 19.407s
%------------------------------------------------------------------------------