%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT237-1 : 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 : n002.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 1.91s 1.91s
% Output : CNFRefutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of clauses : 47 ( 45 unt; 0 nHn; 11 RR)
% Number of literals : 51 ( 50 equ; 7 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 : 72 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
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(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption1) ).
cnf(complement_meet,axiom,
meet(X1,complement(X1)) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',complement_meet) ).
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(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_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_join,axiom,
join(X1,complement(X1)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',complement_join) ).
cnf(equation_H40,axiom,
meet(X1,join(X2,meet(X3,join(X1,X4)))) = meet(X1,join(X2,meet(X3,join(X4,meet(X3,join(X1,X2)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H40) ).
cnf(prove_distributivity,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity) ).
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(c_0_13,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_14,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_15,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_16,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,axiom,
meet(X1,complement(X1)) = zero,
complement_meet ).
cnf(c_0_18,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
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(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_22,plain,
meet(X1,zero) = zero,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,hypothesis,
meet(a,b) = a,
inference(rw,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_25,plain,
meet(X1,complement(join(X1,X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_17]),c_0_22]) ).
cnf(c_0_26,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_27,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_28,hypothesis,
join(b,a) = b,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,axiom,
join(X1,complement(X1)) = one,
complement_join ).
cnf(c_0_30,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,hypothesis,
join(b,join(a,X1)) = join(b,X1),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
meet(X1,one) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_29]) ).
cnf(c_0_33,axiom,
meet(X1,join(X2,meet(X3,join(X1,X4)))) = meet(X1,join(X2,meet(X3,join(X4,meet(X3,join(X1,X2)))))),
equation_H40 ).
cnf(c_0_34,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_26]) ).
cnf(c_0_35,hypothesis,
meet(join(a,X1),complement(join(b,X1))) = zero,
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
meet(one,X1) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_19]) ).
cnf(c_0_37,plain,
meet(X1,join(complement(X1),meet(X2,join(X1,X3)))) = meet(X1,join(complement(X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_29]),c_0_32]),c_0_34]) ).
cnf(c_0_38,hypothesis,
meet(complement(b),join(a,meet(b,X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_18]),c_0_19]) ).
cnf(c_0_39,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_40,plain,
join(one,X1) = one,
inference(spm,[status(thm)],[c_0_15,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
prove_distributivity ).
cnf(c_0_42,axiom,
( complement(X1) = X2
| meet(X1,X2) != zero
| join(X1,X2) != one ),
meet_join_complement ).
cnf(c_0_43,hypothesis,
meet(a,join(complement(a),complement(b))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_17]) ).
cnf(c_0_44,plain,
join(X1,join(complement(X1),X2)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_29]),c_0_40]) ).
cnf(c_0_45,negated_conjecture,
join(complement(a),complement(b)) != complement(a),
inference(rw,[status(thm)],[c_0_41,c_0_26]) ).
cnf(c_0_46,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]),c_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT237-1 : 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 : n002.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 20:55:46 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.91/1.91 % Version : CSE_E---1.7
% 1.91/1.91 % Problem : theBenchmark.p
% 1.91/1.91 % SZS status Unsatisfiable for theBenchmark.p
% 1.91/1.91 % SZS output start CNFRefutation
% See solution above
% 1.91/1.92 % Total time : 1.371s
%------------------------------------------------------------------------------