%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT249-1 : 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 : n015.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 04:37:45 PM UTC 2026
% Result : Unsatisfiable 1.83s 1.86s
% Output : CNFRefutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of clauses : 41 ( 39 unt; 0 nHn; 12 RR)
% Number of literals : 45 ( 44 equ; 7 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 : 56 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_distributivity_hypothesis,hypothesis,
meet(b,a) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity_hypothesis) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox/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/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(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(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).
cnf(complement_meet,axiom,
meet(X1,complement(X1)) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',complement_meet) ).
cnf(equation_H64,axiom,
meet(X1,join(X2,X3)) = meet(X1,join(X2,meet(X1,join(X3,meet(X1,join(X2,meet(X1,X3))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H64) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LAT001-0.ax',associativity_of_join) ).
cnf(prove_distributivity,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity) ).
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(c_0_13,hypothesis,
meet(b,a) = a,
prove_distributivity_hypothesis ).
cnf(c_0_14,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_15,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_16,hypothesis,
meet(a,b) = a,
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_18,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_19,axiom,
join(X1,complement(X1)) = one,
complement_join ).
cnf(c_0_20,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_21,axiom,
meet(X1,complement(X1)) = zero,
complement_meet ).
cnf(c_0_22,hypothesis,
meet(a,meet(b,X1)) = meet(a,X1),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_23,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_24,plain,
meet(X1,one) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,axiom,
meet(X1,join(X2,X3)) = meet(X1,join(X2,meet(X1,join(X3,meet(X1,join(X2,meet(X1,X3))))))),
equation_H64 ).
cnf(c_0_26,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,hypothesis,
meet(a,complement(b)) = meet(a,zero),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_28,plain,
meet(X1,zero) = zero,
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_29,plain,
meet(one,X1) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_14]) ).
cnf(c_0_30,plain,
meet(X1,join(X2,meet(X1,join(complement(X1),meet(X1,X2))))) = meet(X1,join(X2,complement(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_21]),c_0_26]) ).
cnf(c_0_31,hypothesis,
meet(a,complement(b)) = zero,
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_33,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_34,plain,
join(one,X1) = one,
inference(spm,[status(thm)],[c_0_18,c_0_29]) ).
cnf(c_0_35,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
prove_distributivity ).
cnf(c_0_36,axiom,
( complement(X1) = X2
| meet(X1,X2) != zero
| join(X1,X2) != one ),
meet_join_complement ).
cnf(c_0_37,hypothesis,
meet(a,join(complement(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_30,c_0_31]),c_0_26]),c_0_21]),c_0_26]),c_0_27]),c_0_28]),c_0_32]) ).
cnf(c_0_38,plain,
join(X1,join(complement(X1),X2)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_19]),c_0_34]) ).
cnf(c_0_39,negated_conjecture,
join(complement(a),complement(b)) != complement(a),
inference(rw,[status(thm)],[c_0_35,c_0_32]) ).
cnf(c_0_40,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]),c_0_39]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LAT249-1 : TPTP v9.2.1. Released v3.1.0.
% 0.00/0.11 % 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
% 0.16/0.32 % Computer : n015.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Mon May 4 20:55:31 EDT 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.33 % start to proof: theBenchmark
% 1.83/1.86 % Version : CSE_E---1.7
% 1.83/1.86 % Problem : theBenchmark.p
% 1.83/1.86 % SZS status Unsatisfiable for theBenchmark.p
% 1.83/1.86 % SZS output start CNFRefutation
% See solution above
% 1.83/1.86 % Total time : 1.371s
%------------------------------------------------------------------------------