%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT236-1 : 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 : n024.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 1.80s 1.80s
% Output : CNFRefutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of clauses : 44 ( 42 unt; 0 nHn; 12 RR)
% Number of literals : 48 ( 47 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 : 63 ( 8 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(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(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(equation_H39,axiom,
meet(X1,join(X2,meet(X3,join(X1,X4)))) = meet(X1,join(X2,meet(X3,join(X4,meet(X1,X3))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H39) ).
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(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_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,
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_15,c_0_16]) ).
cnf(c_0_20,axiom,
meet(X1,complement(X1)) = zero,
complement_meet ).
cnf(c_0_21,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_22,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_23,axiom,
join(X1,complement(X1)) = one,
complement_join ).
cnf(c_0_24,axiom,
meet(X1,join(X2,meet(X3,join(X1,X4)))) = meet(X1,join(X2,meet(X3,join(X4,meet(X1,X3))))),
equation_H39 ).
cnf(c_0_25,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_14]) ).
cnf(c_0_26,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_27,hypothesis,
meet(a,complement(b)) = meet(a,zero),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_28,plain,
meet(X1,zero) = zero,
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_29,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_30,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_31,plain,
meet(X1,one) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_32,plain,
meet(X1,join(X2,join(meet(X1,X3),meet(X3,join(X1,X2))))) = meet(X1,join(X2,meet(X1,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_33,hypothesis,
meet(a,complement(b)) = zero,
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
meet(one,X1) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_14]) ).
cnf(c_0_36,hypothesis,
meet(a,join(X1,meet(complement(b),join(a,X1)))) = meet(a,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_29]) ).
cnf(c_0_37,plain,
join(one,X1) = one,
inference(spm,[status(thm)],[c_0_22,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
prove_distributivity ).
cnf(c_0_39,axiom,
( complement(X1) = X2
| meet(X1,X2) != zero
| join(X1,X2) != one ),
meet_join_complement ).
cnf(c_0_40,hypothesis,
meet(a,join(complement(a),complement(b))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_23]),c_0_31]),c_0_20]) ).
cnf(c_0_41,plain,
join(X1,join(complement(X1),X2)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_23]),c_0_37]) ).
cnf(c_0_42,negated_conjecture,
join(complement(a),complement(b)) != complement(a),
inference(rw,[status(thm)],[c_0_38,c_0_30]) ).
cnf(c_0_43,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : LAT236-1 : TPTP v9.2.1. Released v3.1.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 15:56:26 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 1.80/1.80 % Version : CSE_E---1.7
% 1.80/1.80 % Problem : theBenchmark.p
% 1.80/1.80 % SZS status Unsatisfiable for theBenchmark.p
% 1.80/1.80 % SZS output start CNFRefutation
% See solution above
% 1.80/1.81 % Total time : 1.361s
%------------------------------------------------------------------------------