%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT026-1 : TPTP v9.2.1. Released v2.2.0.
% 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 : n009.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 04:37:22 PM UTC 2026
% Result : Unsatisfiable 11.11s 7.33s
% Output : CNFRefutation 11.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of clauses : 44 ( 44 unt; 0 nHn; 4 RR)
% Number of literals : 44 ( 43 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 110 ( 32 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(wal_2,axiom,
join(join(meet(X1,X2),meet(X3,X2)),X2) = X2,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT005-0.ax',wal_2) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT005-0.ax',commutativity_of_join) ).
cnf(absorbtion,hypothesis,
meet(X1,join(X2,join(X1,X3))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorbtion) ).
cnf(idempotence_of_join,axiom,
join(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT005-0.ax',idempotence_of_join) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT005-0.ax',commutativity_of_meet) ).
cnf(wal_1,axiom,
meet(meet(join(X1,X2),join(X3,X2)),X2) = X2,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT005-0.ax',wal_1) ).
cnf(prove_associativity_of_meet,negated_conjecture,
meet(meet(a,b),c) != meet(a,meet(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity_of_meet) ).
cnf(c_0_7,axiom,
join(join(meet(X1,X2),meet(X3,X2)),X2) = X2,
wal_2 ).
cnf(c_0_8,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_9,hypothesis,
meet(X1,join(X2,join(X1,X3))) = X1,
absorbtion ).
cnf(c_0_10,plain,
join(X1,join(meet(X2,X1),meet(X3,X1))) = X1,
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_12,hypothesis,
meet(X1,join(X2,join(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_13,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,hypothesis,
meet(meet(X1,X2),join(X3,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_16,hypothesis,
meet(X1,meet(X2,meet(X3,X1))) = meet(X2,meet(X3,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_13]),c_0_15]) ).
cnf(c_0_17,axiom,
meet(meet(join(X1,X2),join(X3,X2)),X2) = X2,
wal_1 ).
cnf(c_0_18,hypothesis,
meet(X1,meet(meet(X2,X1),X3)) = meet(meet(X2,X1),X3),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_19,plain,
meet(X1,meet(join(X2,X1),join(X3,X1))) = X1,
inference(rw,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_20,plain,
join(X1,meet(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_21,hypothesis,
meet(X1,meet(meet(X1,X2),X3)) = meet(meet(X1,X2),X3),
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_22,plain,
meet(meet(X1,X2),meet(X2,join(X3,meet(X1,X2)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_13]) ).
cnf(c_0_23,hypothesis,
join(X1,meet(meet(X2,X1),X3)) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_24,hypothesis,
join(X1,meet(meet(X1,X2),X3)) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,hypothesis,
meet(meet(X1,X2),meet(meet(X3,X2),X1)) = meet(meet(X3,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_15]) ).
cnf(c_0_26,hypothesis,
meet(meet(X1,X2),meet(meet(X2,X3),X1)) = meet(meet(X2,X3),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_24]),c_0_15]) ).
cnf(c_0_27,plain,
meet(meet(X1,X2),meet(X1,join(X3,meet(X1,X2)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_28,hypothesis,
join(join(X1,X2),meet(X3,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_29,hypothesis,
join(meet(X1,X2),meet(meet(X3,X2),X1)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_25]) ).
cnf(c_0_30,hypothesis,
meet(meet(X1,X2),meet(X1,meet(X2,X3))) = meet(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_26,c_0_15]) ).
cnf(c_0_31,hypothesis,
meet(meet(X1,X2),meet(X1,join(X3,X2))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,hypothesis,
meet(meet(X1,X2),meet(meet(X3,X1),X2)) = meet(meet(X3,X1),X2),
inference(spm,[status(thm)],[c_0_25,c_0_15]) ).
cnf(c_0_33,hypothesis,
meet(meet(X1,X2),meet(X3,X2)) = meet(meet(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_29]),c_0_30]) ).
cnf(c_0_34,hypothesis,
meet(meet(X1,X2),meet(join(X3,X2),X1)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_31,c_0_15]) ).
cnf(c_0_35,hypothesis,
meet(meet(X1,X2),meet(X3,X1)) = meet(meet(X3,X1),X2),
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,hypothesis,
meet(meet(X1,X2),meet(meet(X1,X3),X2)) = meet(meet(X1,X3),X2),
inference(spm,[status(thm)],[c_0_26,c_0_15]) ).
cnf(c_0_37,hypothesis,
meet(X1,meet(join(X2,X1),X3)) = meet(X3,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_15]) ).
cnf(c_0_38,hypothesis,
meet(meet(X1,X2),meet(X1,X3)) = meet(meet(X1,X3),X2),
inference(rw,[status(thm)],[c_0_36,c_0_33]) ).
cnf(c_0_39,negated_conjecture,
meet(meet(a,b),c) != meet(a,meet(b,c)),
prove_associativity_of_meet ).
cnf(c_0_40,hypothesis,
meet(meet(X1,X2),X3) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_20]),c_0_38]) ).
cnf(c_0_41,negated_conjecture,
meet(c,meet(a,b)) != meet(a,meet(b,c)),
inference(rw,[status(thm)],[c_0_39,c_0_15]) ).
cnf(c_0_42,hypothesis,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_40]),c_0_40]),c_0_16]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT026-1 : TPTP v9.2.1. Released v2.2.0.
% 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 : n009.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 20:47:26 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.35 % start to proof: theBenchmark
% 11.11/7.33 % Version : CSE_E---1.7
% 11.11/7.33 % Problem : theBenchmark.p
% 11.11/7.33 % SZS status Unsatisfiable for theBenchmark.p
% 11.11/7.33 % SZS output start CNFRefutation
% See solution above
% 11.11/7.38 % Total time : 5.369s
%------------------------------------------------------------------------------