%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT021-1 : 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 : 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 04:37:22 PM UTC 2026
% Result : Unsatisfiable 6.55s 4.59s
% Output : CNFRefutation 6.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of clauses : 60 ( 60 unt; 0 nHn; 3 RR)
% Number of literals : 60 ( 59 equ; 2 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 : 150 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(quasi_lattice1,axiom,
join(meet(X1,join(X2,X3)),meet(X1,X2)) = meet(X1,join(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT004-0.ax',quasi_lattice1) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT004-0.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/LAT004-0.ax',associativity_of_join) ).
cnf(idempotence_of_join,axiom,
join(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT004-0.ax',idempotence_of_join) ).
cnf(bowden,hypothesis,
join(join(X1,meet(X2,X3)),meet(join(X1,X2),X3)) = join(X1,meet(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bowden) ).
cnf(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT004-0.ax',idempotence_of_meet) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT004-0.ax',commutativity_of_meet) ).
cnf(quasi_lattice2,axiom,
meet(join(X1,meet(X2,X3)),join(X1,X2)) = join(X1,meet(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT004-0.ax',quasi_lattice2) ).
cnf(associativity_of_meet,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT004-0.ax',associativity_of_meet) ).
cnf(prove_distributivity,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity) ).
cnf(c_0_10,axiom,
join(meet(X1,join(X2,X3)),meet(X1,X2)) = meet(X1,join(X2,X3)),
quasi_lattice1 ).
cnf(c_0_11,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_12,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_13,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_14,hypothesis,
join(join(X1,meet(X2,X3)),meet(join(X1,X2),X3)) = join(X1,meet(X2,X3)),
bowden ).
cnf(c_0_15,plain,
join(meet(X1,X2),meet(X1,join(X2,X3))) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_17,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,hypothesis,
join(X1,join(meet(X2,X3),meet(join(X1,X2),X3))) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_19,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_20,plain,
join(X1,meet(X1,join(X1,X2))) = meet(X1,join(X1,X2)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_17,c_0_11]) ).
cnf(c_0_22,hypothesis,
join(X1,join(meet(X2,X3),meet(join(X2,X1),X3))) = join(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_18,c_0_11]) ).
cnf(c_0_23,plain,
join(meet(X1,X2),meet(X2,join(X1,X3))) = meet(X2,join(X1,X3)),
inference(spm,[status(thm)],[c_0_15,c_0_19]) ).
cnf(c_0_24,axiom,
meet(join(X1,meet(X2,X3)),join(X1,X2)) = join(X1,meet(X2,X3)),
quasi_lattice2 ).
cnf(c_0_25,plain,
join(X1,meet(X1,join(X2,X1))) = meet(X1,join(X2,X1)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,hypothesis,
join(X1,meet(X2,join(X3,X1))) = join(X1,meet(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_19]),c_0_23]) ).
cnf(c_0_27,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_28,plain,
meet(join(X1,X2),join(X1,meet(X2,X3))) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[c_0_24,c_0_19]) ).
cnf(c_0_29,plain,
meet(X1,join(X2,X1)) = join(X1,meet(X2,X1)),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(spm,[status(thm)],[c_0_19,c_0_27]) ).
cnf(c_0_31,plain,
meet(X1,join(X1,meet(X1,X2))) = join(X1,meet(X1,X2)),
inference(spm,[status(thm)],[c_0_28,c_0_13]) ).
cnf(c_0_32,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_19]),c_0_27]) ).
cnf(c_0_33,plain,
meet(join(X1,meet(X2,X1)),X3) = meet(X1,meet(join(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_27,c_0_29]) ).
cnf(c_0_34,hypothesis,
join(X1,join(meet(X2,X3),meet(join(X1,X3),X2))) = join(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_35,plain,
join(meet(X1,X2),meet(X1,join(X3,X2))) = meet(X1,join(X3,X2)),
inference(spm,[status(thm)],[c_0_15,c_0_11]) ).
cnf(c_0_36,plain,
meet(X1,join(X2,meet(X2,X1))) = meet(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_13]),c_0_11]),c_0_30]),c_0_19]),c_0_31]) ).
cnf(c_0_37,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_27,c_0_16]) ).
cnf(c_0_38,plain,
meet(X1,meet(join(X1,meet(X1,X2)),join(X2,X3))) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_15]),c_0_11]),c_0_32]) ).
cnf(c_0_39,plain,
meet(join(X1,meet(X1,X2)),X3) = meet(X1,meet(join(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_33,c_0_19]) ).
cnf(c_0_40,hypothesis,
join(X1,meet(X2,join(X1,X3))) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_19]),c_0_35]) ).
cnf(c_0_41,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_42,plain,
join(meet(X1,X2),meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_15,c_0_36]) ).
cnf(c_0_43,plain,
meet(X1,meet(X2,meet(X3,X1))) = meet(X3,meet(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_37]),c_0_27]) ).
cnf(c_0_44,plain,
meet(X1,meet(join(X2,X1),join(X2,X3))) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39]),c_0_37]) ).
cnf(c_0_45,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_30,c_0_16]) ).
cnf(c_0_46,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X2,X1)),
inference(spm,[status(thm)],[c_0_30,c_0_19]) ).
cnf(c_0_47,plain,
meet(join(X1,X2),join(X1,meet(X3,X2))) = join(X1,meet(X3,X2)),
inference(spm,[status(thm)],[c_0_28,c_0_19]) ).
cnf(c_0_48,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_11]),c_0_12]) ).
cnf(c_0_49,plain,
meet(X1,join(meet(X1,X2),X3)) = join(meet(X1,X2),meet(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_37]),c_0_40]) ).
cnf(c_0_50,plain,
join(X1,join(X2,X3)) = join(X3,join(X2,X1)),
inference(spm,[status(thm)],[c_0_41,c_0_11]) ).
cnf(c_0_51,plain,
join(meet(X1,X2),join(meet(X2,X1),X3)) = join(meet(X2,X1),X3),
inference(spm,[status(thm)],[c_0_12,c_0_42]) ).
cnf(c_0_52,plain,
meet(X1,meet(join(X2,X3),join(X2,X1))) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46]) ).
cnf(c_0_53,plain,
meet(join(X1,join(X2,X3)),join(X2,meet(X4,join(X1,X3)))) = join(X2,meet(X4,join(X1,X3))),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,plain,
meet(X1,join(X2,meet(X1,X3))) = join(meet(X1,X3),meet(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_21]),c_0_26]) ).
cnf(c_0_55,plain,
join(meet(X1,X2),X3) = join(X3,meet(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_42]) ).
cnf(c_0_56,plain,
join(meet(X1,X2),meet(X3,X1)) = meet(X1,join(X3,X2)),
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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_40]),c_0_27]),c_0_47]),c_0_54]),c_0_17]),c_0_27]),c_0_16]) ).
cnf(c_0_57,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
prove_distributivity ).
cnf(c_0_58,plain,
join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_59,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT021-1 : 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
% 0.15/0.34 % Computer : n022.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Mon May 4 20:46:21 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.20/0.35 % start to proof: theBenchmark
% 6.55/4.59 % Version : CSE_E---1.7
% 6.55/4.59 % Problem : theBenchmark.p
% 6.55/4.59 % SZS status Unsatisfiable for theBenchmark.p
% 6.55/4.59 % SZS output start CNFRefutation
% See solution above
% 6.65/4.62 % Total time : 3.372s
%------------------------------------------------------------------------------