%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT019-1 : TPTP v9.2.1. Released v2.2.0.
% 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 : n031.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 1.58s 1.84s
% Output : CNFRefutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of clauses : 42 ( 42 unt; 0 nHn; 4 RR)
% Number of literals : 42 ( 41 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 100 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_of_meet,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',associativity_of_meet) ).
cnf(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',idempotence_of_meet) ).
cnf(distributivity_law,hypothesis,
meet(X1,join(X2,X3)) = join(meet(X1,X2),meet(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity_law) ).
cnf(quasi_lattice2,axiom,
meet(join(X1,meet(X2,X3)),join(X1,X2)) = join(X1,meet(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',quasi_lattice2) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',commutativity_of_meet) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LAT004-0.ax',associativity_of_join) ).
cnf(idempotence_of_join,axiom,
join(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',idempotence_of_join) ).
cnf(prove_distributivity_law_dual,negated_conjecture,
join(a,meet(b,c)) != meet(join(a,b),join(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity_law_dual) ).
cnf(c_0_9,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_10,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_11,hypothesis,
meet(X1,join(X2,X3)) = join(meet(X1,X2),meet(X1,X3)),
distributivity_law ).
cnf(c_0_12,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,axiom,
meet(join(X1,meet(X2,X3)),join(X1,X2)) = join(X1,meet(X2,X3)),
quasi_lattice2 ).
cnf(c_0_14,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_15,hypothesis,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_11]) ).
cnf(c_0_16,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_17,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_18,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_19,plain,
meet(join(X1,X2),join(X1,meet(X2,X3))) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,hypothesis,
meet(X1,join(X2,meet(X3,X1))) = meet(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_21,hypothesis,
meet(X1,join(X2,X1)) = join(X1,meet(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_10]),c_0_16]) ).
cnf(c_0_22,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_16]),c_0_17]) ).
cnf(c_0_24,hypothesis,
join(X1,join(X2,meet(X2,X1))) = join(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_10]),c_0_21]) ).
cnf(c_0_25,plain,
meet(join(X1,X2),join(meet(X2,X3),X1)) = join(meet(X2,X3),X1),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_26,hypothesis,
meet(X1,join(meet(X1,X2),X3)) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_11]) ).
cnf(c_0_27,plain,
meet(join(X1,X2),join(X1,X3)) = join(X1,meet(join(X1,X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_22]),c_0_15]) ).
cnf(c_0_28,hypothesis,
join(X1,join(X2,meet(X1,X2))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
meet(join(X1,X2),join(X3,X1)) = join(X1,meet(join(X1,X2),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_22]),c_0_26]),c_0_16]) ).
cnf(c_0_30,hypothesis,
meet(join(X1,X2),join(X2,X3)) = join(X2,meet(join(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(spm,[status(thm)],[c_0_14,c_0_9]) ).
cnf(c_0_32,plain,
join(X1,meet(join(X2,X1),X3)) = join(X1,meet(join(X1,X3),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_29]),c_0_30]) ).
cnf(c_0_33,plain,
meet(join(X1,X2),join(X1,meet(X3,meet(X2,X4)))) = join(X1,meet(X3,meet(X2,X4))),
inference(spm,[status(thm)],[c_0_19,c_0_31]) ).
cnf(c_0_34,plain,
join(X1,meet(join(X2,X1),X3)) = join(X1,meet(X2,join(X1,X3))),
inference(spm,[status(thm)],[c_0_32,c_0_14]) ).
cnf(c_0_35,plain,
join(X1,meet(join(X1,X2),meet(X3,meet(X2,X4)))) = join(X1,meet(X3,meet(X2,X4))),
inference(rw,[status(thm)],[c_0_33,c_0_27]) ).
cnf(c_0_36,plain,
join(X1,meet(join(X1,X2),X3)) = join(X1,meet(X2,join(X1,X3))),
inference(spm,[status(thm)],[c_0_34,c_0_16]) ).
cnf(c_0_37,negated_conjecture,
join(a,meet(b,c)) != meet(join(a,b),join(a,c)),
prove_distributivity_law_dual ).
cnf(c_0_38,plain,
join(X1,meet(X2,join(X1,meet(X3,meet(X2,X4))))) = join(X1,meet(X3,meet(X2,X4))),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
join(a,meet(c,join(a,b))) != join(a,meet(b,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_27]),c_0_14]) ).
cnf(c_0_40,plain,
join(X1,meet(X2,join(X1,X3))) = join(X1,meet(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_10]),c_0_20]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT019-1 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.12 % 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
% 0.14/0.33 % Computer : n031.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 20:48:38 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.58/1.84 % Version : CSE_E---1.7
% 1.58/1.84 % Problem : theBenchmark.p
% 1.58/1.84 % SZS status Unsatisfiable for theBenchmark.p
% 1.58/1.84 % SZS output start CNFRefutation
% See solution above
% 1.58/1.85 % Total time : 1.370s
%------------------------------------------------------------------------------