%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT002-1 : TPTP v9.2.1. Released v1.0.0.
% 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 : 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 04:37:17 PM UTC 2026
% Result : Unsatisfiable 35.40s 23.33s
% Output : CNFRefutation 35.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of clauses : 76 ( 65 unt; 0 nHn; 24 RR)
% Number of literals : 90 ( 74 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 141 ( 19 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption1) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
cnf(modular,axiom,
( meet(X2,join(X1,X3)) = join(X1,meet(X3,X2))
| meet(X1,X2) != X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-1.ax',modular) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LAT001-0.ax',associativity_of_meet) ).
cnf(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',idempotence_of_meet) ).
cnf(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption2) ).
cnf(associativity_of_join,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',associativity_of_join) ).
cnf(complement_of_a_join_b,hypothesis,
complement(r1,join(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_a_join_b) ).
cnf(complement_meet,axiom,
( meet(X1,X2) = n0
| ~ complement(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-2.ax',complement_meet) ).
cnf(x_join_0,axiom,
join(X1,n0) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-1.ax',x_join_0) ).
cnf(complement_of_a_meet_b,hypothesis,
complement(r2,meet(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_a_meet_b) ).
cnf(meet_join_complement,axiom,
( complement(X1,X2)
| meet(X1,X2) != n0
| join(X1,X2) != n1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-2.ax',meet_join_complement) ).
cnf(complement_join,axiom,
( join(X1,X2) = n1
| ~ complement(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-2.ax',complement_join) ).
cnf(prove_complememt_exists,negated_conjecture,
~ complement(a,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_complememt_exists) ).
cnf(x_join_1,axiom,
join(X1,n1) = n1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-1.ax',x_join_1) ).
cnf(x_meet_1,axiom,
meet(X1,n1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-1.ax',x_meet_1) ).
cnf(c_0_17,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_18,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_19,axiom,
( meet(X2,join(X1,X3)) = join(X1,meet(X3,X2))
| meet(X1,X2) != X1 ),
modular ).
cnf(c_0_20,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_21,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_22,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_23,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_25,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_26,hypothesis,
complement(r1,join(a,b)),
complement_of_a_join_b ).
cnf(c_0_27,plain,
( join(X1,meet(X2,X3)) = meet(X3,join(X1,X2))
| meet(X3,X1) != X1 ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_28,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,plain,
meet(X1,meet(X2,X1)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_21]) ).
cnf(c_0_30,plain,
meet(X1,X2) = meet(X2,X1),
c_0_20 ).
cnf(c_0_31,plain,
join(X1,X2) = join(X2,X1),
c_0_18 ).
cnf(c_0_32,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
c_0_21 ).
cnf(c_0_33,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
c_0_25 ).
cnf(c_0_34,axiom,
( meet(X1,X2) = n0
| ~ complement(X1,X2) ),
complement_meet ).
cnf(c_0_35,hypothesis,
complement(r1,join(b,a)),
inference(rw,[status(thm)],[c_0_26,c_0_18]) ).
cnf(c_0_36,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_20]) ).
cnf(c_0_37,plain,
meet(X1,meet(X2,join(X3,meet(X1,X2)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_23]) ).
cnf(c_0_38,plain,
join(meet(X1,X2),meet(X3,X1)) = meet(X1,join(meet(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_39,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_40,plain,
join(meet(X1,X2),meet(X3,X2)) = meet(X2,join(meet(X1,X2),X3)),
inference(ar,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_29]),c_0_30,c_0_31,c_0_32,c_0_33]) ).
cnf(c_0_41,plain,
meet(X1,join(X2,join(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_25]) ).
cnf(c_0_42,plain,
join(X1,meet(X2,join(X1,X3))) = meet(join(X1,X3),join(X1,X2)),
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_43,hypothesis,
meet(r1,join(b,a)) = n0,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_44,axiom,
join(X1,n0) = X1,
x_join_0 ).
cnf(c_0_45,plain,
meet(X1,join(X2,meet(X1,join(X3,meet(X2,X1))))) = meet(X1,join(X3,meet(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_18]) ).
cnf(c_0_46,plain,
join(X1,meet(X2,join(meet(X1,X2),X3))) = join(X1,meet(X3,X2)),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_21]) ).
cnf(c_0_48,hypothesis,
complement(r2,meet(a,b)),
complement_of_a_meet_b ).
cnf(c_0_49,axiom,
( complement(X1,X2)
| meet(X1,X2) != n0
| join(X1,X2) != n1 ),
meet_join_complement ).
cnf(c_0_50,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_51,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_24]),c_0_21]) ).
cnf(c_0_52,hypothesis,
meet(join(r1,b),join(b,a)) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_18]),c_0_20]) ).
cnf(c_0_53,plain,
join(meet(X1,X2),meet(X2,X3)) = meet(X2,join(meet(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_40,c_0_20]) ).
cnf(c_0_54,plain,
meet(X1,join(meet(X2,X1),X3)) = meet(X1,join(X2,meet(X3,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_18]),c_0_46]) ).
cnf(c_0_55,plain,
join(X1,join(X2,meet(X3,X1))) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_17]),c_0_25]) ).
cnf(c_0_56,axiom,
( join(X1,X2) = n1
| ~ complement(X1,X2) ),
complement_join ).
cnf(c_0_57,hypothesis,
complement(r2,meet(b,a)),
inference(rw,[status(thm)],[c_0_48,c_0_20]) ).
cnf(c_0_58,plain,
( complement(X1,meet(X2,X3))
| meet(X3,meet(X1,X2)) != n0
| join(X1,meet(X2,X3)) != n1 ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_59,hypothesis,
meet(a,join(r1,b)) = meet(b,a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_20]) ).
cnf(c_0_60,negated_conjecture,
~ complement(a,X1),
prove_complememt_exists ).
cnf(c_0_61,plain,
join(meet(X1,X2),meet(X2,X3)) = meet(X2,join(X1,meet(X3,X2))),
inference(rw,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_62,plain,
join(meet(X1,join(X2,X3)),join(X4,meet(X3,X1))) = join(meet(X1,join(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_55,c_0_51]) ).
cnf(c_0_63,hypothesis,
join(r2,meet(b,a)) = n1,
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_64,axiom,
join(X1,n1) = n1,
x_join_1 ).
cnf(c_0_65,hypothesis,
( join(a,meet(join(r1,b),X1)) != n1
| meet(X1,meet(b,a)) != n0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]) ).
cnf(c_0_66,hypothesis,
meet(r2,meet(b,a)) = n0,
inference(spm,[status(thm)],[c_0_34,c_0_57]) ).
cnf(c_0_67,plain,
join(X1,meet(X2,join(X3,meet(X1,X2)))) = join(X1,meet(X3,X2)),
inference(spm,[status(thm)],[c_0_55,c_0_61]) ).
cnf(c_0_68,hypothesis,
join(r2,meet(a,join(X1,b))) = n1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]),c_0_18]) ).
cnf(c_0_69,axiom,
meet(X1,n1) = X1,
x_meet_1 ).
cnf(c_0_70,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[c_0_18,c_0_25]) ).
cnf(c_0_71,hypothesis,
join(a,meet(r2,join(r1,b))) != n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_20]) ).
cnf(c_0_72,hypothesis,
join(a,meet(r2,join(X1,b))) = join(b,join(a,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]),c_0_70]) ).
cnf(c_0_73,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_18]),c_0_25]) ).
cnf(c_0_74,hypothesis,
join(r1,join(b,a)) = n1,
inference(spm,[status(thm)],[c_0_56,c_0_35]) ).
cnf(c_0_75,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72]),c_0_18]),c_0_73]),c_0_74])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LAT002-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n015.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 20:45:46 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 35.40/23.33 % Version : CSE_E---1.7
% 35.40/23.33 % Problem : theBenchmark.p
% 35.40/23.33 % SZS status Unsatisfiable for theBenchmark.p
% 35.40/23.33 % SZS output start CNFRefutation
% See solution above
% 35.50/23.44 % Total time : 18.405s
%------------------------------------------------------------------------------