%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT210-1 : TPTP v9.2.1. Released v3.1.0.
% 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 : n005.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 04:37:40 PM UTC 2026
% Result : Unsatisfiable 3.39s 3.09s
% Output : CNFRefutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 12
% Syntax : Number of clauses : 85 ( 82 unt; 0 nHn; 7 RR)
% Number of literals : 91 ( 90 equ; 8 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 167 ( 24 sgn)
% Comments :
%------------------------------------------------------------------------------
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(complement_meet,axiom,
meet(X1,complement(X1)) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',complement_meet) ).
cnf(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption2) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
cnf(complement_join,axiom,
join(X1,complement(X1)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',complement_join) ).
cnf(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption1) ).
cnf(equation_H68,axiom,
meet(X1,join(X2,X3)) = meet(X1,join(X2,meet(X1,join(X3,meet(X1,X2))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H68) ).
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(meet_join_complement,axiom,
( complement(X1) = X2
| meet(X1,X2) != zero
| join(X1,X2) != one ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',meet_join_complement) ).
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_12,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_13,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_14,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,axiom,
meet(X1,complement(X1)) = zero,
complement_meet ).
cnf(c_0_16,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_17,plain,
meet(X1,zero) = zero,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_19,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_20,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_21,plain,
meet(X1,meet(X2,complement(meet(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_15,c_0_12]) ).
cnf(c_0_22,plain,
meet(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,axiom,
join(X1,complement(X1)) = one,
complement_join ).
cnf(c_0_24,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_26,plain,
meet(X1,meet(X2,complement(meet(X2,X1)))) = zero,
inference(spm,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_27,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_15]),c_0_22]) ).
cnf(c_0_28,plain,
complement(zero) = one,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
meet(X1,one) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_30,axiom,
meet(X1,join(X2,X3)) = meet(X1,join(X2,meet(X1,join(X3,meet(X1,X2))))),
equation_H68 ).
cnf(c_0_31,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_29]),c_0_12]) ).
cnf(c_0_32,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_33,plain,
meet(one,X1) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_18]) ).
cnf(c_0_34,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(complement(X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_15]),c_0_19]) ).
cnf(c_0_35,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_18]) ).
cnf(c_0_36,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_37,plain,
join(one,X1) = one,
inference(spm,[status(thm)],[c_0_25,c_0_33]) ).
cnf(c_0_38,axiom,
( complement(X1) = X2
| meet(X1,X2) != zero
| join(X1,X2) != one ),
meet_join_complement ).
cnf(c_0_39,plain,
meet(X1,join(complement(X1),complement(join(X2,X1)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_19]),c_0_15]) ).
cnf(c_0_40,plain,
join(X1,join(complement(X1),X2)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_23]),c_0_37]) ).
cnf(c_0_41,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).
cnf(c_0_42,plain,
meet(X1,join(complement(X1),meet(X2,complement(meet(X1,X2))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_21]),c_0_19]),c_0_15]) ).
cnf(c_0_43,plain,
( complement(X1) = X2
| meet(X2,X1) != zero
| join(X1,X2) != one ),
inference(spm,[status(thm)],[c_0_38,c_0_18]) ).
cnf(c_0_44,plain,
meet(complement(X1),complement(join(X2,X1))) = complement(join(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_41]),c_0_18]) ).
cnf(c_0_45,plain,
join(complement(X1),meet(X2,complement(meet(X1,X2)))) = complement(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_42]),c_0_40])]) ).
cnf(c_0_46,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_15]),c_0_20]),c_0_23])]) ).
cnf(c_0_47,plain,
meet(complement(X1),complement(meet(X1,X2))) = complement(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_16]),c_0_18]) ).
cnf(c_0_48,plain,
join(X1,meet(X2,complement(meet(complement(X1),X2)))) = X1,
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_49,plain,
meet(X1,complement(meet(complement(X1),X2))) = X1,
inference(spm,[status(thm)],[c_0_47,c_0_46]) ).
cnf(c_0_50,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_51,plain,
join(X1,meet(X2,complement(meet(X2,complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_26]),c_0_28]),c_0_12]),c_0_29]) ).
cnf(c_0_52,plain,
meet(X1,complement(meet(X2,complement(X1)))) = X1,
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_53,plain,
meet(X1,complement(join(X1,X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_25]),c_0_18]) ).
cnf(c_0_54,plain,
meet(X1,complement(meet(X1,complement(X2)))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_51]),c_0_12]),c_0_18]),c_0_52]) ).
cnf(c_0_55,plain,
join(complement(X1),complement(meet(X1,X2))) = complement(meet(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_16]),c_0_20]) ).
cnf(c_0_56,plain,
meet(X1,join(complement(X1),complement(join(X1,X2)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_53]),c_0_19]),c_0_15]) ).
cnf(c_0_57,plain,
meet(X1,join(complement(X1),X2)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_54]),c_0_34]),c_0_55]),c_0_54]) ).
cnf(c_0_58,plain,
join(complement(X1),complement(join(X1,X2))) = complement(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_56]),c_0_40])]) ).
cnf(c_0_59,plain,
meet(X1,complement(meet(X1,X2))) = meet(X1,complement(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_54]),c_0_14]) ).
cnf(c_0_60,plain,
meet(complement(X1),join(X1,X2)) = meet(complement(X1),X2),
inference(spm,[status(thm)],[c_0_57,c_0_46]) ).
cnf(c_0_61,plain,
meet(complement(X1),complement(join(X1,X2))) = complement(join(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_58]),c_0_18]) ).
cnf(c_0_62,plain,
complement(join(X1,X2)) = meet(complement(X1),complement(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_59]),c_0_61]) ).
cnf(c_0_63,plain,
complement(meet(complement(X1),complement(X2))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_46,c_0_62]) ).
cnf(c_0_64,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_63,c_0_46]) ).
cnf(c_0_65,plain,
complement(meet(X1,X2)) = join(complement(X1),complement(X2)),
inference(spm,[status(thm)],[c_0_64,c_0_46]) ).
cnf(c_0_66,plain,
join(X1,meet(complement(X1),complement(X2))) = join(X1,complement(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_60]),c_0_65]),c_0_46]),c_0_46]),c_0_62]) ).
cnf(c_0_67,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_66,c_0_46]) ).
cnf(c_0_68,plain,
meet(X1,meet(join(complement(X1),X2),X3)) = meet(X1,meet(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_57]),c_0_12]) ).
cnf(c_0_69,plain,
join(X1,meet(join(X1,X2),X3)) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_67]),c_0_46]) ).
cnf(c_0_70,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_33]),c_0_33]),c_0_33]),c_0_33]) ).
cnf(c_0_71,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_12,c_0_25]) ).
cnf(c_0_72,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_73,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_12,c_0_32]) ).
cnf(c_0_74,plain,
join(X1,meet(join(X2,X1),X3)) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_69]) ).
cnf(c_0_75,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_71,c_0_18]) ).
cnf(c_0_76,plain,
meet(X1,join(X2,join(meet(X1,X3),meet(X1,join(X3,X2))))) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_30]),c_0_36]),c_0_36]),c_0_20]),c_0_72]) ).
cnf(c_0_77,plain,
join(meet(X1,X2),meet(join(X3,X1),X2)) = meet(join(X3,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_20]) ).
cnf(c_0_78,plain,
join(X1,meet(X2,join(X3,X1))) = join(X1,meet(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_50]),c_0_75]) ).
cnf(c_0_79,plain,
meet(X1,join(X2,join(complement(X1),X3))) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_57]),c_0_36]),c_0_57]),c_0_76]) ).
cnf(c_0_80,plain,
meet(join(X1,X2),join(X3,X2)) = join(X2,meet(X3,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_32]),c_0_74]),c_0_78]) ).
cnf(c_0_81,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_67]),c_0_79]),c_0_46]) ).
cnf(c_0_82,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
prove_distributivity ).
cnf(c_0_83,plain,
join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_16]),c_0_18]),c_0_81]) ).
cnf(c_0_84,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_83]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LAT210-1 : TPTP v9.2.1. Released v3.1.0.
% 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
% 0.15/0.32 % Computer : n005.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 20:54:30 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 3.39/3.09 % Version : CSE_E---1.7
% 3.39/3.09 % Problem : theBenchmark.p
% 3.39/3.09 % SZS status Unsatisfiable for theBenchmark.p
% 3.39/3.09 % SZS output start CNFRefutation
% See solution above
% 3.39/3.10 % Total time : 2.371s
%------------------------------------------------------------------------------