%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LAT020-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:04:04 PM UTC 2026
% Result : Unsatisfiable 197.16s 38.98s
% Output : CNFRefutation 197.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of clauses : 116 ( 116 unt; 0 nHn; 4 RR)
% Number of literals : 116 ( 115 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 : 306 ( 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(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(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(quasi_lattice1,axiom,
join(meet(X1,join(X2,X3)),meet(X1,X2)) = meet(X1,join(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',quasi_lattice1) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',commutativity_of_join) ).
cnf(self_dual_distributivity,hypothesis,
join(meet(join(meet(X1,X2),X3),X2),meet(X3,X1)) = meet(join(meet(join(X1,X2),X3),X2),join(X3,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',self_dual_distributivity) ).
cnf(prove_distributivity,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity) ).
cnf(c_0_10,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_11,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
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,axiom,
meet(join(X1,meet(X2,X3)),join(X1,X2)) = join(X1,meet(X2,X3)),
quasi_lattice2 ).
cnf(c_0_15,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_16,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_17,axiom,
join(meet(X1,join(X2,X3)),meet(X1,X2)) = meet(X1,join(X2,X3)),
quasi_lattice1 ).
cnf(c_0_18,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_19,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_20,plain,
meet(join(X1,X2),join(X1,meet(X2,X3))) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_22,plain,
join(meet(X1,X2),meet(X1,join(X2,X3))) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_24,hypothesis,
join(meet(join(meet(X1,X2),X3),X2),meet(X3,X1)) = meet(join(meet(join(X1,X2),X3),X2),join(X3,X1)),
self_dual_distributivity ).
cnf(c_0_25,plain,
meet(join(X1,X2),join(X1,meet(X3,X2))) = join(X1,meet(X3,X2)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
join(meet(X1,X2),meet(X1,join(X3,X2))) = meet(X1,join(X3,X2)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,hypothesis,
meet(join(X1,X2),join(X3,meet(join(X2,X3),X1))) = join(meet(X1,X2),meet(X3,join(meet(X2,X3),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_18]),c_0_15]),c_0_15]),c_0_18]) ).
cnf(c_0_28,plain,
meet(join(X1,X2),join(X2,meet(X3,X1))) = join(X2,meet(X3,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_29,plain,
join(meet(X1,X2),meet(X2,join(X3,X1))) = meet(X2,join(X3,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_15]) ).
cnf(c_0_30,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_15]),c_0_10]) ).
cnf(c_0_31,plain,
meet(X1,meet(X2,join(X1,meet(X1,X2)))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_13]),c_0_18]),c_0_15]),c_0_10]) ).
cnf(c_0_32,plain,
meet(X1,join(X1,meet(X1,X2))) = join(X1,meet(X1,X2)),
inference(spm,[status(thm)],[c_0_20,c_0_13]) ).
cnf(c_0_33,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_18]),c_0_12]) ).
cnf(c_0_34,plain,
join(X1,join(X2,meet(X1,join(X1,X2)))) = join(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_11]),c_0_15]),c_0_18]),c_0_12]) ).
cnf(c_0_35,plain,
join(X1,meet(X1,join(X1,X2))) = meet(X1,join(X1,X2)),
inference(spm,[status(thm)],[c_0_22,c_0_11]) ).
cnf(c_0_36,hypothesis,
join(X1,meet(X1,X2)) = meet(X1,join(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_13]),c_0_11]),c_0_29]) ).
cnf(c_0_37,plain,
meet(X1,join(X2,meet(X2,X1))) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_38,plain,
join(X1,meet(X2,join(X2,X1))) = join(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_39,hypothesis,
join(meet(X1,join(X1,X2)),X3) = join(X1,join(meet(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_12,c_0_36]) ).
cnf(c_0_40,plain,
meet(X1,meet(join(X1,X2),join(X2,X3))) = meet(X1,join(X2,X3)),
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_20,c_0_22]),c_0_18]),c_0_36]),c_0_10]),c_0_30]),c_0_16]) ).
cnf(c_0_41,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[c_0_18,c_0_12]) ).
cnf(c_0_42,plain,
join(meet(X1,X2),meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_22,c_0_37]) ).
cnf(c_0_43,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(spm,[status(thm)],[c_0_15,c_0_10]) ).
cnf(c_0_44,plain,
meet(join(X1,X2),join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_20,c_0_38]) ).
cnf(c_0_45,plain,
join(X1,join(meet(X1,X2),meet(X2,X3))) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_20]),c_0_15]),c_0_39]),c_0_33]),c_0_19]) ).
cnf(c_0_46,plain,
meet(X1,meet(join(X2,X3),join(X1,X2))) = meet(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_40,c_0_15]) ).
cnf(c_0_47,plain,
meet(join(X1,X2),join(meet(X2,X3),X1)) = join(meet(X2,X3),X1),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_48,plain,
join(X1,join(X2,X3)) = join(X3,join(X2,X1)),
inference(spm,[status(thm)],[c_0_41,c_0_18]) ).
cnf(c_0_49,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_50,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X2,X1)),
inference(spm,[status(thm)],[c_0_43,c_0_15]) ).
cnf(c_0_51,plain,
meet(join(X1,X2),meet(join(X2,X1),X3)) = meet(join(X2,X1),X3),
inference(spm,[status(thm)],[c_0_10,c_0_44]) ).
cnf(c_0_52,plain,
join(meet(X1,X2),join(X3,meet(X2,X1))) = join(X3,meet(X1,X2)),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_53,plain,
join(X1,join(meet(X2,X3),meet(X1,X2))) = join(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_45,c_0_18]) ).
cnf(c_0_54,plain,
join(meet(X1,X2),meet(join(X2,X3),X1)) = meet(join(X2,X3),X1),
inference(spm,[status(thm)],[c_0_22,c_0_15]) ).
cnf(c_0_55,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,meet(X2,join(X3,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_10]),c_0_10]) ).
cnf(c_0_56,plain,
join(meet(X1,X2),X3) = join(X3,meet(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_42]) ).
cnf(c_0_57,plain,
meet(X1,meet(join(X1,X2),join(X3,X2))) = meet(X1,join(X3,X2)),
inference(spm,[status(thm)],[c_0_40,c_0_23]) ).
cnf(c_0_58,plain,
meet(join(X1,X2),X3) = meet(X3,join(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_44]) ).
cnf(c_0_59,plain,
join(meet(X1,X2),meet(join(X3,X2),X1)) = meet(join(X3,X2),X1),
inference(spm,[status(thm)],[c_0_26,c_0_15]) ).
cnf(c_0_60,hypothesis,
join(X1,meet(X2,X1)) = meet(X1,join(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_36]),c_0_29]) ).
cnf(c_0_61,plain,
join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,join(X2,meet(X3,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_12]),c_0_12]) ).
cnf(c_0_62,plain,
meet(X1,meet(X2,join(X3,meet(X2,X1)))) = meet(X1,meet(X2,join(X3,X1))),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_63,plain,
meet(join(X1,X2),join(X2,meet(join(X1,X2),X3))) = join(X2,meet(join(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_20,c_0_23]) ).
cnf(c_0_64,plain,
meet(X1,meet(join(X2,X3),join(X3,X1))) = meet(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_65,plain,
meet(join(X1,X2),join(X1,meet(join(X1,X2),X3))) = join(X1,meet(join(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_66,plain,
meet(X1,meet(join(X2,X3),join(X2,X1))) = meet(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_40,c_0_58]) ).
cnf(c_0_67,plain,
join(X1,join(X2,meet(X3,X1))) = join(X1,meet(X2,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_53,c_0_59]),c_0_12]),c_0_12]),c_0_60]),c_0_61]) ).
cnf(c_0_68,plain,
join(X1,join(X2,join(X1,X3))) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_23]),c_0_12]),c_0_12]) ).
cnf(c_0_69,plain,
meet(X1,join(X2,meet(join(X3,X2),X1))) = meet(X1,join(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]) ).
cnf(c_0_70,plain,
meet(X1,join(X2,meet(join(X2,X3),X1))) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_65]),c_0_66]) ).
cnf(c_0_71,plain,
join(X1,join(X2,meet(join(X3,X2),X1))) = join(X1,meet(X2,join(X3,X2))),
inference(spm,[status(thm)],[c_0_67,c_0_23]) ).
cnf(c_0_72,hypothesis,
join(X1,join(X2,meet(X1,join(X1,X3)))) = join(X2,meet(X1,join(X1,X3))),
inference(spm,[status(thm)],[c_0_68,c_0_36]) ).
cnf(c_0_73,plain,
meet(X1,join(X2,join(X3,meet(X1,X2)))) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_19]),c_0_12]),c_0_61]) ).
cnf(c_0_74,hypothesis,
meet(join(X1,X2),join(X3,meet(X1,join(X1,join(X2,X3))))) = join(X1,join(meet(X1,X2),meet(X3,join(X1,X2)))),
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_27,c_0_19]),c_0_12]),c_0_39]),c_0_18]),c_0_70]),c_0_15]) ).
cnf(c_0_75,plain,
join(X1,meet(X2,join(X2,join(X3,X1)))) = join(X2,meet(X1,join(X3,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_71]),c_0_60]) ).
cnf(c_0_76,hypothesis,
join(X1,join(X2,meet(X1,join(X3,X1)))) = join(X2,meet(X1,join(X3,X1))),
inference(spm,[status(thm)],[c_0_72,c_0_23]) ).
cnf(c_0_77,plain,
meet(X1,join(X2,join(meet(X2,X1),X3))) = meet(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_73,c_0_56]) ).
cnf(c_0_78,hypothesis,
meet(join(X1,X2),join(X1,meet(X3,join(X2,X3)))) = join(X1,join(meet(X1,X2),meet(X3,join(X1,X2)))),
inference(rw,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_79,plain,
meet(X1,meet(join(X2,X1),join(X2,X3))) = meet(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_40,c_0_18]) ).
cnf(c_0_80,plain,
meet(X1,join(X2,meet(X3,join(X1,X3)))) = meet(X1,join(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_73]),c_0_40]),c_0_15]),c_0_76]) ).
cnf(c_0_81,plain,
meet(X1,meet(X2,join(X3,meet(X3,X1)))) = meet(X2,meet(X3,X1)),
inference(spm,[status(thm)],[c_0_30,c_0_37]) ).
cnf(c_0_82,hypothesis,
meet(X1,join(X2,meet(X3,join(X2,X1)))) = meet(X1,join(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]),c_0_80]) ).
cnf(c_0_83,plain,
meet(X1,meet(X2,join(X1,X2))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_25]),c_0_37]),c_0_15]),c_0_10]) ).
cnf(c_0_84,hypothesis,
meet(X1,join(X2,meet(join(X2,X1),X3))) = meet(X1,join(X3,X2)),
inference(spm,[status(thm)],[c_0_82,c_0_15]) ).
cnf(c_0_85,plain,
join(X1,meet(X1,join(X2,X1))) = meet(X1,join(X2,X1)),
inference(spm,[status(thm)],[c_0_35,c_0_23]) ).
cnf(c_0_86,plain,
meet(X1,meet(X2,join(X2,X1))) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_30,c_0_83]) ).
cnf(c_0_87,hypothesis,
join(X1,meet(join(X1,X2),X3)) = meet(join(X1,X2),join(X3,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_19]),c_0_65]) ).
cnf(c_0_88,plain,
join(X1,meet(X2,join(X1,X2))) = join(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_23]),c_0_12]),c_0_85]) ).
cnf(c_0_89,plain,
join(X1,join(meet(X1,X2),meet(X3,X2))) = join(X1,meet(X3,X2)),
inference(spm,[status(thm)],[c_0_45,c_0_86]) ).
cnf(c_0_90,hypothesis,
join(X1,meet(join(X2,X1),X3)) = meet(join(X2,X1),join(X3,X1)),
inference(spm,[status(thm)],[c_0_87,c_0_23]) ).
cnf(c_0_91,plain,
meet(join(X1,X2),join(X2,meet(X1,X3))) = join(X2,meet(X1,X3)),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_92,plain,
join(meet(X1,X2),meet(X2,join(meet(X1,X2),X3))) = meet(X2,join(meet(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_93,hypothesis,
join(X1,meet(X2,join(X1,X3))) = meet(join(X1,X3),join(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_87]),c_0_10]),c_0_46]),c_0_21]) ).
cnf(c_0_94,plain,
join(X1,join(X2,meet(X3,join(X2,X1)))) = join(X1,join(X2,meet(X3,X1))),
inference(spm,[status(thm)],[c_0_61,c_0_58]) ).
cnf(c_0_95,plain,
join(X1,join(meet(X2,X3),meet(X3,X1))) = join(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_89,c_0_56]) ).
cnf(c_0_96,plain,
join(meet(X1,X2),meet(X1,join(meet(X1,X2),X3))) = meet(X1,join(meet(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_97,plain,
join(X1,join(meet(X2,X3),meet(X2,X1))) = join(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_45,c_0_56]) ).
cnf(c_0_98,hypothesis,
meet(join(X1,X2),meet(join(X2,X3),join(X1,X3))) = join(meet(X1,X2),meet(X3,join(meet(X2,X3),X1))),
inference(rw,[status(thm)],[c_0_27,c_0_90]) ).
cnf(c_0_99,plain,
meet(join(X1,X2),join(meet(X3,X1),X2)) = join(meet(X3,X1),X2),
inference(spm,[status(thm)],[c_0_91,c_0_56]) ).
cnf(c_0_100,plain,
meet(X1,meet(join(X1,X2),join(meet(X2,X1),X3))) = meet(X1,join(meet(X2,X1),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_93]),c_0_60]),c_0_43]),c_0_15]),c_0_30]) ).
cnf(c_0_101,plain,
join(X1,meet(X2,join(meet(X3,X2),X1))) = join(X1,meet(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_92]),c_0_95]) ).
cnf(c_0_102,plain,
join(meet(X1,X2),meet(X2,join(X1,X3))) = meet(X2,join(X1,X3)),
inference(spm,[status(thm)],[c_0_22,c_0_15]) ).
cnf(c_0_103,plain,
join(X1,meet(X2,join(meet(X2,X3),X1))) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_96]),c_0_97]) ).
cnf(c_0_104,hypothesis,
join(meet(X1,X2),join(meet(join(X1,X2),X3),meet(X3,join(meet(X2,X3),X1)))) = join(meet(X1,X2),meet(X3,join(meet(X2,X3),X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_27]),c_0_33]) ).
cnf(c_0_105,hypothesis,
join(meet(X1,X2),meet(X2,X3)) = meet(X2,join(meet(X1,X2),X3)),
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_98,c_0_99]),c_0_18]),c_0_60]),c_0_10]),c_0_100]),c_0_10]),c_0_11]),c_0_101]) ).
cnf(c_0_106,plain,
join(meet(X1,X2),meet(join(X3,X1),X2)) = meet(join(X3,X1),X2),
inference(spm,[status(thm)],[c_0_102,c_0_58]) ).
cnf(c_0_107,plain,
join(X1,meet(X2,join(X1,meet(X2,X3)))) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_103]),c_0_10]),c_0_44]) ).
cnf(c_0_108,hypothesis,
join(meet(X1,X2),meet(X3,join(meet(X2,X3),X1))) = join(meet(X1,X2),meet(X3,join(X1,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)],[c_0_104,c_0_105]),c_0_41]),c_0_18]),c_0_106]),c_0_87]),c_0_46]) ).
cnf(c_0_109,plain,
meet(X1,meet(join(X2,X1),join(X3,X2))) = meet(X1,join(X3,X2)),
inference(spm,[status(thm)],[c_0_57,c_0_18]) ).
cnf(c_0_110,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
inference(fof_simplification,[status(thm)],[prove_distributivity]) ).
cnf(c_0_111,plain,
meet(X1,join(meet(X1,X2),meet(X1,X3))) = join(meet(X1,X2),meet(X1,X3)),
inference(spm,[status(thm)],[c_0_96,c_0_107]) ).
cnf(c_0_112,hypothesis,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_108]),c_0_77]),c_0_93]),c_0_109]),c_0_101]) ).
cnf(c_0_113,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
c_0_110 ).
cnf(c_0_114,plain,
join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_112]),c_0_112]) ).
cnf(c_0_115,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_114])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT020-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/5.38 % Computer : n006.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Sun Sep 20 23:06:18 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.12/5.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/5.43 Running first-order theorem proving
% 0.14/5.43 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 197.16/38.98 % Version: 3.5.1
% 197.16/38.98 % Preprocessing class: FSSSSMSSSSSNFFN.
% 197.16/38.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 197.16/38.98 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 197.16/38.98 % Starting new_bool_3 with 300s (1) cores
% 197.16/38.98 % Starting new_bool_1 with 300s (1) cores
% 197.16/38.98 % Starting sh5l with 300s (1) cores
% 197.16/38.98 % new_bool_3 with pid 1449924 completed with status 0
% 197.16/38.98 % Result found by new_bool_3
% 197.16/38.98 % Preprocessing class: FSSSSMSSSSSNFFN.
% 197.16/38.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 197.16/38.98 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 197.16/38.98 % Starting new_bool_3 with 300s (1) cores
% 197.16/38.98 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 197.16/38.98 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 197.16/38.98 % Search class: FUUPM-FFSF22-MFFFFFNN
% 197.16/38.98 % Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 197.16/38.98 % Starting SubtermCWHack with 28s (1) cores
% 197.16/38.98 % SubtermCWHack with pid 1449929 completed with status 8
% 197.16/38.98 % Starting new_bool_3 with 31s (1) cores
% 197.16/38.98 % new_bool_3 with pid 1450197 completed with status 0
% 197.16/38.98 % Result found by new_bool_3
% 197.16/38.98 % Preprocessing class: FSSSSMSSSSSNFFN.
% 197.16/38.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 197.16/38.98 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 197.16/38.98 % Starting new_bool_3 with 300s (1) cores
% 197.16/38.98 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 197.16/38.98 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 197.16/38.98 % Search class: FUUPM-FFSF22-MFFFFFNN
% 197.16/38.98 % Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 197.16/38.98 % Starting SubtermCWHack with 28s (1) cores
% 197.16/38.98 % SubtermCWHack with pid 1449929 completed with status 8
% 197.16/38.98 % Starting new_bool_3 with 31s (1) cores
% 197.16/38.98 % Preprocessing time : 0.002 s
% 197.16/38.98 % Presaturation interreduction done
% 197.16/38.98
% 197.16/38.98 % Proof found!
% 197.16/38.98 % SZS status Unsatisfiable
% 197.16/38.98 % SZS output start CNFRefutation
% See solution above
% 197.16/38.98 % Parsed axioms : 10
% 197.16/38.98 % Removed by relevancy pruning/SinE : 0
% 197.16/38.98 % Initial clauses : 10
% 197.16/38.98 % Removed in clause preprocessing : 0
% 197.16/38.98 % Initial clauses in saturation : 10
% 197.16/38.98 % Processed clauses : 3682
% 197.16/38.98 % ...of these trivial : 848
% 197.16/38.98 % ...subsumed : 2508
% 197.16/38.98 % ...remaining for further processing : 326
% 197.16/38.98 % Other redundant clauses eliminated : 0
% 197.16/38.98 % Clauses deleted for lack of memory : 0
% 197.16/38.98 % Backward-subsumed : 0
% 197.16/38.98 % Backward-rewritten : 153
% 197.16/38.98 % Generated clauses : 123438
% 197.16/38.98 % ...of the previous two non-redundant : 107434
% 197.16/38.98 % ...aggressively subsumed : 0
% 197.16/38.98 % Contextual simplify-reflections : 0
% 197.16/38.98 % Paramodulations : 123438
% 197.16/38.98 % Factorizations : 0
% 197.16/38.98 % NegExts : 0
% 197.16/38.98 % Equation resolutions : 0
% 197.16/38.98 % Disequality decompositions : 0
% 197.16/38.98 % Total rewrite steps : 325535
% 197.16/38.98 % ...of those cached : 254400
% 197.16/38.98 % Propositional unsat checks : 0
% 197.16/38.98 % Propositional check models : 0
% 197.16/38.98 % Propositional check unsatisfiable : 0
% 197.16/38.98 % Propositional clauses : 0
% 197.16/38.98 % Propositional clauses after purity: 0
% 197.16/38.98 % Propositional unsat core size : 0
% 197.16/38.98 % Propositional preprocessing time : 0.000
% 197.16/38.98 % Propositional encoding time : 0.000
% 197.16/38.98 % Propositional solver time : 0.000
% 197.16/38.98 % Success case prop preproc time : 0.000
% 197.16/38.98 % Success case prop encoding time : 0.000
% 197.16/38.98 % Success case prop solver time : 0.000
% 197.16/38.98 % Current number of processed clauses : 163
% 197.16/38.98 % Positive orientable unit clauses : 143
% 197.16/38.98 % Positive unorientable unit clauses: 20
% 197.16/38.98 % Negative unit clauses : 0
% 197.16/38.98 % Non-unit-clauses : 0
% 197.16/38.98 % Current number of unprocessed clauses: 103494
% 197.16/38.98 % ...number of literals in the above : 103494
% 197.16/38.98 % Current number of archived formulas : 0
% 197.16/38.98 % Current number of archived clauses : 163
% 197.16/38.98 % Clause-clause subsumption calls (NU) : 0
% 197.16/38.98 % Rec. Clause-clause subsumption calls : 0
% 197.16/38.98 % Non-unit clause-clause subsumptions : 0
% 197.16/38.98 % Unit Clause-clause subsumption calls : 655
% 197.16/38.98 % Rewrite failures with RHS unbound : 0
% 197.16/38.98 % BW rewrite match attempts : 5428
% 197.16/38.98 % BW rewrite match successes : 406
% 197.16/38.98 % Condensation attempts : 0
% 197.16/38.98 % Condensation successes : 0
% 197.16/38.98 % Termbank termtop insertions : 2566235
% 197.16/38.98 % Search garbage collected termcells : 2
% 197.16/38.98
% 197.16/38.98 % -------------------------------------------------
% 197.16/38.98 % User time : 31.934 s
% 197.16/38.98 % System time : 1.208 s
% 197.16/38.98 % Total time : 33.142 s
% 197.16/38.98 % Maximum resident set size: 3636 pages
% 197.16/38.98
% 197.16/38.98 % -------------------------------------------------
% 197.16/38.98 % User time : 31.935 s
% 197.16/38.98 % System time : 1.213 s
% 197.16/38.98 % Total time : 33.148 s
% 197.16/38.98 % Maximum resident set size: 4608 pages
% 197.16/38.98 % E exiting
%------------------------------------------------------------------------------