%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT020-1 : 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 : n003.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 149.13s 62.96s
% Output : CNFRefutation 149.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of clauses : 130 ( 130 unt; 0 nHn; 5 RR)
% Number of literals : 130 ( 129 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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 : 354 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT004-0.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/LAT004-0.ax',associativity_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(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(idempotence_of_join,axiom,
join(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT004-0.ax',idempotence_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_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT004-0.ax',idempotence_of_meet) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',prove_distributivity) ).
cnf(c_0_10,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_11,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_12,axiom,
meet(join(X1,meet(X2,X3)),join(X1,X2)) = join(X1,meet(X2,X3)),
quasi_lattice2 ).
cnf(c_0_13,axiom,
join(meet(X1,join(X2,X3)),meet(X1,X2)) = meet(X1,join(X2,X3)),
quasi_lattice1 ).
cnf(c_0_14,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_15,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
meet(join(X1,X2),join(X1,meet(X2,X3))) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_17,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_18,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_19,plain,
join(meet(X1,X2),meet(X1,join(X2,X3))) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_21,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_22,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X2,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_10]) ).
cnf(c_0_23,plain,
meet(X1,join(X1,meet(X1,X2))) = join(X1,meet(X1,X2)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_25,plain,
join(X1,meet(X1,join(X1,X2))) = meet(X1,join(X1,X2)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,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_21,c_0_14]),c_0_10]),c_0_10]),c_0_14]) ).
cnf(c_0_27,plain,
meet(X1,join(X2,meet(X2,X1))) = meet(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_14]),c_0_22]),c_0_23]) ).
cnf(c_0_28,plain,
join(X1,meet(X2,join(X2,X1))) = join(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_10]),c_0_24]),c_0_14]),c_0_25]) ).
cnf(c_0_29,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_14]),c_0_18]) ).
cnf(c_0_30,hypothesis,
join(X1,meet(X1,X2)) = meet(X1,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_26,c_0_17]),c_0_20]),c_0_14]),c_0_27]),c_0_10]),c_0_28]) ).
cnf(c_0_31,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_10]),c_0_11]) ).
cnf(c_0_32,plain,
join(X1,join(meet(X1,join(X1,X2)),meet(X2,X3))) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_16]),c_0_10]),c_0_29]) ).
cnf(c_0_33,hypothesis,
join(meet(X1,join(X1,X2)),X3) = join(X1,join(meet(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_18,c_0_30]) ).
cnf(c_0_34,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_35,plain,
join(meet(X1,X2),meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_19,c_0_27]) ).
cnf(c_0_36,plain,
meet(X1,meet(X2,join(X2,X1))) = meet(X2,X1),
inference(rw,[status(thm)],[c_0_27,c_0_30]) ).
cnf(c_0_37,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_16,c_0_19]),c_0_14]),c_0_31]) ).
cnf(c_0_38,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_11,c_0_20]) ).
cnf(c_0_39,plain,
join(X1,join(meet(X1,X2),meet(X2,X3))) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_40,plain,
join(X1,join(X2,X3)) = join(X3,join(X2,X1)),
inference(spm,[status(thm)],[c_0_24,c_0_14]) ).
cnf(c_0_41,plain,
join(meet(X1,X2),join(meet(X2,X1),X3)) = join(meet(X2,X1),X3),
inference(spm,[status(thm)],[c_0_18,c_0_35]) ).
cnf(c_0_42,plain,
meet(join(X1,X2),join(X1,meet(X3,X2))) = join(X1,meet(X3,X2)),
inference(spm,[status(thm)],[c_0_16,c_0_10]) ).
cnf(c_0_43,hypothesis,
join(meet(X1,join(X2,X1)),X3) = join(X1,join(meet(X2,X1),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_28]),c_0_36]) ).
cnf(c_0_44,plain,
meet(join(X1,X2),join(X2,meet(X1,X3))) = join(X2,meet(X1,X3)),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_45,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)],[c_0_37,c_0_30]),c_0_11]),c_0_38]) ).
cnf(c_0_46,plain,
join(X1,join(meet(X2,X3),meet(X1,X2))) = join(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_39,c_0_14]) ).
cnf(c_0_47,plain,
join(meet(X1,X2),X3) = join(X3,meet(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_35]) ).
cnf(c_0_48,plain,
meet(join(X1,X2),meet(X3,join(X1,join(meet(X3,X1),X2)))) = meet(X3,join(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_19]),c_0_29]),c_0_22]) ).
cnf(c_0_49,hypothesis,
join(X1,join(meet(X2,X1),X3)) = join(X3,meet(X1,join(X2,X1))),
inference(spm,[status(thm)],[c_0_14,c_0_43]) ).
cnf(c_0_50,plain,
meet(join(X1,X2),meet(X3,join(X2,meet(X1,X4)))) = meet(X3,join(X2,meet(X1,X4))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_44]),c_0_22]) ).
cnf(c_0_51,plain,
meet(X1,meet(join(X2,X1),join(X2,X3))) = meet(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_45,c_0_14]) ).
cnf(c_0_52,plain,
join(X1,join(meet(X1,X2),meet(X3,X2))) = join(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_53,hypothesis,
meet(X1,join(X2,meet(X3,join(X1,X3)))) = meet(X1,join(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_54,plain,
join(X1,meet(X2,join(X1,X2))) = join(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_28]),c_0_28]),c_0_34]),c_0_28]) ).
cnf(c_0_55,plain,
join(X1,join(X2,join(meet(X2,X1),X3))) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_28]),c_0_18]),c_0_33]) ).
cnf(c_0_56,plain,
meet(join(X1,meet(X2,X3)),join(X1,meet(X2,meet(X3,X4)))) = join(X1,meet(X2,meet(X3,X4))),
inference(spm,[status(thm)],[c_0_16,c_0_11]) ).
cnf(c_0_57,plain,
join(X1,join(X2,join(X1,X3))) = join(X2,join(X1,X3)),
inference(spm,[status(thm)],[c_0_34,c_0_24]) ).
cnf(c_0_58,plain,
meet(X1,meet(join(X2,X3),join(X2,X1))) = meet(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_51,c_0_10]) ).
cnf(c_0_59,plain,
meet(join(X1,X2),join(X1,meet(X3,join(X1,X2)))) = join(X1,meet(X3,join(X1,X2))),
inference(spm,[status(thm)],[c_0_42,c_0_34]) ).
cnf(c_0_60,plain,
join(meet(X1,X2),meet(join(X2,X3),X1)) = meet(join(X2,X3),X1),
inference(spm,[status(thm)],[c_0_19,c_0_10]) ).
cnf(c_0_61,plain,
join(meet(X1,X2),meet(X3,join(X3,X2))) = join(X3,meet(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_52]),c_0_30]) ).
cnf(c_0_62,hypothesis,
meet(X1,join(X2,join(meet(X1,X2),X3))) = 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_53,c_0_54]),c_0_11]),c_0_20]),c_0_53]),c_0_43]) ).
cnf(c_0_63,plain,
join(X1,join(X2,join(X3,meet(X1,X2)))) = join(X2,join(X1,X3)),
inference(spm,[status(thm)],[c_0_55,c_0_47]) ).
cnf(c_0_64,plain,
join(X1,join(meet(X1,meet(X2,X3)),meet(X2,meet(X3,X4)))) = join(X1,meet(X2,meet(X3,X4))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_56]),c_0_10]),c_0_33]),c_0_57]),c_0_29]) ).
cnf(c_0_65,hypothesis,
join(X1,meet(X2,X1)) = meet(X1,join(X1,X2)),
inference(spm,[status(thm)],[c_0_30,c_0_10]) ).
cnf(c_0_66,plain,
meet(X1,meet(X2,meet(X3,X1))) = meet(X3,meet(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_38]),c_0_11]) ).
cnf(c_0_67,plain,
meet(X1,meet(join(X2,X3),join(X1,X2))) = meet(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_45,c_0_10]) ).
cnf(c_0_68,plain,
meet(join(X1,X2),join(meet(X2,X3),X1)) = join(meet(X2,X3),X1),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_69,plain,
meet(X1,join(X2,meet(X1,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(spm,[status(thm)],[c_0_58,c_0_59]),c_0_11]),c_0_59]),c_0_11]),c_0_20]) ).
cnf(c_0_70,plain,
meet(X1,meet(join(X2,X3),join(X2,join(meet(X1,X2),X3)))) = meet(join(X2,X3),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_60]),c_0_29]),c_0_22]) ).
cnf(c_0_71,plain,
join(meet(X1,X2),meet(X3,join(X2,X3))) = join(X3,meet(X2,X1)),
inference(spm,[status(thm)],[c_0_61,c_0_14]) ).
cnf(c_0_72,plain,
meet(join(X1,X2),join(X1,join(X2,meet(X1,X3)))) = join(X1,join(X2,meet(X1,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_34]),c_0_18]),c_0_18]) ).
cnf(c_0_73,hypothesis,
meet(X1,join(X2,join(X3,meet(X2,X1)))) = meet(X1,join(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_61]),c_0_28]) ).
cnf(c_0_74,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_34,c_0_14]) ).
cnf(c_0_75,plain,
join(X1,meet(X2,meet(X3,join(meet(X2,X3),X1)))) = join(X1,meet(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(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]),c_0_11]),c_0_11]),c_0_66]),c_0_30]),c_0_28]) ).
cnf(c_0_76,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_67,c_0_68]),c_0_11]),c_0_11]) ).
cnf(c_0_77,hypothesis,
join(X1,join(meet(X1,X2),meet(X3,join(X1,meet(join(X1,X2),X3))))) = meet(join(X1,X2),join(X3,meet(X1,join(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_26,c_0_34]),c_0_18]),c_0_33]),c_0_14]),c_0_10]) ).
cnf(c_0_78,plain,
meet(X1,join(X2,meet(join(X2,X3),X1))) = meet(join(X2,X3),X1),
inference(spm,[status(thm)],[c_0_69,c_0_10]) ).
cnf(c_0_79,plain,
join(meet(X1,X2),meet(X2,join(X1,X3))) = meet(X2,join(X1,X3)),
inference(spm,[status(thm)],[c_0_19,c_0_10]) ).
cnf(c_0_80,plain,
meet(join(X1,X2),join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_68,c_0_20]) ).
cnf(c_0_81,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_46,c_0_60]),c_0_18]),c_0_18]) ).
cnf(c_0_82,plain,
meet(X1,join(X2,X3)) = meet(join(X3,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_54]),c_0_72]),c_0_73]),c_0_54]) ).
cnf(c_0_83,hypothesis,
join(X1,join(X2,meet(X1,join(X1,X3)))) = join(X2,meet(X1,join(X1,X3))),
inference(spm,[status(thm)],[c_0_57,c_0_30]) ).
cnf(c_0_84,plain,
meet(X1,meet(join(X2,X3),join(X1,X3))) = meet(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_67,c_0_74]) ).
cnf(c_0_85,hypothesis,
join(X1,join(meet(X1,meet(X2,X3)),meet(X3,join(X1,meet(X3,X2))))) = meet(join(meet(X2,X3),X1),join(X3,join(X1,meet(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(spm,[status(thm)],[c_0_26,c_0_42]),c_0_18]),c_0_74]),c_0_10]),c_0_29]),c_0_52]),c_0_33]) ).
cnf(c_0_86,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_15,c_0_20]) ).
cnf(c_0_87,plain,
join(X1,meet(X2,meet(X3,join(X1,X2)))) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_88,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(X2,meet(X1,X3)),
inference(spm,[status(thm)],[c_0_38,c_0_15]) ).
cnf(c_0_89,hypothesis,
meet(join(X1,X2),join(X3,meet(X1,join(X1,join(X2,X3))))) = join(X1,join(meet(X1,X2),meet(join(X1,X2),X3))),
inference(rw,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_90,plain,
join(X1,meet(X2,join(X2,join(X3,X1)))) = meet(join(X2,X1),join(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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_18]),c_0_18]),c_0_18]),c_0_81]),c_0_82]),c_0_18]),c_0_83]) ).
cnf(c_0_91,plain,
meet(X1,meet(join(X2,X3),join(X3,X1))) = meet(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_84,c_0_14]) ).
cnf(c_0_92,plain,
join(meet(X1,X2),join(meet(X1,join(X2,X3)),X4)) = join(meet(X1,join(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_93,hypothesis,
join(X1,meet(X2,meet(X3,join(X1,meet(X3,X2))))) = join(X1,meet(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(spm,[status(thm)],[c_0_85,c_0_38]),c_0_11]),c_0_86]),c_0_11]),c_0_64]),c_0_74]),c_0_80]) ).
cnf(c_0_94,plain,
join(X1,meet(X2,meet(X3,join(X3,X1)))) = join(X1,meet(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_87]),c_0_39]),c_0_14]),c_0_65]),c_0_88]) ).
cnf(c_0_95,plain,
join(X1,meet(X2,meet(X3,join(X1,meet(X2,X3))))) = join(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_54,c_0_11]) ).
cnf(c_0_96,hypothesis,
join(X1,join(meet(X1,X2),meet(join(X1,X2),X3))) = meet(join(X1,X2),join(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_90]),c_0_91]) ).
cnf(c_0_97,plain,
join(X1,join(meet(X1,X2),join(meet(X3,X2),X4))) = join(X1,join(meet(X3,X2),X4)),
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_92,c_0_42]),c_0_18]),c_0_18]),c_0_10]),c_0_33]),c_0_29]),c_0_34]) ).
cnf(c_0_98,hypothesis,
join(X1,meet(X2,meet(join(X2,X1),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_93,c_0_94]),c_0_11]),c_0_50]),c_0_95]),c_0_11]) ).
cnf(c_0_99,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_19,c_0_38]) ).
cnf(c_0_100,hypothesis,
join(X1,meet(X2,join(X1,X3))) = meet(join(X1,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)],[inference(spm,[status(thm)],[c_0_96,c_0_87]),c_0_96]),c_0_24]),c_0_14]),c_0_30]),c_0_28]),c_0_59]) ).
cnf(c_0_101,hypothesis,
join(X1,meet(X2,join(meet(X1,X2),X3))) = join(X1,meet(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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_96]),c_0_14]),c_0_65]),c_0_11]),c_0_98]),c_0_11]),c_0_20]),c_0_14]),c_0_65]),c_0_11]),c_0_39]),c_0_98]) ).
cnf(c_0_102,plain,
meet(X1,meet(join(X1,X2),join(meet(X1,X2),X3))) = meet(X1,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)],[c_0_99,c_0_100]),c_0_14]),c_0_30]),c_0_22]),c_0_31]) ).
cnf(c_0_103,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_19,c_0_86]) ).
cnf(c_0_104,hypothesis,
join(X1,meet(X2,join(meet(X2,X1),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_101,c_0_36]),c_0_11]),c_0_102]),c_0_11]),c_0_98]) ).
cnf(c_0_105,plain,
join(meet(X1,X2),meet(X1,join(X3,X2))) = meet(X1,join(X3,X2)),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_106,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_103,c_0_100]),c_0_14]),c_0_65]),c_0_22]),c_0_31]) ).
cnf(c_0_107,hypothesis,
join(meet(X1,X2),meet(X1,X3)) = meet(X1,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(spm,[status(thm)],[c_0_104,c_0_38]),c_0_100]),c_0_14]),c_0_30]),c_0_22]),c_0_31]),c_0_102]) ).
cnf(c_0_108,plain,
join(X1,join(meet(X2,X1),meet(X2,X3))) = join(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_39,c_0_10]) ).
cnf(c_0_109,plain,
join(meet(X1,X2),meet(join(X3,X2),X1)) = meet(join(X3,X2),X1),
inference(spm,[status(thm)],[c_0_105,c_0_10]) ).
cnf(c_0_110,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_16,c_0_34]) ).
cnf(c_0_111,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(spm,[status(thm)],[c_0_104,c_0_86]),c_0_100]),c_0_14]),c_0_65]),c_0_22]),c_0_31]),c_0_106]) ).
cnf(c_0_112,hypothesis,
join(meet(X1,X2),meet(X3,X1)) = meet(X1,join(X3,meet(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_107]),c_0_28]) ).
cnf(c_0_113,plain,
join(X1,join(meet(X2,X3),meet(X2,X1))) = join(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_108,c_0_14]) ).
cnf(c_0_114,hypothesis,
join(meet(X1,X2),join(meet(X3,join(X1,X2)),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_79,c_0_26]),c_0_29]) ).
cnf(c_0_115,plain,
join(meet(X1,X2),meet(join(X3,X1),X2)) = meet(join(X3,X1),X2),
inference(spm,[status(thm)],[c_0_41,c_0_109]) ).
cnf(c_0_116,hypothesis,
join(X1,meet(join(X1,X2),X3)) = meet(join(X1,X2),join(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_38]),c_0_96]),c_0_110]) ).
cnf(c_0_117,hypothesis,
meet(X1,join(meet(X2,X1),X3)) = meet(X1,join(X2,meet(X1,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_111]),c_0_112]) ).
cnf(c_0_118,plain,
join(X1,join(meet(X2,X1),meet(X3,X2))) = join(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_113,c_0_47]) ).
cnf(c_0_119,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
prove_distributivity ).
cnf(c_0_120,hypothesis,
join(meet(X1,X2),meet(X3,X2)) = meet(X2,join(X1,meet(X2,X3))),
inference(spm,[status(thm)],[c_0_47,c_0_112]) ).
cnf(c_0_121,hypothesis,
meet(X1,join(X2,join(meet(X2,X1),X3))) = 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_51,c_0_62]),c_0_51]),c_0_10]),c_0_33]),c_0_34]) ).
cnf(c_0_122,hypothesis,
join(meet(X1,X2),meet(X3,join(X2,meet(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)],[inference(rw,[status(thm)],[c_0_114,c_0_107]),c_0_24]),c_0_47]),c_0_115]),c_0_116]),c_0_58]),c_0_117]) ).
cnf(c_0_123,plain,
join(X1,meet(X2,join(X3,meet(X2,X1)))) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[c_0_118,c_0_112]) ).
cnf(c_0_124,negated_conjecture,
meet(a,join(c,meet(a,b))) != meet(a,join(b,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_107]),c_0_47]),c_0_10]) ).
cnf(c_0_125,hypothesis,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X3,meet(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_36]),c_0_120]) ).
cnf(c_0_126,hypothesis,
meet(X1,join(X2,meet(X3,X1))) = 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_121,c_0_122]),c_0_121]),c_0_100]),c_0_51]),c_0_123]) ).
cnf(c_0_127,negated_conjecture,
meet(a,join(b,meet(a,c))) != meet(a,join(b,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_124,c_0_125]),c_0_10]) ).
cnf(c_0_128,hypothesis,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X3,X2)),
inference(rw,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_129,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_127,c_0_128]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT020-1 : 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
% 0.16/0.33 % Computer : n003.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 20:46:26 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 149.13/62.96 % Version : CSE_E---1.7
% 149.13/62.96 % Problem : theBenchmark.p
% 149.13/62.96 % SZS status Unsatisfiable for theBenchmark.p
% 149.13/62.96 % SZS output start CNFRefutation
% See solution above
% 149.53/63.34 % Total time : 49.138s
%------------------------------------------------------------------------------