TSTP Solution File: LAT020-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT020-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n010.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 : Thu Aug 31 05:59:13 EDT 2023
% Result : Unsatisfiable 3.00s 3.16s
% Output : CNFRefutation 3.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 15
% Syntax : Number of formulae : 126 ( 121 unt; 5 typ; 0 def)
% Number of atoms : 121 ( 120 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% 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 : 323 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
meet: ( $i * $i ) > $i ).
tff(decl_23,type,
join: ( $i * $i ) > $i ).
tff(decl_24,type,
a: $i ).
tff(decl_25,type,
b: $i ).
tff(decl_26,type,
c: $i ).
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(idempotence_of_join,axiom,
join(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',idempotence_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(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_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',idempotence_of_meet) ).
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(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(join(X1,meet(X2,X3)),join(X1,X2)) = join(X1,meet(X2,X3)),
quasi_lattice2 ).
cnf(c_0_11,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_12,plain,
meet(join(X1,X2),join(X1,meet(X2,X3))) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
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(join(X1,X2),join(X1,meet(X3,X2))) = join(X1,meet(X3,X2)),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_16,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_17,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_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,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_22,plain,
meet(X1,join(X1,meet(X2,X1))) = join(X1,meet(X2,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_23,hypothesis,
join(meet(X1,X2),meet(X3,join(meet(X2,X3),X1))) = meet(join(X1,X2),join(X3,meet(join(X2,X3),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_11]),c_0_14]),c_0_14]),c_0_11]) ).
cnf(c_0_24,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_25,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_19,c_0_20]),c_0_11]),c_0_14]),c_0_18]) ).
cnf(c_0_26,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_27,plain,
meet(X1,join(X2,meet(X1,X2))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_14]),c_0_11]),c_0_21]),c_0_22]) ).
cnf(c_0_28,hypothesis,
join(meet(join(X1,X2),join(X3,meet(join(X2,X3),X1))),X4) = join(meet(X1,X2),join(meet(X3,join(meet(X2,X3),X1)),X4)),
inference(spm,[status(thm)],[c_0_18,c_0_23]) ).
cnf(c_0_29,plain,
join(X1,meet(X2,join(X2,X1))) = join(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_30,plain,
meet(X1,join(X2,meet(X2,X1))) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_27,c_0_11]) ).
cnf(c_0_31,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_32,plain,
meet(join(X1,X2),join(X2,meet(X3,X1))) = join(X2,meet(X3,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_33,plain,
meet(join(X1,X2),join(meet(X2,X3),X1)) = join(meet(X2,X3),X1),
inference(spm,[status(thm)],[c_0_12,c_0_14]) ).
cnf(c_0_34,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_12]),c_0_11]),c_0_24]) ).
cnf(c_0_35,hypothesis,
join(meet(X1,join(X1,X2)),X3) = join(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(spm,[status(thm)],[c_0_28,c_0_16]),c_0_11]),c_0_29]),c_0_20]),c_0_14]),c_0_30]) ).
cnf(c_0_36,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_37,plain,
join(meet(X1,meet(X2,X3)),meet(X1,meet(X2,join(X3,X4)))) = meet(X1,meet(X2,join(X3,X4))),
inference(spm,[status(thm)],[c_0_19,c_0_19]) ).
cnf(c_0_38,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_12,c_0_16]),c_0_14]),c_0_11]),c_0_21]) ).
cnf(c_0_39,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_31,c_0_11]) ).
cnf(c_0_40,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_11]),c_0_21]) ).
cnf(c_0_41,hypothesis,
join(meet(X1,X2),meet(X2,join(X2,X1))) = join(X2,meet(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_20]),c_0_16]),c_0_32]) ).
cnf(c_0_42,plain,
join(meet(X1,X2),meet(X2,join(X1,X3))) = meet(X2,join(X1,X3)),
inference(spm,[status(thm)],[c_0_19,c_0_11]) ).
cnf(c_0_43,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(spm,[status(thm)],[c_0_11,c_0_21]) ).
cnf(c_0_44,plain,
meet(join(X1,X2),join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_33,c_0_20]) ).
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)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_46,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_47,plain,
join(meet(X1,X2),meet(X2,X1)) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_48,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_12,c_0_19]),c_0_14]),c_0_40]) ).
cnf(c_0_49,hypothesis,
join(X1,meet(X1,X2)) = meet(X1,join(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_14]),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_11]) ).
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_21,c_0_44]) ).
cnf(c_0_52,plain,
join(X1,join(meet(X2,X3),meet(X1,X2))) = join(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_45,c_0_14]) ).
cnf(c_0_53,plain,
join(meet(X1,X2),meet(join(X2,X3),X1)) = meet(join(X2,X3),X1),
inference(spm,[status(thm)],[c_0_19,c_0_11]) ).
cnf(c_0_54,plain,
join(X1,join(X2,X3)) = join(X3,join(X2,X1)),
inference(spm,[status(thm)],[c_0_46,c_0_14]) ).
cnf(c_0_55,plain,
join(meet(X1,X2),join(meet(X2,X1),X3)) = join(meet(X2,X1),X3),
inference(spm,[status(thm)],[c_0_18,c_0_47]) ).
cnf(c_0_56,hypothesis,
meet(X1,meet(join(X2,X1),join(X2,X3))) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_21]),c_0_31]) ).
cnf(c_0_57,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_58,plain,
meet(X1,join(X1,meet(X1,X2))) = join(X1,meet(X1,X2)),
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_59,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_52,c_0_53]),c_0_18]),c_0_18]) ).
cnf(c_0_60,plain,
join(X1,join(meet(X1,X2),meet(X3,X2))) = join(X1,meet(X3,X2)),
inference(spm,[status(thm)],[c_0_45,c_0_39]) ).
cnf(c_0_61,plain,
join(meet(X1,X2),X3) = join(X3,meet(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_47]) ).
cnf(c_0_62,hypothesis,
join(X1,join(X2,meet(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_45,c_0_23]),c_0_16]),c_0_32]),c_0_20]),c_0_29]) ).
cnf(c_0_63,hypothesis,
meet(X1,meet(join(X2,X3),join(X1,X2))) = meet(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_64,plain,
meet(join(X1,X2),meet(X3,join(X1,X3))) = meet(X3,join(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_48]),c_0_58]),c_0_49]) ).
cnf(c_0_65,plain,
meet(join(X1,X2),meet(X3,join(X1,meet(X2,X4)))) = meet(X3,join(X1,meet(X2,X4))),
inference(spm,[status(thm)],[c_0_40,c_0_12]) ).
cnf(c_0_66,plain,
join(X1,join(X2,meet(X3,join(X2,X1)))) = join(X1,join(X2,meet(X3,X1))),
inference(spm,[status(thm)],[c_0_59,c_0_57]) ).
cnf(c_0_67,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_39]) ).
cnf(c_0_68,plain,
join(X1,join(meet(X2,X3),meet(X3,X1))) = join(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_69,hypothesis,
join(X1,meet(X2,X1)) = meet(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_41,c_0_62]),c_0_11]),c_0_30]),c_0_42]),c_0_30]) ).
cnf(c_0_70,hypothesis,
join(X1,meet(X2,meet(X1,X3))) = meet(X1,join(meet(X3,X2),X1)),
inference(spm,[status(thm)],[c_0_49,c_0_43]) ).
cnf(c_0_71,hypothesis,
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_63,c_0_33]),c_0_21]),c_0_21]) ).
cnf(c_0_72,plain,
meet(X1,meet(X2,join(X3,meet(X1,X2)))) = meet(X1,meet(X2,join(X3,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_21]),c_0_21]) ).
cnf(c_0_73,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_39]),c_0_21]),c_0_21]) ).
cnf(c_0_74,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_66,c_0_67]),c_0_68]) ).
cnf(c_0_75,hypothesis,
meet(X1,meet(join(X2,X1),join(X3,meet(X1,join(meet(X2,X1),X3))))) = join(meet(X2,X1),meet(X3,meet(X1,join(meet(X3,X2),X1)))),
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_23,c_0_39]),c_0_21]),c_0_69]),c_0_11]),c_0_21]),c_0_14]),c_0_70]) ).
cnf(c_0_76,hypothesis,
meet(X1,meet(X2,join(meet(X1,X3),X2))) = meet(X2,meet(X1,join(X3,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)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_49]),c_0_21]),c_0_72]),c_0_73]),c_0_31]),c_0_21]),c_0_14]),c_0_49]),c_0_73]) ).
cnf(c_0_77,plain,
join(X1,meet(X2,meet(X3,join(X1,X2)))) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_31]),c_0_21]),c_0_71]) ).
cnf(c_0_78,plain,
join(X1,meet(X2,join(X1,X2))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_29,c_0_14]) ).
cnf(c_0_79,plain,
join(meet(X1,X2),join(X3,meet(X1,join(X2,X4)))) = join(X3,meet(X1,join(X2,X4))),
inference(spm,[status(thm)],[c_0_24,c_0_19]) ).
cnf(c_0_80,plain,
join(meet(X1,X2),meet(X3,join(X1,X3))) = join(X3,meet(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_45]),c_0_49]) ).
cnf(c_0_81,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_36,c_0_14]) ).
cnf(c_0_82,hypothesis,
join(meet(X1,X2),meet(X2,meet(X3,join(X1,X2)))) = meet(X2,meet(join(X1,X2),join(X3,meet(X1,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_74]),c_0_76]) ).
cnf(c_0_83,plain,
join(X1,meet(X2,meet(join(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(spm,[status(thm)],[c_0_77,c_0_78]),c_0_21]),c_0_39]),c_0_77]),c_0_21]) ).
cnf(c_0_84,plain,
meet(X1,meet(X2,join(X1,X2))) = meet(X1,X2),
inference(rw,[status(thm)],[c_0_27,c_0_69]) ).
cnf(c_0_85,hypothesis,
meet(join(X1,X2),join(X3,join(X1,X2))) = join(X1,join(X2,meet(X3,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_69]),c_0_80]),c_0_18]) ).
cnf(c_0_86,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_18,c_0_81]),c_0_18]),c_0_18]) ).
cnf(c_0_87,hypothesis,
join(X1,meet(X2,join(X3,meet(X1,X2)))) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_82]),c_0_83]),c_0_77]) ).
cnf(c_0_88,hypothesis,
meet(X1,meet(join(X1,X2),join(X2,X3))) = meet(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_56,c_0_14]) ).
cnf(c_0_89,hypothesis,
meet(X1,join(X2,join(X3,meet(X1,X2)))) = meet(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_90,hypothesis,
join(X1,join(X2,meet(X1,join(X3,X1)))) = join(X2,meet(X1,join(X3,X1))),
inference(spm,[status(thm)],[c_0_86,c_0_69]) ).
cnf(c_0_91,hypothesis,
join(X1,meet(X2,join(meet(X2,X1),X3))) = join(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_87,c_0_61]) ).
cnf(c_0_92,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_31]) ).
cnf(c_0_93,plain,
meet(join(X1,X2),meet(join(X1,meet(X2,X3)),X4)) = meet(join(X1,meet(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_21,c_0_12]) ).
cnf(c_0_94,hypothesis,
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_88,c_0_89]),c_0_88]),c_0_11]),c_0_90]) ).
cnf(c_0_95,hypothesis,
join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(meet(X1,X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_31]),c_0_92]) ).
cnf(c_0_96,hypothesis,
join(meet(X1,X2),meet(X2,X3)) = meet(X2,join(meet(X1,X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_39]),c_0_67]) ).
cnf(c_0_97,plain,
meet(join(X1,meet(X2,X3)),meet(X4,meet(X5,join(X1,X2)))) = meet(X5,meet(join(X1,meet(X2,X3)),X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_93]),c_0_21]) ).
cnf(c_0_98,hypothesis,
meet(X1,join(X2,meet(X3,join(X3,X1)))) = meet(X1,join(X3,X2)),
inference(spm,[status(thm)],[c_0_94,c_0_14]) ).
cnf(c_0_99,hypothesis,
meet(X1,join(meet(X2,X1),X3)) = meet(X1,join(meet(X1,X3),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_95]),c_0_96]) ).
cnf(c_0_100,plain,
meet(X1,meet(X2,join(X3,meet(X2,X1)))) = meet(X2,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_39,c_0_72]),c_0_21]),c_0_97]),c_0_31]),c_0_11]) ).
cnf(c_0_101,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_12,c_0_36]) ).
cnf(c_0_102,hypothesis,
meet(X1,join(meet(X2,X1),X3)) = meet(X1,join(X2,meet(X1,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_21]),c_0_11]),c_0_84]) ).
cnf(c_0_103,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_12,c_0_81]) ).
cnf(c_0_104,plain,
meet(X1,join(X2,meet(join(X2,X3),X1))) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_36]),c_0_39]) ).
cnf(c_0_105,hypothesis,
join(meet(X1,X2),meet(X3,join(X2,meet(X3,X1)))) = meet(join(X1,X2),join(X3,meet(join(X2,X3),X1))),
inference(rw,[status(thm)],[c_0_23,c_0_102]) ).
cnf(c_0_106,plain,
join(X1,meet(X2,meet(join(X2,X1),X3))) = join(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_77,c_0_57]) ).
cnf(c_0_107,plain,
meet(X1,join(X2,meet(join(X3,X2),X1))) = meet(X1,join(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_103]),c_0_81]),c_0_39]) ).
cnf(c_0_108,hypothesis,
join(meet(X1,X2),meet(X3,X2)) = meet(X2,join(meet(X1,X2),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_96]),c_0_21]),c_0_73]),c_0_77]) ).
cnf(c_0_109,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(spm,[status(thm)],[c_0_48,c_0_104]),c_0_48]),c_0_49]),c_0_64]) ).
cnf(c_0_110,hypothesis,
join(X1,meet(X2,join(X1,X3))) = 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_91,c_0_105]),c_0_106]),c_0_107]),c_0_100]),c_0_77]) ).
cnf(c_0_111,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
prove_distributivity ).
cnf(c_0_112,hypothesis,
meet(X1,join(meet(X2,X1),X3)) = meet(X1,join(meet(X3,X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_96]),c_0_108]) ).
cnf(c_0_113,plain,
meet(X1,join(X2,meet(X3,X1))) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_114,negated_conjecture,
meet(a,join(c,meet(a,b))) != meet(a,join(b,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_95]),c_0_14]) ).
cnf(c_0_115,hypothesis,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X3,meet(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_102]),c_0_102]) ).
cnf(c_0_116,plain,
meet(X1,join(X2,meet(X1,join(X3,X2)))) = meet(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_104,c_0_57]) ).
cnf(c_0_117,hypothesis,
join(X1,meet(X2,join(X3,X1))) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[c_0_87,c_0_113]) ).
cnf(c_0_118,negated_conjecture,
meet(a,join(b,meet(a,c))) != meet(a,join(b,c)),
inference(rw,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_119,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_120,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_118,c_0_119])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT020-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 09:43:50 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 3.00/3.16 % Version : CSE_E---1.5
% 3.00/3.16 % Problem : theBenchmark.p
% 3.00/3.16 % Proof found
% 3.00/3.16 % SZS status Theorem for theBenchmark.p
% 3.00/3.16 % SZS output start Proof
% See solution above
% 3.00/3.18 % Total time : 2.592000 s
% 3.00/3.18 % SZS output end Proof
% 3.00/3.18 % Total time : 2.595000 s
%------------------------------------------------------------------------------