TSTP Solution File: LAT005-10 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT005-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n012.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 05:59:05 EDT 2023
% Result : Unsatisfiable 36.39s 36.67s
% Output : CNFRefutation 36.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 33
% Syntax : Number of formulae : 144 ( 131 unt; 13 typ; 0 def)
% Number of atoms : 131 ( 130 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 18 ( 6 >; 12 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 236 ( 54 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
ifeq3: ( $i * $i * $i * $i ) > $i ).
tff(decl_23,type,
ifeq2: ( $i * $i * $i * $i ) > $i ).
tff(decl_24,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(decl_25,type,
meet: ( $i * $i ) > $i ).
tff(decl_26,type,
join: ( $i * $i ) > $i ).
tff(decl_27,type,
n0: $i ).
tff(decl_28,type,
n1: $i ).
tff(decl_29,type,
complement: ( $i * $i ) > $i ).
tff(decl_30,type,
true: $i ).
tff(decl_31,type,
r1: $i ).
tff(decl_32,type,
a: $i ).
tff(decl_33,type,
b: $i ).
tff(decl_34,type,
r2: $i ).
cnf(associativity_of_meet,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
cnf(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption1) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
cnf(modular,axiom,
ifeq3(meet(X1,X2),X1,meet(X2,join(X1,X3)),join(X1,meet(X3,X2))) = join(X1,meet(X3,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modular) ).
cnf(ifeq_axiom,axiom,
ifeq3(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(complement_meet,axiom,
ifeq(complement(X1,X2),true,meet(X1,X2),n0) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_meet) ).
cnf(complement_of_a_join_b,hypothesis,
complement(r1,join(a,b)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_a_join_b) ).
cnf(ifeq_axiom_002,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_002) ).
cnf(complement_join,axiom,
ifeq(complement(X1,X2),true,join(X1,X2),n1) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_join) ).
cnf(complement_of_a_meet_b,hypothesis,
complement(r2,meet(a,b)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_a_meet_b) ).
cnf(x_join_1,axiom,
join(X1,n1) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_join_1) ).
cnf(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption2) ).
cnf(x_join_0,axiom,
join(X1,n0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_join_0) ).
cnf(x_meet_0,axiom,
meet(X1,n0) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_meet_0) ).
cnf(associativity_of_join,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_join) ).
cnf(x_meet_1,axiom,
meet(X1,n1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_meet_1) ).
cnf(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_meet) ).
cnf(idempotence_of_join,axiom,
join(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_join) ).
cnf(prove_lemma,negated_conjecture,
r1 != meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lemma) ).
cnf(c_0_20,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_21,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_22,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_23,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_24,axiom,
ifeq3(meet(X1,X2),X1,meet(X2,join(X1,X3)),join(X1,meet(X3,X2))) = join(X1,meet(X3,X2)),
modular ).
cnf(c_0_25,axiom,
ifeq3(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_26,axiom,
ifeq(complement(X1,X2),true,meet(X1,X2),n0) = n0,
complement_meet ).
cnf(c_0_27,hypothesis,
complement(r1,join(a,b)) = true,
complement_of_a_join_b ).
cnf(c_0_28,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom_002 ).
cnf(c_0_29,axiom,
ifeq(complement(X1,X2),true,join(X1,X2),n1) = n1,
complement_join ).
cnf(c_0_30,hypothesis,
complement(r2,meet(a,b)) = true,
complement_of_a_meet_b ).
cnf(c_0_31,axiom,
join(X1,n1) = n1,
x_join_1 ).
cnf(c_0_32,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_33,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_20]) ).
cnf(c_0_34,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_35,plain,
join(X1,meet(X2,join(X1,X3))) = meet(join(X1,X3),join(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_22]),c_0_25]) ).
cnf(c_0_36,hypothesis,
meet(r1,join(a,b)) = n0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_37,axiom,
join(X1,n0) = X1,
x_join_0 ).
cnf(c_0_38,axiom,
meet(X1,n0) = n0,
x_meet_0 ).
cnf(c_0_39,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_40,hypothesis,
join(r2,meet(a,b)) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_28]) ).
cnf(c_0_41,plain,
join(n1,X1) = n1,
inference(spm,[status(thm)],[c_0_31,c_0_23]) ).
cnf(c_0_42,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_21]) ).
cnf(c_0_43,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_20,c_0_22]) ).
cnf(c_0_44,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_45,hypothesis,
meet(join(r1,a),join(a,b)) = a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_23]),c_0_21]) ).
cnf(c_0_46,plain,
meet(n0,X1) = n0,
inference(spm,[status(thm)],[c_0_38,c_0_21]) ).
cnf(c_0_47,hypothesis,
join(r2,join(meet(a,b),X1)) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_48,plain,
join(meet(X1,X2),meet(join(X1,X3),X2)) = meet(join(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_23]) ).
cnf(c_0_49,hypothesis,
meet(b,join(r1,a)) = meet(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_21]),c_0_21]) ).
cnf(c_0_50,plain,
join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_32,c_0_39]) ).
cnf(c_0_51,plain,
meet(X1,meet(X2,X1)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_32]),c_0_20]) ).
cnf(c_0_52,hypothesis,
meet(r1,meet(join(a,b),X1)) = n0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_36]),c_0_46]) ).
cnf(c_0_53,plain,
ifeq3(meet(X1,meet(X2,X3)),meet(X1,X2),meet(X3,join(meet(X1,X2),X4)),join(meet(X1,X2),meet(X4,X3))) = join(meet(X1,X2),meet(X4,X3)),
inference(spm,[status(thm)],[c_0_24,c_0_20]) ).
cnf(c_0_54,hypothesis,
join(r2,meet(b,join(a,X1))) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_21]) ).
cnf(c_0_55,plain,
ifeq3(meet(X1,X2),X1,meet(X2,join(X1,X3)),join(X1,meet(X2,X3))) = join(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_56,plain,
join(meet(X1,X2),meet(X1,meet(X2,X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_32,c_0_20]) ).
cnf(c_0_57,hypothesis,
meet(b,meet(join(r1,a),X1)) = meet(a,meet(b,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_49]),c_0_20]) ).
cnf(c_0_58,plain,
meet(join(X1,X2),join(X2,meet(join(X1,X2),X3))) = join(X2,meet(join(X1,X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_50]),c_0_21]) ).
cnf(c_0_59,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_51]),c_0_43]) ).
cnf(c_0_60,hypothesis,
meet(r1,meet(X1,join(a,b))) = n0,
inference(spm,[status(thm)],[c_0_52,c_0_21]) ).
cnf(c_0_61,axiom,
meet(X1,n1) = X1,
x_meet_1 ).
cnf(c_0_62,plain,
meet(X1,meet(X2,join(X3,meet(X1,X2)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_34]) ).
cnf(c_0_63,plain,
join(meet(X1,X2),meet(X3,X1)) = meet(X1,join(meet(X1,X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_51]),c_0_25]) ).
cnf(c_0_64,hypothesis,
join(r2,join(meet(b,join(a,X1)),X2)) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_54]),c_0_41]) ).
cnf(c_0_65,plain,
meet(X1,join(meet(X1,X2),meet(X2,X3))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_20]),c_0_51]),c_0_25]) ).
cnf(c_0_66,hypothesis,
meet(b,join(a,meet(join(r1,a),X1))) = meet(a,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).
cnf(c_0_67,hypothesis,
meet(r1,b) = n0,
inference(spm,[status(thm)],[c_0_60,c_0_34]) ).
cnf(c_0_68,plain,
meet(n1,X1) = X1,
inference(spm,[status(thm)],[c_0_61,c_0_21]) ).
cnf(c_0_69,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_42,c_0_62]),c_0_63]),c_0_23]) ).
cnf(c_0_70,hypothesis,
join(r2,meet(b,join(meet(b,join(a,X1)),X2))) = n1,
inference(spm,[status(thm)],[c_0_64,c_0_63]) ).
cnf(c_0_71,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_39,c_0_32]) ).
cnf(c_0_72,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_22]),c_0_39]) ).
cnf(c_0_73,hypothesis,
meet(X1,join(meet(X1,b),meet(a,b))) = meet(X1,b),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_74,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_75,hypothesis,
meet(r1,meet(b,X1)) = n0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_67]),c_0_46]) ).
cnf(c_0_76,plain,
ifeq3(meet(X1,X2),X1,X2,join(X1,X2)) = join(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_68]),c_0_31]),c_0_61]) ).
cnf(c_0_77,hypothesis,
meet(b,join(meet(b,r2),meet(b,join(a,X1)))) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_61]),c_0_21]),c_0_23]) ).
cnf(c_0_78,plain,
join(X1,join(X2,meet(X1,X3))) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_71]) ).
cnf(c_0_79,hypothesis,
meet(X1,join(meet(a,b),meet(X1,b))) = meet(X1,b),
inference(spm,[status(thm)],[c_0_73,c_0_23]) ).
cnf(c_0_80,hypothesis,
meet(b,meet(X1,meet(X2,r1))) = n0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_38]),c_0_20]) ).
cnf(c_0_81,plain,
join(X1,meet(join(X1,X2),X3)) = meet(join(X1,X2),join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_22]),c_0_25]) ).
cnf(c_0_82,hypothesis,
join(meet(b,r2),meet(b,join(a,X1))) = b,
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_76,c_0_77]),c_0_78]),c_0_32]),c_0_25]),c_0_78]),c_0_32]) ).
cnf(c_0_83,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_84,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[c_0_23,c_0_39]) ).
cnf(c_0_85,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_39,c_0_42]) ).
cnf(c_0_86,plain,
ifeq3(meet(join(X1,X2),X3),join(X1,X2),meet(X3,join(X1,join(X2,X4))),join(X1,join(X2,meet(X4,X3)))) = join(X1,join(X2,meet(X4,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_39]),c_0_39]) ).
cnf(c_0_87,hypothesis,
meet(X1,join(meet(a,b),meet(b,X1))) = meet(b,X1),
inference(spm,[status(thm)],[c_0_79,c_0_21]) ).
cnf(c_0_88,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_20,c_0_34]) ).
cnf(c_0_89,hypothesis,
meet(join(r1,a),join(r1,b)) = join(r1,meet(a,b)),
inference(spm,[status(thm)],[c_0_35,c_0_49]) ).
cnf(c_0_90,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_91,hypothesis,
ifeq3(meet(X1,b),X1,meet(b,join(X1,meet(X2,meet(X3,r1)))),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_80]),c_0_37]),c_0_37]) ).
cnf(c_0_92,hypothesis,
join(meet(b,r2),meet(b,X1)) = meet(b,join(meet(b,r2),X1)),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_93,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_83]) ).
cnf(c_0_94,plain,
join(X1,join(X2,X3)) = join(X3,join(X2,X1)),
inference(spm,[status(thm)],[c_0_84,c_0_23]) ).
cnf(c_0_95,plain,
join(meet(X1,X2),join(meet(X2,X1),X3)) = join(meet(X1,X2),X3),
inference(spm,[status(thm)],[c_0_85,c_0_51]) ).
cnf(c_0_96,plain,
join(meet(X1,X2),meet(X2,X1)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_42,c_0_51]) ).
cnf(c_0_97,hypothesis,
ifeq3(meet(b,join(X1,X2)),join(X1,X2),meet(b,join(X1,join(X2,r1))),join(X1,X2)) = join(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_67]),c_0_37]),c_0_37]),c_0_21]) ).
cnf(c_0_98,hypothesis,
meet(X1,join(meet(X1,X2),meet(b,X2))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_65,c_0_87]) ).
cnf(c_0_99,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_100,plain,
ifeq3(meet(X1,X2),X1,meet(X2,join(X3,X1)),join(X1,meet(X3,X2))) = join(X1,meet(X3,X2)),
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_101,hypothesis,
meet(a,join(r1,meet(a,b))) = meet(a,join(r1,b)),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_102,hypothesis,
meet(r1,a) = n0,
inference(spm,[status(thm)],[c_0_60,c_0_22]) ).
cnf(c_0_103,plain,
ifeq3(meet(X1,X2),X1,meet(X2,meet(join(meet(X1,X2),X3),join(X1,X4))),join(X1,meet(X4,meet(X2,join(meet(X1,X2),X3))))) = join(X1,meet(X4,meet(X2,join(meet(X1,X2),X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_90]),c_0_20]) ).
cnf(c_0_104,hypothesis,
meet(b,join(meet(b,r2),meet(X1,r1))) = meet(b,r2),
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_91,c_0_92]),c_0_20]),c_0_21]),c_0_93]),c_0_93]),c_0_25]) ).
cnf(c_0_105,plain,
join(meet(X1,X2),X3) = join(X3,meet(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96]) ).
cnf(c_0_106,hypothesis,
meet(b,join(r1,meet(b,X1))) = meet(b,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_99]),c_0_23]),c_0_72]),c_0_23]),c_0_99]),c_0_25]),c_0_99]) ).
cnf(c_0_107,hypothesis,
meet(r2,meet(a,b)) = n0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_30]),c_0_28]) ).
cnf(c_0_108,hypothesis,
meet(a,join(r1,b)) = meet(a,b),
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_100,c_0_101]),c_0_20]),c_0_21]),c_0_93]),c_0_102]),c_0_37]),c_0_25]),c_0_102]),c_0_37]) ).
cnf(c_0_109,hypothesis,
ifeq3(meet(X1,join(r1,a)),X1,meet(join(r1,a),meet(join(X1,b),join(meet(X1,join(r1,a)),X2))),join(X1,meet(a,meet(b,join(meet(X1,join(r1,a)),X2))))) = join(X1,meet(a,meet(b,join(meet(X1,join(r1,a)),X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_57]),c_0_21]) ).
cnf(c_0_110,hypothesis,
meet(b,join(meet(r1,X1),meet(b,r2))) = meet(b,r2),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_111,hypothesis,
meet(join(r1,b),join(r1,meet(b,X1))) = join(r1,meet(b,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_106]),c_0_21]) ).
cnf(c_0_112,hypothesis,
meet(a,meet(b,r2)) = n0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_107]),c_0_38]),c_0_20]) ).
cnf(c_0_113,hypothesis,
meet(a,meet(join(r1,b),X1)) = meet(a,meet(b,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_108]),c_0_20]) ).
cnf(c_0_114,plain,
join(X1,meet(X2,join(X3,X1))) = meet(join(X3,X1),join(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_34]),c_0_25]) ).
cnf(c_0_115,plain,
meet(X1,meet(X2,join(meet(join(X3,X1),X2),X4))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_90]),c_0_88]) ).
cnf(c_0_116,hypothesis,
meet(join(r1,a),join(r1,meet(b,r2))) = r1,
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_109,c_0_110]),c_0_22]),c_0_22]),c_0_111]),c_0_112]),c_0_37]),c_0_25]),c_0_112]),c_0_37]) ).
cnf(c_0_117,hypothesis,
meet(a,join(r1,meet(b,X1))) = meet(a,meet(b,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_111]),c_0_106]) ).
cnf(c_0_118,plain,
join(meet(X1,meet(X2,X3)),meet(X4,meet(X1,X2))) = meet(X1,meet(X2,join(meet(X1,meet(X2,X3)),X4))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_56]),c_0_20]) ).
cnf(c_0_119,hypothesis,
meet(a,meet(join(r1,meet(b,r2)),join(r1,X1))) = n0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_117]),c_0_112]) ).
cnf(c_0_120,plain,
join(n0,X1) = X1,
inference(spm,[status(thm)],[c_0_37,c_0_23]) ).
cnf(c_0_121,plain,
ifeq3(meet(X1,X2),X1,meet(X2,join(X1,meet(X3,X4))),join(X1,meet(X3,meet(X4,X2)))) = join(X1,meet(X3,meet(X4,X2))),
inference(spm,[status(thm)],[c_0_24,c_0_20]) ).
cnf(c_0_122,plain,
meet(X1,meet(X2,meet(X3,join(meet(X1,X3),X4)))) = meet(X2,meet(X1,X3)),
inference(spm,[status(thm)],[c_0_33,c_0_90]) ).
cnf(c_0_123,hypothesis,
meet(a,meet(join(r1,meet(b,r2)),X1)) = n0,
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_118,c_0_119]),c_0_117]),c_0_112]),c_0_38]),c_0_99]),c_0_120]) ).
cnf(c_0_124,plain,
join(X1,meet(X2,meet(X3,join(X1,X4)))) = meet(join(X1,X4),join(X1,meet(X2,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_22]),c_0_25]) ).
cnf(c_0_125,hypothesis,
meet(a,meet(X1,join(r1,meet(b,r2)))) = n0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_38]) ).
cnf(c_0_126,negated_conjecture,
r1 != meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))),
prove_lemma ).
cnf(c_0_127,hypothesis,
meet(join(r1,meet(b,r2)),join(r1,meet(a,X1))) = r1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_37]) ).
cnf(c_0_128,negated_conjecture,
meet(join(r1,meet(a,r2)),join(r1,meet(b,r2))) != r1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_21]),c_0_21]),c_0_21]) ).
cnf(c_0_129,hypothesis,
meet(join(r1,meet(a,X1)),join(r1,meet(b,r2))) = r1,
inference(spm,[status(thm)],[c_0_21,c_0_127]) ).
cnf(c_0_130,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_128,c_0_129])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT005-10 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.16/0.34 % Computer : n012.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Thu Aug 24 05:21:26 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 36.39/36.67 % Version : CSE_E---1.5
% 36.39/36.67 % Problem : theBenchmark.p
% 36.39/36.67 % Proof found
% 36.39/36.67 % SZS status Theorem for theBenchmark.p
% 36.39/36.67 % SZS output start Proof
% See solution above
% 36.64/36.68 % Total time : 36.089000 s
% 36.64/36.68 % SZS output end Proof
% 36.64/36.68 % Total time : 36.094000 s
%------------------------------------------------------------------------------