TSTP Solution File: KLE044-10 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE044-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n007.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 05:25:50 EDT 2023
% Result : Unsatisfiable 1.71s 1.78s
% Output : CNFRefutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 31
% Syntax : Number of formulae : 108 ( 95 unt; 13 typ; 0 def)
% Number of atoms : 95 ( 94 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 : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 21 ( 8 >; 13 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-4 aty)
% Number of variables : 168 ( 18 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,
addition: ( $i * $i ) > $i ).
tff(decl_26,type,
zero: $i ).
tff(decl_27,type,
multiplication: ( $i * $i ) > $i ).
tff(decl_28,type,
one: $i ).
tff(decl_29,type,
leq: ( $i * $i ) > $i ).
tff(decl_30,type,
true: $i ).
tff(decl_31,type,
star: $i > $i ).
tff(decl_32,type,
sK2_goals_X0: $i ).
tff(decl_33,type,
sK1_goals_X0: $i ).
tff(decl_34,type,
tuple: ( $i * $i ) > $i ).
cnf(additive_associativity,axiom,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
cnf(additive_idempotence,axiom,
addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
cnf(order_1,axiom,
ifeq2(leq(X1,X2),true,addition(X1,X2),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order_1) ).
cnf(star_unfold_right,axiom,
leq(addition(one,multiplication(X1,star(X1))),star(X1)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold_right) ).
cnf(ifeq_axiom_001,axiom,
ifeq2(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(additive_commutativity,axiom,
addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
cnf(order,axiom,
ifeq3(addition(X1,X2),X2,leq(X1,X2),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
cnf(left_distributivity,axiom,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
cnf(star_unfold_left,axiom,
leq(addition(one,multiplication(star(X1),X1)),star(X1)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold_left) ).
cnf(ifeq_axiom,axiom,
ifeq3(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(multiplicative_left_identity,axiom,
multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
cnf(right_distributivity,axiom,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
cnf(multiplicative_right_identity,axiom,
multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
cnf(star_induction_right,axiom,
ifeq(leq(addition(multiplication(X1,X2),X3),X1),true,leq(multiplication(X3,star(X2)),X1),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction_right) ).
cnf(ifeq_axiom_002,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_002) ).
cnf(star_induction_left,axiom,
ifeq(leq(addition(multiplication(X1,X2),X3),X2),true,leq(multiplication(star(X1),X3),X2),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction_left) ).
cnf(multiplicative_associativity,axiom,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
cnf(goals,negated_conjecture,
tuple(leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) != tuple(true,true),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c_0_18,axiom,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
additive_associativity ).
cnf(c_0_19,axiom,
addition(X1,X1) = X1,
additive_idempotence ).
cnf(c_0_20,axiom,
ifeq2(leq(X1,X2),true,addition(X1,X2),X2) = X2,
order_1 ).
cnf(c_0_21,axiom,
leq(addition(one,multiplication(X1,star(X1))),star(X1)) = true,
star_unfold_right ).
cnf(c_0_22,axiom,
ifeq2(X1,X1,X2,X3) = X2,
ifeq_axiom_001 ).
cnf(c_0_23,axiom,
addition(X1,X2) = addition(X2,X1),
additive_commutativity ).
cnf(c_0_24,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_18]),c_0_22]),c_0_23]) ).
cnf(c_0_26,axiom,
ifeq3(addition(X1,X2),X2,leq(X1,X2),true) = true,
order ).
cnf(c_0_27,axiom,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
left_distributivity ).
cnf(c_0_28,axiom,
leq(addition(one,multiplication(star(X1),X1)),star(X1)) = true,
star_unfold_left ).
cnf(c_0_29,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,axiom,
ifeq3(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_31,plain,
ifeq3(multiplication(addition(X1,X2),X3),multiplication(X2,X3),leq(multiplication(X1,X3),multiplication(X2,X3)),true) = true,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,axiom,
multiplication(one,X1) = X1,
multiplicative_left_identity ).
cnf(c_0_33,plain,
addition(one,addition(star(X1),multiplication(star(X1),X1))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_28]),c_0_18]),c_0_22]),c_0_23]) ).
cnf(c_0_34,plain,
addition(one,addition(star(X1),X2)) = addition(star(X1),X2),
inference(spm,[status(thm)],[c_0_18,c_0_29]) ).
cnf(c_0_35,axiom,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
right_distributivity ).
cnf(c_0_36,axiom,
multiplication(X1,one) = X1,
multiplicative_right_identity ).
cnf(c_0_37,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_23,c_0_18]) ).
cnf(c_0_38,plain,
leq(X1,addition(X1,X2)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_24]),c_0_30]) ).
cnf(c_0_39,plain,
leq(X1,multiplication(star(X2),X1)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_29]),c_0_32]),c_0_30]) ).
cnf(c_0_40,plain,
addition(star(X1),multiplication(star(X1),X1)) = star(X1),
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_41,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_23]) ).
cnf(c_0_42,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_37,c_0_19]) ).
cnf(c_0_43,axiom,
ifeq(leq(addition(multiplication(X1,X2),X3),X1),true,leq(multiplication(X3,star(X2)),X1),true) = true,
star_induction_right ).
cnf(c_0_44,plain,
leq(X1,addition(X2,addition(X1,X3))) = true,
inference(spm,[status(thm)],[c_0_38,c_0_37]) ).
cnf(c_0_45,plain,
addition(X1,multiplication(star(X2),X1)) = multiplication(star(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_39]),c_0_22]) ).
cnf(c_0_46,plain,
multiplication(star(X1),addition(X1,one)) = star(X1),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,plain,
addition(star(X1),multiplication(X1,star(X1))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_25]),c_0_18]),c_0_23]),c_0_24]) ).
cnf(c_0_48,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_32]),c_0_23]) ).
cnf(c_0_49,plain,
ifeq(leq(addition(one,multiplication(X1,X2)),X1),true,leq(star(X2),X1),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_32]),c_0_23]) ).
cnf(c_0_50,plain,
leq(X1,X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_19]),c_0_30]) ).
cnf(c_0_51,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom_002 ).
cnf(c_0_52,plain,
leq(X1,addition(X2,multiplication(star(X3),X1))) = true,
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_53,plain,
multiplication(star(X1),addition(one,X1)) = star(X1),
inference(spm,[status(thm)],[c_0_46,c_0_23]) ).
cnf(c_0_54,axiom,
ifeq(leq(addition(multiplication(X1,X2),X3),X2),true,leq(multiplication(star(X1),X3),X2),true) = true,
star_induction_left ).
cnf(c_0_55,plain,
multiplication(addition(X1,one),star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_56,plain,
ifeq3(multiplication(X1,addition(X2,X3)),multiplication(X1,X3),leq(multiplication(X1,X2),multiplication(X1,X3)),true) = true,
inference(spm,[status(thm)],[c_0_26,c_0_35]) ).
cnf(c_0_57,plain,
leq(star(addition(X1,one)),star(X1)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_46]),c_0_29]),c_0_50]),c_0_51]) ).
cnf(c_0_58,plain,
leq(X1,multiplication(star(X2),addition(X3,X1))) = true,
inference(spm,[status(thm)],[c_0_52,c_0_35]) ).
cnf(c_0_59,plain,
multiplication(star(addition(one,X1)),addition(one,X1)) = star(addition(one,X1)),
inference(spm,[status(thm)],[c_0_53,c_0_24]) ).
cnf(c_0_60,plain,
ifeq(leq(multiplication(X1,X2),X2),true,leq(multiplication(star(X1),multiplication(X1,X2)),X2),true) = true,
inference(spm,[status(thm)],[c_0_54,c_0_19]) ).
cnf(c_0_61,plain,
multiplication(addition(one,X1),star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_55,c_0_23]) ).
cnf(c_0_62,plain,
ifeq(leq(addition(X1,multiplication(X2,X3)),X2),true,leq(multiplication(X1,star(X3)),X2),true) = true,
inference(spm,[status(thm)],[c_0_43,c_0_23]) ).
cnf(c_0_63,plain,
leq(X1,multiplication(X1,star(X2))) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_29]),c_0_36]),c_0_30]) ).
cnf(c_0_64,plain,
leq(X1,addition(X2,addition(X3,X1))) = true,
inference(spm,[status(thm)],[c_0_38,c_0_37]) ).
cnf(c_0_65,plain,
addition(star(X1),star(addition(X1,one))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_57]),c_0_22]),c_0_23]) ).
cnf(c_0_66,plain,
leq(X1,star(addition(one,X1))) = true,
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_67,plain,
ifeq2(leq(X1,X2),true,addition(X2,X1),X2) = X2,
inference(spm,[status(thm)],[c_0_20,c_0_23]) ).
cnf(c_0_68,plain,
leq(multiplication(star(addition(one,X1)),star(X1)),star(X1)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_50]),c_0_51]) ).
cnf(c_0_69,axiom,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
multiplicative_associativity ).
cnf(c_0_70,plain,
leq(multiplication(star(X1),star(X1)),star(X1)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_40]),c_0_50]),c_0_51]) ).
cnf(c_0_71,plain,
addition(X1,multiplication(X1,star(X2))) = multiplication(X1,star(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_63]),c_0_22]) ).
cnf(c_0_72,plain,
leq(star(addition(X1,one)),addition(X2,star(X1))) = true,
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_73,plain,
addition(X1,star(addition(one,X1))) = star(addition(one,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_66]),c_0_22]) ).
cnf(c_0_74,plain,
multiplication(star(addition(one,X1)),star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_45]),c_0_22]) ).
cnf(c_0_75,plain,
ifeq(leq(multiplication(X1,X2),X1),true,leq(multiplication(X1,multiplication(X2,star(X2))),X1),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_19]),c_0_69]) ).
cnf(c_0_76,plain,
multiplication(star(X1),multiplication(addition(X1,one),X2)) = multiplication(star(X1),X2),
inference(spm,[status(thm)],[c_0_69,c_0_46]) ).
cnf(c_0_77,plain,
multiplication(star(X1),star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_70]),c_0_71]),c_0_22]) ).
cnf(c_0_78,plain,
leq(star(addition(X1,one)),star(addition(one,X1))) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_18]),c_0_42]) ).
cnf(c_0_79,plain,
ifeq(leq(multiplication(X1,addition(X2,X3)),X1),true,leq(multiplication(X1,multiplication(X3,star(X2))),X1),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_35]),c_0_69]) ).
cnf(c_0_80,plain,
multiplication(star(addition(X1,one)),addition(X1,one)) = star(addition(X1,one)),
inference(spm,[status(thm)],[c_0_53,c_0_42]) ).
cnf(c_0_81,plain,
multiplication(star(addition(X1,one)),star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_74,c_0_23]) ).
cnf(c_0_82,plain,
leq(multiplication(star(X1),star(addition(X1,one))),star(X1)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_46]),c_0_50]),c_0_51]) ).
cnf(c_0_83,plain,
multiplication(addition(star(X1),X2),star(X1)) = addition(star(X1),multiplication(X2,star(X1))),
inference(spm,[status(thm)],[c_0_27,c_0_77]) ).
cnf(c_0_84,plain,
addition(star(addition(one,X1)),star(addition(X1,one))) = star(addition(one,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_78]),c_0_22]) ).
cnf(c_0_85,plain,
leq(star(X1),star(addition(X1,one))) = true,
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_50]),c_0_32]),c_0_51]),c_0_81]) ).
cnf(c_0_86,plain,
multiplication(star(X1),star(addition(X1,one))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_82]),c_0_71]),c_0_22]) ).
cnf(c_0_87,negated_conjecture,
tuple(leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) != tuple(true,true),
goals ).
cnf(c_0_88,plain,
leq(star(addition(one,X1)),star(X1)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_53]),c_0_29]),c_0_50]),c_0_51]) ).
cnf(c_0_89,plain,
multiplication(star(addition(X1,one)),star(addition(one,X1))) = star(addition(one,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_77]),c_0_45]) ).
cnf(c_0_90,plain,
star(addition(X1,one)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_85]),c_0_65]),c_0_22]) ).
cnf(c_0_91,plain,
multiplication(star(X1),star(addition(one,X1))) = star(X1),
inference(spm,[status(thm)],[c_0_86,c_0_23]) ).
cnf(c_0_92,negated_conjecture,
tuple(true,leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) != tuple(true,true),
inference(rw,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_93,plain,
star(addition(one,X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_90]),c_0_91]) ).
cnf(c_0_94,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_50])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE044-10 : TPTP v8.1.2. Released v7.3.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 11:51:13 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.54 start to proof: theBenchmark
% 1.71/1.78 % Version : CSE_E---1.5
% 1.71/1.78 % Problem : theBenchmark.p
% 1.71/1.78 % Proof found
% 1.71/1.78 % SZS status Theorem for theBenchmark.p
% 1.71/1.78 % SZS output start Proof
% See solution above
% 1.71/1.79 % Total time : 1.230000 s
% 1.71/1.79 % SZS output end Proof
% 1.71/1.79 % Total time : 1.232000 s
%------------------------------------------------------------------------------