TSTP Solution File: KLE064+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE064+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n024.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 05:25:55 EDT 2023
% Result : Theorem 0.65s 0.73s
% Output : CNFRefutation 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 20
% Syntax : Number of formulae : 78 ( 67 unt; 8 typ; 0 def)
% Number of atoms : 73 ( 72 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 0 |; 1 &)
% ( 0 <=>; 1 =>; 1 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 96 ( 5 sgn; 44 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
addition: ( $i * $i ) > $i ).
tff(decl_23,type,
zero: $i ).
tff(decl_24,type,
multiplication: ( $i * $i ) > $i ).
tff(decl_25,type,
one: $i ).
tff(decl_26,type,
leq: ( $i * $i ) > $o ).
tff(decl_27,type,
domain: $i > $i ).
tff(decl_28,type,
esk1_0: $i ).
tff(decl_29,type,
esk2_0: $i ).
fof(goals,conjecture,
! [X4,X5] :
( addition(X4,multiplication(domain(X5),X4)) = multiplication(domain(X5),X4)
<= addition(domain(X4),domain(X5)) = domain(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(domain5,axiom,
! [X4,X5] : domain(addition(X4,X5)) = addition(domain(X4),domain(X5)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain5) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(domain1,axiom,
! [X4] : addition(X4,multiplication(domain(X4),X4)) = multiplication(domain(X4),X4),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain1) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(domain3,axiom,
! [X4] : addition(domain(X4),one) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain3) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(domain2,axiom,
! [X4,X5] : domain(multiplication(X4,X5)) = domain(multiplication(X4,domain(X5))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain2) ).
fof(c_0_12,negated_conjecture,
~ ! [X4,X5] :
( addition(domain(X4),domain(X5)) = domain(X5)
=> addition(X4,multiplication(domain(X5),X4)) = multiplication(domain(X5),X4) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goals])]) ).
fof(c_0_13,negated_conjecture,
( addition(domain(esk1_0),domain(esk2_0)) = domain(esk2_0)
& addition(esk1_0,multiplication(domain(esk2_0),esk1_0)) != multiplication(domain(esk2_0),esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_14,plain,
! [X32,X33] : domain(addition(X32,X33)) = addition(domain(X32),domain(X33)),
inference(variable_rename,[status(thm)],[domain5]) ).
fof(c_0_15,plain,
! [X8,X9,X10] : addition(X10,addition(X9,X8)) = addition(addition(X10,X9),X8),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_16,plain,
! [X12] : addition(X12,X12) = X12,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_17,plain,
! [X28] : addition(X28,multiplication(domain(X28),X28)) = multiplication(domain(X28),X28),
inference(variable_rename,[status(thm)],[domain1]) ).
cnf(c_0_18,negated_conjecture,
addition(domain(esk1_0),domain(esk2_0)) = domain(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
domain(addition(X1,X2)) = addition(domain(X1),domain(X2)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_22,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_23,plain,
! [X21,X22,X23] : multiplication(addition(X21,X22),X23) = addition(multiplication(X21,X23),multiplication(X22,X23)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_24,plain,
! [X17] : multiplication(one,X17) = X17,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_25,plain,
! [X31] : addition(domain(X31),one) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_26,plain,
! [X18,X19,X20] : multiplication(X18,addition(X19,X20)) = addition(multiplication(X18,X19),multiplication(X18,X20)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_27,plain,
! [X16] : multiplication(X16,one) = X16,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_28,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_29,negated_conjecture,
domain(addition(esk1_0,esk2_0)) = domain(esk2_0),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_30,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_31,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_32,plain,
! [X29,X30] : domain(multiplication(X29,X30)) = domain(multiplication(X29,domain(X30))),
inference(variable_rename,[status(thm)],[domain2]) ).
cnf(c_0_33,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_34,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_35,plain,
addition(domain(X1),one) = one,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_36,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_37,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_38,negated_conjecture,
addition(esk1_0,addition(esk2_0,multiplication(domain(esk2_0),addition(esk1_0,esk2_0)))) = multiplication(domain(esk2_0),addition(esk1_0,esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_20]) ).
cnf(c_0_39,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_40,plain,
domain(multiplication(X1,X2)) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_31]) ).
cnf(c_0_42,plain,
addition(one,domain(X1)) = one,
inference(rw,[status(thm)],[c_0_35,c_0_31]) ).
cnf(c_0_43,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,negated_conjecture,
addition(esk1_0,multiplication(domain(esk2_0),addition(esk1_0,esk2_0))) = multiplication(domain(esk2_0),addition(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_30,c_0_38]) ).
cnf(c_0_45,negated_conjecture,
addition(esk2_0,multiplication(domain(esk2_0),addition(esk1_0,esk2_0))) = multiplication(domain(esk2_0),addition(esk1_0,esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_38]),c_0_20]),c_0_21]) ).
cnf(c_0_46,plain,
domain(domain(X1)) = domain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_34]),c_0_34]) ).
cnf(c_0_47,plain,
multiplication(domain(X1),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_41]),c_0_31]),c_0_42]),c_0_34]) ).
cnf(c_0_48,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_49,plain,
addition(X1,multiplication(X1,domain(X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_42]),c_0_37]) ).
cnf(c_0_50,negated_conjecture,
addition(esk1_0,addition(multiplication(domain(esk2_0),addition(esk1_0,esk2_0)),X1)) = addition(multiplication(domain(esk2_0),addition(esk1_0,esk2_0)),X1),
inference(spm,[status(thm)],[c_0_20,c_0_44]) ).
cnf(c_0_51,negated_conjecture,
addition(esk2_0,addition(multiplication(domain(esk2_0),addition(esk1_0,esk2_0)),X1)) = addition(multiplication(domain(esk2_0),addition(esk1_0,esk2_0)),X1),
inference(spm,[status(thm)],[c_0_20,c_0_45]) ).
cnf(c_0_52,negated_conjecture,
domain(multiplication(X1,addition(esk1_0,esk2_0))) = domain(multiplication(X1,esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_29]),c_0_40]) ).
cnf(c_0_53,plain,
addition(domain(X1),multiplication(domain(X1),domain(X1))) = multiplication(domain(X1),domain(X1)),
inference(spm,[status(thm)],[c_0_28,c_0_46]) ).
cnf(c_0_54,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_31]) ).
cnf(c_0_55,plain,
multiplication(addition(domain(X1),X2),X1) = addition(X1,multiplication(X2,X1)),
inference(spm,[status(thm)],[c_0_33,c_0_47]) ).
cnf(c_0_56,plain,
addition(X1,multiplication(domain(X2),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_34]),c_0_34]) ).
cnf(c_0_57,negated_conjecture,
addition(esk1_0,multiplication(domain(esk2_0),addition(esk1_0,addition(esk2_0,X1)))) = multiplication(domain(esk2_0),addition(esk1_0,addition(esk2_0,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_36]),c_0_20]),c_0_20]) ).
cnf(c_0_58,negated_conjecture,
addition(esk2_0,multiplication(domain(multiplication(domain(esk2_0),esk2_0)),multiplication(domain(esk2_0),addition(esk1_0,esk2_0)))) = multiplication(domain(multiplication(domain(esk2_0),esk2_0)),multiplication(domain(esk2_0),addition(esk1_0,esk2_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_28]),c_0_52]),c_0_52]) ).
cnf(c_0_59,negated_conjecture,
addition(esk1_0,multiplication(domain(multiplication(domain(esk2_0),esk2_0)),multiplication(domain(esk2_0),addition(esk1_0,esk2_0)))) = multiplication(domain(multiplication(domain(esk2_0),esk2_0)),multiplication(domain(esk2_0),addition(esk1_0,esk2_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_28]),c_0_52]),c_0_52]) ).
cnf(c_0_60,plain,
multiplication(domain(X1),domain(X1)) = domain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54]),c_0_31]),c_0_42]),c_0_37]) ).
cnf(c_0_61,negated_conjecture,
multiplication(domain(esk2_0),addition(esk1_0,esk2_0)) = addition(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_47,c_0_29]) ).
cnf(c_0_62,plain,
multiplication(domain(X1),addition(X2,X1)) = addition(X1,multiplication(domain(X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_47]),c_0_31]) ).
cnf(c_0_63,negated_conjecture,
addition(esk1_0,multiplication(domain(esk2_0),esk1_0)) != multiplication(domain(esk2_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_64,plain,
multiplication(domain(addition(X1,X2)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_19]),c_0_56]) ).
cnf(c_0_65,negated_conjecture,
addition(esk1_0,multiplication(domain(esk2_0),multiplication(domain(multiplication(domain(esk2_0),esk2_0)),multiplication(domain(esk2_0),addition(esk1_0,esk2_0))))) = multiplication(domain(esk2_0),multiplication(domain(multiplication(domain(esk2_0),esk2_0)),multiplication(domain(esk2_0),addition(esk1_0,esk2_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_59]) ).
cnf(c_0_66,plain,
domain(multiplication(domain(X1),X1)) = domain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_60]),c_0_46]) ).
cnf(c_0_67,negated_conjecture,
addition(esk2_0,multiplication(domain(esk2_0),esk1_0)) = addition(esk1_0,esk2_0),
inference(rw,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_68,negated_conjecture,
multiplication(domain(esk2_0),esk1_0) != esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_41]),c_0_31]),c_0_42]),c_0_34]) ).
cnf(c_0_69,negated_conjecture,
$false,
inference(sr,[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_64,c_0_65]),c_0_66]),c_0_62]),c_0_67]),c_0_62]),c_0_67]),c_0_62]),c_0_67]),c_0_29]),c_0_68]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE064+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 11:23:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.58 start to proof: theBenchmark
% 0.65/0.73 % Version : CSE_E---1.5
% 0.65/0.73 % Problem : theBenchmark.p
% 0.65/0.73 % Proof found
% 0.65/0.73 % SZS status Theorem for theBenchmark.p
% 0.65/0.73 % SZS output start Proof
% See solution above
% 0.65/0.73 % Total time : 0.144000 s
% 0.65/0.73 % SZS output end Proof
% 0.65/0.73 % Total time : 0.147000 s
%------------------------------------------------------------------------------