TSTP Solution File: KLE035+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE035+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 : n011.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 05:25:47 EDT 2023
% Result : Theorem 0.21s 0.63s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 21
% Syntax : Number of formulae : 53 ( 33 unt; 13 typ; 0 def)
% Number of atoms : 58 ( 30 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 26 ( 8 ~; 4 |; 11 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 7 >; 4 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn; 38 !; 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,
test: $i > $o ).
tff(decl_28,type,
complement: ( $i * $i ) > $o ).
tff(decl_29,type,
c: $i > $i ).
tff(decl_30,type,
esk1_1: $i > $i ).
tff(decl_31,type,
esk2_0: $i ).
tff(decl_32,type,
esk3_0: $i ).
tff(decl_33,type,
esk4_0: $i ).
tff(decl_34,type,
esk5_0: $i ).
fof(goals,conjecture,
! [X4,X5,X6,X7] :
( ( test(X7)
& test(X6)
& leq(multiplication(multiplication(X6,X4),c(X7)),zero)
& leq(multiplication(multiplication(X6,X5),c(X7)),zero) )
=> leq(multiplication(multiplication(X6,addition(X4,X5)),c(X7)),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
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(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(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(c_0_8,negated_conjecture,
~ ! [X4,X5,X6,X7] :
( ( test(X7)
& test(X6)
& leq(multiplication(multiplication(X6,X4),c(X7)),zero)
& leq(multiplication(multiplication(X6,X5),c(X7)),zero) )
=> leq(multiplication(multiplication(X6,addition(X4,X5)),c(X7)),zero) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_9,negated_conjecture,
( test(esk5_0)
& test(esk4_0)
& leq(multiplication(multiplication(esk4_0,esk2_0),c(esk5_0)),zero)
& leq(multiplication(multiplication(esk4_0,esk3_0),c(esk5_0)),zero)
& ~ leq(multiplication(multiplication(esk4_0,addition(esk2_0,esk3_0)),c(esk5_0)),zero) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_10,plain,
! [X15,X16,X17] : multiplication(X15,multiplication(X16,X17)) = multiplication(multiplication(X15,X16),X17),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_11,plain,
! [X28,X29] :
( ( ~ leq(X28,X29)
| addition(X28,X29) = X29 )
& ( addition(X28,X29) != X29
| leq(X28,X29) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
cnf(c_0_12,negated_conjecture,
leq(multiplication(multiplication(esk4_0,esk3_0),c(esk5_0)),zero),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X13] : addition(X13,zero) = X13,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_15,negated_conjecture,
leq(multiplication(multiplication(esk4_0,esk2_0),c(esk5_0)),zero),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_16,plain,
! [X20,X21,X22] : multiplication(X20,addition(X21,X22)) = addition(multiplication(X20,X21),multiplication(X20,X22)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_17,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
leq(multiplication(esk4_0,multiplication(esk3_0,c(esk5_0))),zero),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
leq(multiplication(esk4_0,multiplication(esk2_0,c(esk5_0))),zero),
inference(rw,[status(thm)],[c_0_15,c_0_13]) ).
fof(c_0_21,plain,
! [X23,X24,X25] : multiplication(addition(X23,X24),X25) = addition(multiplication(X23,X25),multiplication(X24,X25)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_22,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
multiplication(esk4_0,multiplication(esk3_0,c(esk5_0))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_24,negated_conjecture,
multiplication(esk4_0,multiplication(esk2_0,c(esk5_0))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_20]),c_0_19]) ).
fof(c_0_25,plain,
! [X8,X9] : addition(X8,X9) = addition(X9,X8),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_26,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,negated_conjecture,
multiplication(esk4_0,addition(X1,multiplication(esk3_0,c(esk5_0)))) = multiplication(esk4_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_19]) ).
cnf(c_0_28,negated_conjecture,
multiplication(esk4_0,addition(X1,multiplication(esk2_0,c(esk5_0)))) = multiplication(esk4_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_24]),c_0_19]) ).
cnf(c_0_29,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_30,plain,
! [X14] : addition(X14,X14) = X14,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_31,negated_conjecture,
~ leq(multiplication(multiplication(esk4_0,addition(esk2_0,esk3_0)),c(esk5_0)),zero),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_32,negated_conjecture,
addition(multiplication(esk4_0,X1),multiplication(X2,addition(X1,multiplication(esk3_0,c(esk5_0))))) = multiplication(addition(esk4_0,X2),addition(X1,multiplication(esk3_0,c(esk5_0)))),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
multiplication(esk4_0,addition(multiplication(esk2_0,c(esk5_0)),X1)) = multiplication(esk4_0,X1),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_36,negated_conjecture,
~ leq(multiplication(esk4_0,multiplication(addition(esk2_0,esk3_0),c(esk5_0))),zero),
inference(rw,[status(thm)],[c_0_31,c_0_13]) ).
cnf(c_0_37,negated_conjecture,
multiplication(esk4_0,multiplication(addition(esk2_0,esk3_0),c(esk5_0))) = zero,
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_32,c_0_33]),c_0_24]),c_0_23]),c_0_34]),c_0_34]),c_0_26]) ).
cnf(c_0_38,plain,
leq(X1,X1),
inference(spm,[status(thm)],[c_0_35,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KLE035+1 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n011.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
% 0.20/0.34 % WCLimit : 300
% 0.20/0.34 % DateTime : Tue Aug 29 11:54:56 EDT 2023
% 0.20/0.34 % CPUTime :
% 0.21/0.56 start to proof: theBenchmark
% 0.21/0.63 % Version : CSE_E---1.5
% 0.21/0.63 % Problem : theBenchmark.p
% 0.21/0.63 % Proof found
% 0.21/0.63 % SZS status Theorem for theBenchmark.p
% 0.21/0.63 % SZS output start Proof
% See solution above
% 0.21/0.64 % Total time : 0.065000 s
% 0.21/0.64 % SZS output end Proof
% 0.21/0.64 % Total time : 0.068000 s
%------------------------------------------------------------------------------