TSTP Solution File: KLE024+2 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE024+2 : 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 : n013.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 05:25:43 EDT 2023
% Result : Theorem 1.54s 1.62s
% Output : CNFRefutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 23
% Syntax : Number of formulae : 66 ( 29 unt; 12 typ; 0 def)
% Number of atoms : 105 ( 58 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 84 ( 33 ~; 29 |; 13 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 85 ( 2 sgn; 46 !; 1 ?; 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 ).
fof(test_2,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( multiplication(X4,X5) = zero
& multiplication(X5,X4) = zero
& addition(X4,X5) = one ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
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_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(test_3,axiom,
! [X4,X5] :
( test(X4)
=> ( c(X4) = X5
<=> complement(X4,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(goals,conjecture,
! [X4,X5,X6] :
( ( test(X5)
& test(X6) )
=> ( addition(multiplication(X4,c(X6)),multiplication(c(X5),X4)) = multiplication(c(X5),X4)
=> multiplication(multiplication(X5,X4),c(X6)) = 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(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_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(c_0_11,plain,
! [X33,X34] :
( ( multiplication(X33,X34) = zero
| ~ complement(X34,X33) )
& ( multiplication(X34,X33) = zero
| ~ complement(X34,X33) )
& ( addition(X33,X34) = one
| ~ complement(X34,X33) )
& ( multiplication(X33,X34) != zero
| multiplication(X34,X33) != zero
| addition(X33,X34) != one
| complement(X34,X33) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])]) ).
fof(c_0_12,plain,
! [X29,X31,X32] :
( ( ~ test(X29)
| complement(esk1_1(X29),X29) )
& ( ~ complement(X32,X31)
| test(X31) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[test_1])])])])]) ).
fof(c_0_13,plain,
! [X22,X23,X24] : multiplication(addition(X22,X23),X24) = addition(multiplication(X22,X24),multiplication(X23,X24)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_14,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X12] : addition(X12,zero) = X12,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_17,plain,
! [X35,X36] :
( ( c(X35) != X36
| complement(X35,X36)
| ~ test(X35) )
& ( ~ complement(X35,X36)
| c(X35) = X36
| ~ test(X35) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])]) ).
cnf(c_0_18,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( multiplication(esk1_1(X1),X1) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_22,plain,
! [X18] : multiplication(one,X18) = X18,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_23,negated_conjecture,
~ ! [X4,X5,X6] :
( ( test(X5)
& test(X6) )
=> ( addition(multiplication(X4,c(X6)),multiplication(c(X5),X4)) = multiplication(c(X5),X4)
=> multiplication(multiplication(X5,X4),c(X6)) = zero ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_24,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
( multiplication(addition(X1,esk1_1(X2)),X2) = multiplication(X1,X2)
| ~ test(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_26,plain,
( addition(X1,esk1_1(X1)) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_27,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_28,negated_conjecture,
( test(esk3_0)
& test(esk4_0)
& addition(multiplication(esk2_0,c(esk4_0)),multiplication(c(esk3_0),esk2_0)) = multiplication(c(esk3_0),esk2_0)
& multiplication(multiplication(esk3_0,esk2_0),c(esk4_0)) != zero ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).
fof(c_0_29,plain,
! [X14,X15,X16] : multiplication(X14,multiplication(X15,X16)) = multiplication(multiplication(X14,X15),X16),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_30,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( multiplication(X1,X1) = X1
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_32,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_33,plain,
! [X27,X28] :
( ( ~ leq(X27,X28)
| addition(X27,X28) = X28 )
& ( addition(X27,X28) != X28
| leq(X27,X28) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(c_0_34,plain,
! [X19,X20,X21] : multiplication(X19,addition(X20,X21)) = addition(multiplication(X19,X20),multiplication(X19,X21)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_35,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
( multiplication(X1,c(X1)) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_30]) ).
cnf(c_0_37,negated_conjecture,
multiplication(esk3_0,esk3_0) = esk3_0,
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,plain,
( multiplication(X1,multiplication(X2,c(multiplication(X1,X2)))) = zero
| ~ test(multiplication(X1,X2)) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
multiplication(esk3_0,multiplication(esk3_0,X1)) = multiplication(esk3_0,X1),
inference(spm,[status(thm)],[c_0_35,c_0_37]) ).
fof(c_0_42,plain,
! [X26] : multiplication(zero,X26) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_43,plain,
( leq(multiplication(X1,X2),multiplication(X1,X3))
| multiplication(X1,addition(X2,X3)) != multiplication(X1,X3) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,negated_conjecture,
addition(multiplication(esk2_0,c(esk4_0)),multiplication(c(esk3_0),esk2_0)) = multiplication(c(esk3_0),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_45,negated_conjecture,
multiplication(esk3_0,c(esk3_0)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_37]),c_0_41]),c_0_32])]) ).
cnf(c_0_46,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_47,negated_conjecture,
leq(multiplication(X1,multiplication(esk2_0,c(esk4_0))),multiplication(X1,multiplication(c(esk3_0),esk2_0))),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,negated_conjecture,
multiplication(esk3_0,multiplication(c(esk3_0),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_45]),c_0_46]) ).
cnf(c_0_49,negated_conjecture,
multiplication(multiplication(esk3_0,esk2_0),c(esk4_0)) != zero,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_50,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_51,negated_conjecture,
leq(multiplication(esk3_0,multiplication(esk2_0,c(esk4_0))),zero),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,negated_conjecture,
multiplication(esk3_0,multiplication(esk2_0,c(esk4_0))) != zero,
inference(rw,[status(thm)],[c_0_49,c_0_35]) ).
cnf(c_0_53,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_20]),c_0_52]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : KLE024+2 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n013.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 : Tue Aug 29 12:00:31 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 1.54/1.62 % Version : CSE_E---1.5
% 1.54/1.62 % Problem : theBenchmark.p
% 1.54/1.62 % Proof found
% 1.54/1.62 % SZS status Theorem for theBenchmark.p
% 1.54/1.62 % SZS output start Proof
% See solution above
% 1.54/1.62 % Total time : 1.053000 s
% 1.54/1.62 % SZS output end Proof
% 1.54/1.62 % Total time : 1.057000 s
%------------------------------------------------------------------------------