%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS145+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:46:08 AM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 4
% Syntax : Number of formulae : 158 ( 15 unt; 0 def)
% Number of atoms : 791 ( 192 equ)
% Maximal formula atoms : 106 ( 5 avg)
% Number of connectives : 985 ( 352 ~; 566 |; 58 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 176 ( 2 sgn 61 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_0,axiom,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
file('theBenchmark.p',axiom_0) ).
fof(axiom_1,axiom,
! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ),
file('theBenchmark.p',axiom_1) ).
fof(axiom_2,axiom,
! [X] :
( cc(X)
=> ( ? [Y0,Y1] :
( Y0 != Y1
& rp(X,Y1)
& rp(X,Y0) )
& ! [Y0,Y1,Y2] :
( ( rp(X,Y2)
& rp(X,Y1)
& rp(X,Y0) )
=> ( Y1 = Y2
| Y0 = Y2
| Y0 = Y1 ) ) ) ),
file('theBenchmark.p',axiom_2) ).
fof(the_axiom,conjecture,
( ! [X] :
( cc(X)
=> ( ! [Y0,Y1,Y2] :
( ( rp(X,Y2)
& rp(X,Y1)
& rp(X,Y0) )
=> ( Y1 = Y2
| Y0 = Y2
| Y0 = Y1 ) )
& ? [Y0,Y1] :
( Y0 != Y1
& rp(X,Y1)
& rp(X,Y0) ) ) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('theBenchmark.p',the_axiom) ).
fof(the_axiom_neg,negated_conjecture,
~ ( ! [X] :
( cc(X)
=> ( ! [Y0,Y1,Y2] :
( ( rp(X,Y2)
& rp(X,Y1)
& rp(X,Y0) )
=> ( Y1 = Y2
| Y0 = Y2
| Y0 = Y1 ) )
& ? [Y0,Y1] :
( Y0 != Y1
& rp(X,Y1)
& rp(X,Y0) ) ) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(assume_negation,[status(cth)],[the_axiom]) ).
cnf(c_19,plain,
cowlThing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_20,plain,
~ cowlNothing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_21,plain,
( ~ xsd_integer(A)
| ~ xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_22,plain,
( xsd_integer(A)
| xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
fof(nnf_10,plain,
! [X] :
( ( ? [Y0,Y1] :
( Y1 != Y0
& rp(X,Y1)
& rp(X,Y0) )
& ! [X0,X1,Y2] :
( Y2 = X1
| Y2 = X0
| X1 = X0
| ~ rp(X,Y2)
| ~ rp(X,X1)
| ~ rp(X,X0) ) )
| ~ cc(X) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( sK1(X) != sK0(X)
& rp(X,sK1(X))
& rp(X,sK0(X))
& ! [X0,X1,Y2] :
( Y2 = X1
| Y2 = X0
| X1 = X0
| ~ rp(X,Y2)
| ~ rp(X,X1)
| ~ rp(X,X0) ) )
| ~ cc(X) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(Y0,sK0(X)),skolemize(Y1,sK1(X))],[nnf_10]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0] :
( sK1(VAR_0) != sK0(VAR_0)
| ~ cc(VAR_0) )
& ! [VAR_0] :
( rp(VAR_0,sK1(VAR_0))
| ~ cc(VAR_0) )
& ! [VAR_0] :
( rp(VAR_0,sK0(VAR_0))
| ~ cc(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 = VAR_2
| VAR_3 = VAR_1
| VAR_2 = VAR_1
| ~ rp(VAR_0,VAR_3)
| ~ rp(VAR_0,VAR_2)
| ~ rp(VAR_0,VAR_1)
| ~ cc(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_23,plain,
( D = C
| D = B
| C = B
| ~ rp(A,D)
| ~ rp(A,C)
| ~ rp(A,B)
| ~ cc(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_24,plain,
( rp(A,sK0(A))
| ~ cc(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_25,plain,
( rp(A,sK1(A))
| ~ cc(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_26,plain,
( sK1(A) != sK0(A)
| ~ cc(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
fof(nnf_11,plain,
( ? [X] :
( ( ? [Y0,Y1,Y2] :
( Y2 != Y1
& Y2 != Y0
& Y1 != Y0
& rp(X,Y2)
& rp(X,Y1)
& rp(X,Y0) )
| ! [X0,X1] :
( X1 = X0
| ~ rp(X,X1)
| ~ rp(X,X0) ) )
& cc(X) )
| ? [X3] :
( ( xsd_integer(X3)
| ~ xsd_string(X3) )
& ( ~ xsd_integer(X3)
| xsd_string(X3) ) )
| ? [X2] :
( cowlNothing(X2)
| ~ cowlThing(X2) ) ),
inference(fof_nnf,[status(thm)],[the_axiom_neg]) ).
fof(sk_the_axiom_neg_sk,plain,
( ( ( ( sK7 != sK6
& sK7 != sK5
& sK6 != sK5
& rp(sK4,sK7)
& rp(sK4,sK6)
& rp(sK4,sK5) )
| ! [X0,X1] :
( X1 = X0
| ~ rp(sK4,X1)
| ~ rp(sK4,X0) ) )
& cc(sK4) )
| ( ( xsd_integer(sK3)
| ~ xsd_string(sK3) )
& ( ~ xsd_integer(sK3)
| xsd_string(sK3) ) )
| cowlNothing(sK2)
| ~ cowlThing(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6,sK7]),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X,sK4),skolemize(Y0,sK5),skolemize(Y1,sK6),skolemize(Y2,sK7)],[nnf_11]) ).
fof(sk_the_axiom_neg,plain,
( ! [VAR_0,VAR_1] :
( sK7 != sK6
| VAR_1 = VAR_0
| ~ rp(sK4,VAR_1)
| ~ rp(sK4,VAR_0)
| xsd_integer(sK3)
| ~ xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) )
& ! [VAR_0,VAR_1] :
( sK7 != sK5
| VAR_1 = VAR_0
| ~ rp(sK4,VAR_1)
| ~ rp(sK4,VAR_0)
| xsd_integer(sK3)
| ~ xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) )
& ! [VAR_0,VAR_1] :
( sK6 != sK5
| VAR_1 = VAR_0
| ~ rp(sK4,VAR_1)
| ~ rp(sK4,VAR_0)
| xsd_integer(sK3)
| ~ xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) )
& ! [VAR_0,VAR_1] :
( rp(sK4,sK7)
| VAR_1 = VAR_0
| ~ rp(sK4,VAR_1)
| ~ rp(sK4,VAR_0)
| xsd_integer(sK3)
| ~ xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) )
& ! [VAR_0,VAR_1] :
( rp(sK4,sK6)
| VAR_1 = VAR_0
| ~ rp(sK4,VAR_1)
| ~ rp(sK4,VAR_0)
| xsd_integer(sK3)
| ~ xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) )
& ! [VAR_0,VAR_1] :
( rp(sK4,sK5)
| VAR_1 = VAR_0
| ~ rp(sK4,VAR_1)
| ~ rp(sK4,VAR_0)
| xsd_integer(sK3)
| ~ xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) )
& ( cc(sK4)
| xsd_integer(sK3)
| ~ xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) )
& ! [VAR_0,VAR_1] :
( sK7 != sK6
| VAR_1 = VAR_0
| ~ rp(sK4,VAR_1)
| ~ rp(sK4,VAR_0)
| ~ xsd_integer(sK3)
| xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) )
& ! [VAR_0,VAR_1] :
( sK7 != sK5
| VAR_1 = VAR_0
| ~ rp(sK4,VAR_1)
| ~ rp(sK4,VAR_0)
| ~ xsd_integer(sK3)
| xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) )
& ! [VAR_0,VAR_1] :
( sK6 != sK5
| VAR_1 = VAR_0
| ~ rp(sK4,VAR_1)
| ~ rp(sK4,VAR_0)
| ~ xsd_integer(sK3)
| xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) )
& ! [VAR_0,VAR_1] :
( rp(sK4,sK7)
| VAR_1 = VAR_0
| ~ rp(sK4,VAR_1)
| ~ rp(sK4,VAR_0)
| ~ xsd_integer(sK3)
| xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) )
& ! [VAR_0,VAR_1] :
( rp(sK4,sK6)
| VAR_1 = VAR_0
| ~ rp(sK4,VAR_1)
| ~ rp(sK4,VAR_0)
| ~ xsd_integer(sK3)
| xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) )
& ! [VAR_0,VAR_1] :
( rp(sK4,sK5)
| VAR_1 = VAR_0
| ~ rp(sK4,VAR_1)
| ~ rp(sK4,VAR_0)
| ~ xsd_integer(sK3)
| xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) )
& ( cc(sK4)
| ~ xsd_integer(sK3)
| xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) ) ),
inference(cnf_transformation,[status(thm)],[sk_the_axiom_neg_sk]) ).
cnf(c_27,negated_conjecture,
( cc(sK4)
| ~ xsd_integer(sK3)
| xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_244,negated_conjecture,
( cc(sK4)
| ~ xsd_integer(sK3)
| xsd_string(sK3)
| cowlNothing(sK2) ),
inference(resolve,[status(thm)],[c_19,c_27]) ).
cnf(c_28,negated_conjecture,
( cc(sK4)
| ~ xsd_integer(sK3)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_20,c_244]) ).
cnf(c_29,negated_conjecture,
( rp(sK4,sK5)
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| ~ xsd_integer(sK3)
| xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_245,negated_conjecture,
( rp(sK4,sK5)
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| ~ xsd_integer(sK3)
| xsd_string(sK3)
| cowlNothing(sK2) ),
inference(resolve,[status(thm)],[c_19,c_29]) ).
cnf(c_30,negated_conjecture,
( rp(sK4,sK5)
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| ~ xsd_integer(sK3)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_20,c_245]) ).
cnf(c_31,negated_conjecture,
( rp(sK4,sK6)
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| ~ xsd_integer(sK3)
| xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_246,negated_conjecture,
( rp(sK4,sK6)
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| ~ xsd_integer(sK3)
| xsd_string(sK3)
| cowlNothing(sK2) ),
inference(resolve,[status(thm)],[c_19,c_31]) ).
cnf(c_32,negated_conjecture,
( rp(sK4,sK6)
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| ~ xsd_integer(sK3)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_20,c_246]) ).
cnf(c_33,negated_conjecture,
( rp(sK4,sK7)
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| ~ xsd_integer(sK3)
| xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_247,negated_conjecture,
( rp(sK4,sK7)
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| ~ xsd_integer(sK3)
| xsd_string(sK3)
| cowlNothing(sK2) ),
inference(resolve,[status(thm)],[c_19,c_33]) ).
cnf(c_34,negated_conjecture,
( rp(sK4,sK7)
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| ~ xsd_integer(sK3)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_20,c_247]) ).
cnf(c_35,negated_conjecture,
( sK6 != sK5
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| ~ xsd_integer(sK3)
| xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_248,negated_conjecture,
( sK6 != sK5
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| ~ xsd_integer(sK3)
| xsd_string(sK3)
| cowlNothing(sK2) ),
inference(resolve,[status(thm)],[c_19,c_35]) ).
cnf(c_36,negated_conjecture,
( sK6 != sK5
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| ~ xsd_integer(sK3)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_20,c_248]) ).
cnf(c_37,negated_conjecture,
( sK7 != sK5
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| ~ xsd_integer(sK3)
| xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_249,negated_conjecture,
( sK7 != sK5
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| ~ xsd_integer(sK3)
| xsd_string(sK3)
| cowlNothing(sK2) ),
inference(resolve,[status(thm)],[c_19,c_37]) ).
cnf(c_38,negated_conjecture,
( sK7 != sK5
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| ~ xsd_integer(sK3)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_20,c_249]) ).
cnf(c_39,negated_conjecture,
( sK7 != sK6
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| ~ xsd_integer(sK3)
| xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_250,negated_conjecture,
( sK7 != sK6
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| ~ xsd_integer(sK3)
| xsd_string(sK3)
| cowlNothing(sK2) ),
inference(resolve,[status(thm)],[c_19,c_39]) ).
cnf(c_40,negated_conjecture,
( sK7 != sK6
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| ~ xsd_integer(sK3)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_20,c_250]) ).
cnf(c_41,negated_conjecture,
( cc(sK4)
| xsd_integer(sK3)
| ~ xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_251,negated_conjecture,
( cc(sK4)
| xsd_integer(sK3)
| ~ xsd_string(sK3)
| cowlNothing(sK2) ),
inference(resolve,[status(thm)],[c_19,c_41]) ).
cnf(c_42,negated_conjecture,
( cc(sK4)
| xsd_integer(sK3)
| ~ xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_20,c_251]) ).
cnf(c_43,negated_conjecture,
( rp(sK4,sK5)
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| xsd_integer(sK3)
| ~ xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_252,negated_conjecture,
( rp(sK4,sK5)
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| xsd_integer(sK3)
| ~ xsd_string(sK3)
| cowlNothing(sK2) ),
inference(resolve,[status(thm)],[c_19,c_43]) ).
cnf(c_44,negated_conjecture,
( rp(sK4,sK5)
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| xsd_integer(sK3)
| ~ xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_20,c_252]) ).
cnf(c_45,negated_conjecture,
( rp(sK4,sK6)
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| xsd_integer(sK3)
| ~ xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_253,negated_conjecture,
( rp(sK4,sK6)
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| xsd_integer(sK3)
| ~ xsd_string(sK3)
| cowlNothing(sK2) ),
inference(resolve,[status(thm)],[c_19,c_45]) ).
cnf(c_46,negated_conjecture,
( rp(sK4,sK6)
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| xsd_integer(sK3)
| ~ xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_20,c_253]) ).
cnf(c_47,negated_conjecture,
( rp(sK4,sK7)
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| xsd_integer(sK3)
| ~ xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_254,negated_conjecture,
( rp(sK4,sK7)
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| xsd_integer(sK3)
| ~ xsd_string(sK3)
| cowlNothing(sK2) ),
inference(resolve,[status(thm)],[c_19,c_47]) ).
cnf(c_48,negated_conjecture,
( rp(sK4,sK7)
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| xsd_integer(sK3)
| ~ xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_20,c_254]) ).
cnf(c_49,negated_conjecture,
( sK6 != sK5
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| xsd_integer(sK3)
| ~ xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_255,negated_conjecture,
( sK6 != sK5
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| xsd_integer(sK3)
| ~ xsd_string(sK3)
| cowlNothing(sK2) ),
inference(resolve,[status(thm)],[c_19,c_49]) ).
cnf(c_50,negated_conjecture,
( sK6 != sK5
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| xsd_integer(sK3)
| ~ xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_20,c_255]) ).
cnf(c_51,negated_conjecture,
( sK7 != sK5
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| xsd_integer(sK3)
| ~ xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_256,negated_conjecture,
( sK7 != sK5
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| xsd_integer(sK3)
| ~ xsd_string(sK3)
| cowlNothing(sK2) ),
inference(resolve,[status(thm)],[c_19,c_51]) ).
cnf(c_52,negated_conjecture,
( sK7 != sK5
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| xsd_integer(sK3)
| ~ xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_20,c_256]) ).
cnf(c_53,negated_conjecture,
( sK7 != sK6
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| xsd_integer(sK3)
| ~ xsd_string(sK3)
| cowlNothing(sK2)
| ~ cowlThing(sK2) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_257,negated_conjecture,
( sK7 != sK6
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| xsd_integer(sK3)
| ~ xsd_string(sK3)
| cowlNothing(sK2) ),
inference(resolve,[status(thm)],[c_19,c_53]) ).
cnf(c_54,negated_conjecture,
( sK7 != sK6
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| xsd_integer(sK3)
| ~ xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_20,c_257]) ).
cnf(c_258,negated_conjecture,
( xsd_string(sK3)
| cc(sK4)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_28,c_22]) ).
cnf(c_57,negated_conjecture,
( cc(sK4)
| xsd_string(sK3) ),
inference(copy,[status(thm)],[c_258]) ).
cnf(c_259,negated_conjecture,
( xsd_integer(sK3)
| cc(sK4)
| xsd_integer(sK3) ),
inference(resolve,[status(thm)],[c_42,c_22]) ).
cnf(c_58,negated_conjecture,
( cc(sK4)
| xsd_integer(sK3) ),
inference(copy,[status(thm)],[c_259]) ).
cnf(c_59,plain,
( ~ xsd_integer(sK3)
| cc(sK4) ),
inference(resolve,[status(thm)],[c_57,c_21]) ).
cnf(c_260,plain,
( cc(sK4)
| cc(sK4) ),
inference(resolve,[status(thm)],[c_59,c_58]) ).
cnf(c_70,plain,
cc(sK4),
inference(copy,[status(thm)],[c_260]) ).
cnf(c_71,plain,
sK1(sK4) != sK0(sK4),
inference(resolve,[status(thm)],[c_70,c_26]) ).
cnf(c_72,plain,
rp(sK4,sK1(sK4)),
inference(resolve,[status(thm)],[c_70,c_25]) ).
cnf(c_73,plain,
rp(sK4,sK0(sK4)),
inference(resolve,[status(thm)],[c_70,c_24]) ).
cnf(c_75,plain,
( sK7 != sK6
| sK1(sK4) = A
| ~ rp(sK4,A)
| xsd_integer(sK3)
| ~ xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_72,c_54]) ).
cnf(c_76,plain,
( sK7 != sK5
| sK1(sK4) = A
| ~ rp(sK4,A)
| xsd_integer(sK3)
| ~ xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_72,c_52]) ).
cnf(c_77,plain,
( sK6 != sK5
| sK1(sK4) = A
| ~ rp(sK4,A)
| xsd_integer(sK3)
| ~ xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_72,c_50]) ).
cnf(c_78,plain,
( rp(sK4,sK7)
| sK1(sK4) = A
| ~ rp(sK4,A)
| xsd_integer(sK3)
| ~ xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_72,c_48]) ).
cnf(c_79,plain,
( rp(sK4,sK6)
| sK1(sK4) = A
| ~ rp(sK4,A)
| xsd_integer(sK3)
| ~ xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_72,c_46]) ).
cnf(c_80,plain,
( rp(sK4,sK5)
| sK1(sK4) = A
| ~ rp(sK4,A)
| xsd_integer(sK3)
| ~ xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_72,c_44]) ).
cnf(c_81,plain,
( sK7 != sK6
| sK1(sK4) = A
| ~ rp(sK4,A)
| ~ xsd_integer(sK3)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_72,c_40]) ).
cnf(c_82,plain,
( sK7 != sK5
| sK1(sK4) = A
| ~ rp(sK4,A)
| ~ xsd_integer(sK3)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_72,c_38]) ).
cnf(c_83,plain,
( sK6 != sK5
| sK1(sK4) = A
| ~ rp(sK4,A)
| ~ xsd_integer(sK3)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_72,c_36]) ).
cnf(c_84,plain,
( rp(sK4,sK7)
| sK1(sK4) = A
| ~ rp(sK4,A)
| ~ xsd_integer(sK3)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_72,c_34]) ).
cnf(c_85,plain,
( rp(sK4,sK6)
| sK1(sK4) = A
| ~ rp(sK4,A)
| ~ xsd_integer(sK3)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_72,c_32]) ).
cnf(c_86,plain,
( rp(sK4,sK5)
| sK1(sK4) = A
| ~ rp(sK4,A)
| ~ xsd_integer(sK3)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_72,c_30]) ).
cnf(c_261,plain,
( sK7 != sK6
| sK1(sK4) = sK0(sK4)
| xsd_integer(sK3)
| ~ xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_75,c_73]) ).
cnf(c_105,plain,
( sK7 != sK6
| xsd_integer(sK3)
| ~ xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_71,c_261]) ).
cnf(c_262,plain,
( sK7 != sK5
| sK1(sK4) = sK0(sK4)
| xsd_integer(sK3)
| ~ xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_76,c_73]) ).
cnf(c_106,plain,
( sK7 != sK5
| xsd_integer(sK3)
| ~ xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_71,c_262]) ).
cnf(c_263,plain,
( xsd_integer(sK3)
| sK7 != sK6
| xsd_integer(sK3) ),
inference(resolve,[status(thm)],[c_105,c_22]) ).
cnf(c_107,plain,
( sK7 != sK6
| xsd_integer(sK3) ),
inference(copy,[status(thm)],[c_263]) ).
cnf(c_264,plain,
( xsd_integer(sK3)
| sK7 != sK5
| xsd_integer(sK3) ),
inference(resolve,[status(thm)],[c_106,c_22]) ).
cnf(c_108,plain,
( sK7 != sK5
| xsd_integer(sK3) ),
inference(copy,[status(thm)],[c_264]) ).
cnf(c_265,plain,
( sK6 != sK5
| sK1(sK4) = sK0(sK4)
| xsd_integer(sK3)
| ~ xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_77,c_73]) ).
cnf(c_109,plain,
( sK6 != sK5
| xsd_integer(sK3)
| ~ xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_71,c_265]) ).
cnf(c_266,plain,
( rp(sK4,sK7)
| sK1(sK4) = sK0(sK4)
| xsd_integer(sK3)
| ~ xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_78,c_73]) ).
cnf(c_110,plain,
( rp(sK4,sK7)
| xsd_integer(sK3)
| ~ xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_71,c_266]) ).
cnf(c_267,plain,
( rp(sK4,sK6)
| sK1(sK4) = sK0(sK4)
| xsd_integer(sK3)
| ~ xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_79,c_73]) ).
cnf(c_111,plain,
( rp(sK4,sK6)
| xsd_integer(sK3)
| ~ xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_71,c_267]) ).
cnf(c_268,plain,
( xsd_integer(sK3)
| sK6 != sK5
| xsd_integer(sK3) ),
inference(resolve,[status(thm)],[c_109,c_22]) ).
cnf(c_112,plain,
( sK6 != sK5
| xsd_integer(sK3) ),
inference(copy,[status(thm)],[c_268]) ).
cnf(c_269,plain,
( xsd_integer(sK3)
| rp(sK4,sK7)
| xsd_integer(sK3) ),
inference(resolve,[status(thm)],[c_110,c_22]) ).
cnf(c_113,plain,
( rp(sK4,sK7)
| xsd_integer(sK3) ),
inference(copy,[status(thm)],[c_269]) ).
cnf(c_270,plain,
( xsd_integer(sK3)
| rp(sK4,sK6)
| xsd_integer(sK3) ),
inference(resolve,[status(thm)],[c_111,c_22]) ).
cnf(c_119,plain,
( rp(sK4,sK6)
| xsd_integer(sK3) ),
inference(copy,[status(thm)],[c_270]) ).
cnf(c_271,plain,
( rp(sK4,sK5)
| sK1(sK4) = sK0(sK4)
| xsd_integer(sK3)
| ~ xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_80,c_73]) ).
cnf(c_127,plain,
( rp(sK4,sK5)
| xsd_integer(sK3)
| ~ xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_71,c_271]) ).
cnf(c_272,plain,
( sK7 != sK6
| sK1(sK4) = sK0(sK4)
| ~ xsd_integer(sK3)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_81,c_73]) ).
cnf(c_128,plain,
( sK7 != sK6
| ~ xsd_integer(sK3)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_71,c_272]) ).
cnf(c_273,plain,
( sK7 != sK5
| sK1(sK4) = sK0(sK4)
| ~ xsd_integer(sK3)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_82,c_73]) ).
cnf(c_129,plain,
( sK7 != sK5
| ~ xsd_integer(sK3)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_71,c_273]) ).
cnf(c_274,plain,
( xsd_integer(sK3)
| rp(sK4,sK5)
| xsd_integer(sK3) ),
inference(resolve,[status(thm)],[c_127,c_22]) ).
cnf(c_130,plain,
( rp(sK4,sK5)
| xsd_integer(sK3) ),
inference(copy,[status(thm)],[c_274]) ).
cnf(c_275,plain,
( xsd_string(sK3)
| sK7 != sK6
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_128,c_22]) ).
cnf(c_138,plain,
( sK7 != sK6
| xsd_string(sK3) ),
inference(copy,[status(thm)],[c_275]) ).
cnf(c_276,plain,
( xsd_string(sK3)
| sK7 != sK5
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_129,c_22]) ).
cnf(c_142,plain,
( sK7 != sK5
| xsd_string(sK3) ),
inference(copy,[status(thm)],[c_276]) ).
cnf(c_277,plain,
( sK6 != sK5
| sK1(sK4) = sK0(sK4)
| ~ xsd_integer(sK3)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_83,c_73]) ).
cnf(c_143,plain,
( sK6 != sK5
| ~ xsd_integer(sK3)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_71,c_277]) ).
cnf(c_278,plain,
( rp(sK4,sK7)
| sK1(sK4) = sK0(sK4)
| ~ xsd_integer(sK3)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_84,c_73]) ).
cnf(c_144,plain,
( rp(sK4,sK7)
| ~ xsd_integer(sK3)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_71,c_278]) ).
cnf(c_279,plain,
( rp(sK4,sK6)
| sK1(sK4) = sK0(sK4)
| ~ xsd_integer(sK3)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_85,c_73]) ).
cnf(c_145,plain,
( rp(sK4,sK6)
| ~ xsd_integer(sK3)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_71,c_279]) ).
cnf(c_280,plain,
( xsd_string(sK3)
| sK6 != sK5
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_143,c_22]) ).
cnf(c_149,plain,
( sK6 != sK5
| xsd_string(sK3) ),
inference(copy,[status(thm)],[c_280]) ).
cnf(c_281,plain,
( rp(sK4,sK7)
| rp(sK4,sK7)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_144,c_113]) ).
cnf(c_152,plain,
( rp(sK4,sK7)
| xsd_string(sK3) ),
inference(copy,[status(thm)],[c_281]) ).
cnf(c_153,plain,
( ~ xsd_integer(sK3)
| rp(sK4,sK7) ),
inference(resolve,[status(thm)],[c_152,c_21]) ).
cnf(c_282,plain,
( rp(sK4,sK7)
| rp(sK4,sK7) ),
inference(resolve,[status(thm)],[c_153,c_113]) ).
cnf(c_161,plain,
rp(sK4,sK7),
inference(copy,[status(thm)],[c_282]) ).
cnf(c_283,plain,
( sK7 = B
| sK7 = A
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| ~ cc(sK4) ),
inference(resolve,[status(thm)],[c_161,c_23]) ).
cnf(c_162,plain,
( sK7 = B
| sK7 = A
| B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A) ),
inference(resolve,[status(thm)],[c_70,c_283]) ).
cnf(c_284,plain,
( rp(sK4,sK5)
| sK1(sK4) = sK0(sK4)
| ~ xsd_integer(sK3)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_86,c_73]) ).
cnf(c_166,plain,
( rp(sK4,sK5)
| ~ xsd_integer(sK3)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_71,c_284]) ).
cnf(c_285,plain,
( rp(sK4,sK6)
| rp(sK4,sK6)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_145,c_119]) ).
cnf(c_175,plain,
( rp(sK4,sK6)
| xsd_string(sK3) ),
inference(copy,[status(thm)],[c_285]) ).
cnf(c_176,plain,
( ~ xsd_integer(sK3)
| rp(sK4,sK6) ),
inference(resolve,[status(thm)],[c_175,c_21]) ).
cnf(c_286,plain,
( rp(sK4,sK6)
| rp(sK4,sK6) ),
inference(resolve,[status(thm)],[c_176,c_119]) ).
cnf(c_184,plain,
rp(sK4,sK6),
inference(copy,[status(thm)],[c_286]) ).
cnf(c_287,plain,
( rp(sK4,sK5)
| rp(sK4,sK5)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_166,c_130]) ).
cnf(c_190,plain,
( rp(sK4,sK5)
| xsd_string(sK3) ),
inference(copy,[status(thm)],[c_287]) ).
cnf(c_191,plain,
( ~ xsd_integer(sK3)
| rp(sK4,sK5) ),
inference(resolve,[status(thm)],[c_190,c_21]) ).
cnf(c_288,plain,
( rp(sK4,sK5)
| rp(sK4,sK5) ),
inference(resolve,[status(thm)],[c_191,c_130]) ).
cnf(c_198,plain,
rp(sK4,sK5),
inference(copy,[status(thm)],[c_288]) ).
cnf(c_289,plain,
( sK7 = A
| sK7 = sK5
| A = sK5
| ~ rp(sK4,A) ),
inference(resolve,[status(thm)],[c_162,c_198]) ).
cnf(c_204,plain,
( sK7 = A
| sK7 = sK5
| sK5 = A
| ~ rp(sK4,A) ),
inference(copy,[status(thm)],[c_289]) ).
cnf(c_290,plain,
( sK7 = sK6
| sK7 = sK5
| sK5 = sK6 ),
inference(resolve,[status(thm)],[c_204,c_184]) ).
cnf(c_211,plain,
( sK7 = sK6
| sK7 = sK5
| sK6 = sK5 ),
inference(copy,[status(thm)],[c_290]) ).
cnf(c_213,plain,
( xsd_string(sK3)
| sK7 = sK6
| sK7 = sK5 ),
inference(resolve,[status(thm)],[c_211,c_149]) ).
cnf(c_218,plain,
( xsd_integer(sK3)
| sK7 = sK6
| sK6 = sK5 ),
inference(resolve,[status(thm)],[c_211,c_108]) ).
cnf(c_291,plain,
( xsd_string(sK3)
| xsd_string(sK3)
| sK7 = sK6 ),
inference(resolve,[status(thm)],[c_213,c_142]) ).
cnf(c_225,plain,
( xsd_string(sK3)
| sK7 = sK6 ),
inference(copy,[status(thm)],[c_291]) ).
cnf(c_292,plain,
( xsd_string(sK3)
| xsd_string(sK3) ),
inference(resolve,[status(thm)],[c_225,c_138]) ).
cnf(c_229,plain,
xsd_string(sK3),
inference(copy,[status(thm)],[c_292]) ).
cnf(c_235,plain,
~ xsd_integer(sK3),
inference(resolve,[status(thm)],[c_229,c_21]) ).
cnf(c_238,plain,
( sK7 = sK6
| sK6 = sK5 ),
inference(resolve,[status(thm)],[c_235,c_218]) ).
cnf(c_240,plain,
sK6 != sK5,
inference(resolve,[status(thm)],[c_235,c_112]) ).
cnf(c_242,plain,
sK7 != sK6,
inference(resolve,[status(thm)],[c_235,c_107]) ).
cnf(c_293,plain,
sK7 = sK6,
inference(resolve,[status(thm)],[c_240,c_238]) ).
cnf(c_243,plain,
$false,
inference(resolve,[status(thm)],[c_242,c_293]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS145+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n014.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 19:40:33 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 932523 was started by sandbox on n014,
% 0.09/0.37 % Fri Sep 25 19:40:33 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 0.13/0.41
% 0.13/0.41 % SZS status Theorem for theBenchmark
% 0.13/0.41
% 0.13/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.13/0.41 % Length of proof is 101.
% 0.13/0.41 % Level of proof is 21.
% 0.13/0.41 % Maximum clause weight is 25.000.
% 0.13/0.41 % Given clauses 103.
% 0.13/0.41
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
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