%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS142+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 : n019.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 10.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 62
% Number of leaves : 4
% Syntax : Number of formulae : 159 ( 9 unt; 0 def)
% Number of atoms : 752 ( 108 equ)
% Maximal formula atoms : 96 ( 4 avg)
% Number of connectives : 831 ( 238 ~; 541 |; 41 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 105 ( 43 sgn 37 !; 10 ?)
% 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] :
( ( rp(X,Y1)
& rp(X,Y0) )
=> Y0 = Y1 )
& ? [Y0] : rp(X,Y0) ) ),
file('theBenchmark.p',axiom_2) ).
fof(the_axiom,conjecture,
( ! [X] :
( cc(X)
=> ! [Y0,Y1] :
( ( rp(X,Y1)
& rp(X,Y0) )
=> Y0 = Y1 ) )
& ! [X] :
( cc(X)
=> ? [Y0] : 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] :
( ( rp(X,Y1)
& rp(X,Y0) )
=> Y0 = Y1 ) )
& ! [X] :
( cc(X)
=> ? [Y0] : 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] : rp(X,X0) )
| ~ cc(X) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ! [Y0,Y1] :
( Y1 = Y0
| ~ rp(X,Y1)
| ~ rp(X,Y0) )
& rp(X,sK0(X)) )
| ~ cc(X) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0(X))],[nnf_10]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = VAR_1
| ~ rp(VAR_0,VAR_2)
| ~ rp(VAR_0,VAR_1)
| ~ cc(VAR_0) )
& ! [VAR_0] :
( rp(VAR_0,sK0(VAR_0))
| ~ cc(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_23,plain,
( rp(A,sK0(A))
| ~ cc(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_24,plain,
( C = B
| ~ rp(A,C)
| ~ rp(A,B)
| ~ cc(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
fof(nnf_11,plain,
( ? [X] :
( ? [Y0,Y1] :
( Y1 != Y0
& rp(X,Y1)
& rp(X,Y0) )
& cc(X) )
| ? [X0] :
( ! [X3] : ~ rp(X0,X3)
& cc(X0) )
| ? [X2] :
( ( xsd_integer(X2)
| ~ xsd_string(X2) )
& ( ~ xsd_integer(X2)
| xsd_string(X2) ) )
| ? [X1] :
( cowlNothing(X1)
| ~ cowlThing(X1) ) ),
inference(fof_nnf,[status(thm)],[the_axiom_neg]) ).
fof(sk_the_axiom_neg_sk,plain,
( ( sK6 != sK5
& rp(sK4,sK6)
& rp(sK4,sK5)
& cc(sK4) )
| ( ! [X3] : ~ rp(sK3,X3)
& cc(sK3) )
| ( ( xsd_integer(sK2)
| ~ xsd_string(sK2) )
& ( ~ xsd_integer(sK2)
| xsd_string(sK2) ) )
| cowlNothing(sK1)
| ~ cowlThing(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X0,sK3),skolemize(X,sK4),skolemize(Y0,sK5),skolemize(Y1,sK6)],[nnf_11]) ).
fof(sk_the_axiom_neg,plain,
( ! [VAR_0] :
( sK6 != sK5
| ~ rp(sK3,VAR_0)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) )
& ! [VAR_0] :
( rp(sK4,sK6)
| ~ rp(sK3,VAR_0)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) )
& ! [VAR_0] :
( rp(sK4,sK5)
| ~ rp(sK3,VAR_0)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) )
& ! [VAR_0] :
( cc(sK4)
| ~ rp(sK3,VAR_0)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) )
& ( sK6 != sK5
| cc(sK3)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) )
& ( rp(sK4,sK6)
| cc(sK3)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) )
& ( rp(sK4,sK5)
| cc(sK3)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) )
& ( cc(sK4)
| cc(sK3)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) )
& ! [VAR_0] :
( sK6 != sK5
| ~ rp(sK3,VAR_0)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) )
& ! [VAR_0] :
( rp(sK4,sK6)
| ~ rp(sK3,VAR_0)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) )
& ! [VAR_0] :
( rp(sK4,sK5)
| ~ rp(sK3,VAR_0)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) )
& ! [VAR_0] :
( cc(sK4)
| ~ rp(sK3,VAR_0)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) )
& ( sK6 != sK5
| cc(sK3)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) )
& ( rp(sK4,sK6)
| cc(sK3)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) )
& ( rp(sK4,sK5)
| cc(sK3)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) )
& ( cc(sK4)
| cc(sK3)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) ) ),
inference(cnf_transformation,[status(thm)],[sk_the_axiom_neg_sk]) ).
cnf(c_25,negated_conjecture,
( cc(sK4)
| cc(sK3)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_217,negated_conjecture,
( cc(sK4)
| cc(sK3)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1) ),
inference(resolve,[status(thm)],[c_19,c_25]) ).
cnf(c_26,negated_conjecture,
( cc(sK4)
| cc(sK3)
| ~ xsd_integer(sK2)
| xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_20,c_217]) ).
cnf(c_27,negated_conjecture,
( rp(sK4,sK5)
| cc(sK3)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_218,negated_conjecture,
( rp(sK4,sK5)
| cc(sK3)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1) ),
inference(resolve,[status(thm)],[c_19,c_27]) ).
cnf(c_28,negated_conjecture,
( rp(sK4,sK5)
| cc(sK3)
| ~ xsd_integer(sK2)
| xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_20,c_218]) ).
cnf(c_29,negated_conjecture,
( rp(sK4,sK6)
| cc(sK3)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_219,negated_conjecture,
( rp(sK4,sK6)
| cc(sK3)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1) ),
inference(resolve,[status(thm)],[c_19,c_29]) ).
cnf(c_30,negated_conjecture,
( rp(sK4,sK6)
| cc(sK3)
| ~ xsd_integer(sK2)
| xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_20,c_219]) ).
cnf(c_31,negated_conjecture,
( sK6 != sK5
| cc(sK3)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_220,negated_conjecture,
( sK6 != sK5
| cc(sK3)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1) ),
inference(resolve,[status(thm)],[c_19,c_31]) ).
cnf(c_32,negated_conjecture,
( sK6 != sK5
| cc(sK3)
| ~ xsd_integer(sK2)
| xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_20,c_220]) ).
cnf(c_33,negated_conjecture,
( cc(sK4)
| ~ rp(sK3,A)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_221,negated_conjecture,
( cc(sK4)
| ~ rp(sK3,A)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1) ),
inference(resolve,[status(thm)],[c_19,c_33]) ).
cnf(c_34,negated_conjecture,
( cc(sK4)
| ~ rp(sK3,A)
| ~ xsd_integer(sK2)
| xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_20,c_221]) ).
cnf(c_35,negated_conjecture,
( rp(sK4,sK5)
| ~ rp(sK3,A)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_222,negated_conjecture,
( rp(sK4,sK5)
| ~ rp(sK3,A)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1) ),
inference(resolve,[status(thm)],[c_19,c_35]) ).
cnf(c_36,negated_conjecture,
( rp(sK4,sK5)
| ~ rp(sK3,A)
| ~ xsd_integer(sK2)
| xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_20,c_222]) ).
cnf(c_37,negated_conjecture,
( rp(sK4,sK6)
| ~ rp(sK3,A)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_223,negated_conjecture,
( rp(sK4,sK6)
| ~ rp(sK3,A)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1) ),
inference(resolve,[status(thm)],[c_19,c_37]) ).
cnf(c_38,negated_conjecture,
( rp(sK4,sK6)
| ~ rp(sK3,A)
| ~ xsd_integer(sK2)
| xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_20,c_223]) ).
cnf(c_39,negated_conjecture,
( sK6 != sK5
| ~ rp(sK3,A)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_224,negated_conjecture,
( sK6 != sK5
| ~ rp(sK3,A)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1) ),
inference(resolve,[status(thm)],[c_19,c_39]) ).
cnf(c_40,negated_conjecture,
( sK6 != sK5
| ~ rp(sK3,A)
| ~ xsd_integer(sK2)
| xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_20,c_224]) ).
cnf(c_41,negated_conjecture,
( cc(sK4)
| cc(sK3)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_225,negated_conjecture,
( cc(sK4)
| cc(sK3)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1) ),
inference(resolve,[status(thm)],[c_19,c_41]) ).
cnf(c_42,negated_conjecture,
( cc(sK4)
| cc(sK3)
| xsd_integer(sK2)
| ~ xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_20,c_225]) ).
cnf(c_43,negated_conjecture,
( rp(sK4,sK5)
| cc(sK3)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_226,negated_conjecture,
( rp(sK4,sK5)
| cc(sK3)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1) ),
inference(resolve,[status(thm)],[c_19,c_43]) ).
cnf(c_44,negated_conjecture,
( rp(sK4,sK5)
| cc(sK3)
| xsd_integer(sK2)
| ~ xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_20,c_226]) ).
cnf(c_45,negated_conjecture,
( rp(sK4,sK6)
| cc(sK3)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_227,negated_conjecture,
( rp(sK4,sK6)
| cc(sK3)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1) ),
inference(resolve,[status(thm)],[c_19,c_45]) ).
cnf(c_46,negated_conjecture,
( rp(sK4,sK6)
| cc(sK3)
| xsd_integer(sK2)
| ~ xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_20,c_227]) ).
cnf(c_47,negated_conjecture,
( sK6 != sK5
| cc(sK3)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_228,negated_conjecture,
( sK6 != sK5
| cc(sK3)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1) ),
inference(resolve,[status(thm)],[c_19,c_47]) ).
cnf(c_48,negated_conjecture,
( sK6 != sK5
| cc(sK3)
| xsd_integer(sK2)
| ~ xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_20,c_228]) ).
cnf(c_49,negated_conjecture,
( cc(sK4)
| ~ rp(sK3,A)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_229,negated_conjecture,
( cc(sK4)
| ~ rp(sK3,A)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1) ),
inference(resolve,[status(thm)],[c_19,c_49]) ).
cnf(c_50,negated_conjecture,
( cc(sK4)
| ~ rp(sK3,A)
| xsd_integer(sK2)
| ~ xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_20,c_229]) ).
cnf(c_51,negated_conjecture,
( rp(sK4,sK5)
| ~ rp(sK3,A)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_230,negated_conjecture,
( rp(sK4,sK5)
| ~ rp(sK3,A)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1) ),
inference(resolve,[status(thm)],[c_19,c_51]) ).
cnf(c_52,negated_conjecture,
( rp(sK4,sK5)
| ~ rp(sK3,A)
| xsd_integer(sK2)
| ~ xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_20,c_230]) ).
cnf(c_53,negated_conjecture,
( rp(sK4,sK6)
| ~ rp(sK3,A)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_231,negated_conjecture,
( rp(sK4,sK6)
| ~ rp(sK3,A)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1) ),
inference(resolve,[status(thm)],[c_19,c_53]) ).
cnf(c_54,negated_conjecture,
( rp(sK4,sK6)
| ~ rp(sK3,A)
| xsd_integer(sK2)
| ~ xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_20,c_231]) ).
cnf(c_55,negated_conjecture,
( sK6 != sK5
| ~ rp(sK3,A)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_232,negated_conjecture,
( sK6 != sK5
| ~ rp(sK3,A)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1) ),
inference(resolve,[status(thm)],[c_19,c_55]) ).
cnf(c_56,negated_conjecture,
( sK6 != sK5
| ~ rp(sK3,A)
| xsd_integer(sK2)
| ~ xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_20,c_232]) ).
cnf(c_233,negated_conjecture,
( xsd_integer(sK2)
| cc(sK4)
| cc(sK3)
| xsd_integer(sK2) ),
inference(resolve,[status(thm)],[c_42,c_22]) ).
cnf(c_58,negated_conjecture,
( cc(sK4)
| cc(sK3)
| xsd_integer(sK2) ),
inference(copy,[status(thm)],[c_233]) ).
cnf(c_234,negated_conjecture,
( xsd_integer(sK2)
| rp(sK4,sK5)
| cc(sK3)
| xsd_integer(sK2) ),
inference(resolve,[status(thm)],[c_44,c_22]) ).
cnf(c_59,negated_conjecture,
( rp(sK4,sK5)
| cc(sK3)
| xsd_integer(sK2) ),
inference(copy,[status(thm)],[c_234]) ).
cnf(c_235,negated_conjecture,
( xsd_integer(sK2)
| rp(sK4,sK6)
| cc(sK3)
| xsd_integer(sK2) ),
inference(resolve,[status(thm)],[c_46,c_22]) ).
cnf(c_60,negated_conjecture,
( rp(sK4,sK6)
| cc(sK3)
| xsd_integer(sK2) ),
inference(copy,[status(thm)],[c_235]) ).
cnf(c_236,negated_conjecture,
( xsd_integer(sK2)
| sK6 != sK5
| cc(sK3)
| xsd_integer(sK2) ),
inference(resolve,[status(thm)],[c_48,c_22]) ).
cnf(c_61,negated_conjecture,
( sK6 != sK5
| cc(sK3)
| xsd_integer(sK2) ),
inference(copy,[status(thm)],[c_236]) ).
cnf(c_237,negated_conjecture,
( xsd_integer(sK2)
| cc(sK4)
| ~ rp(sK3,A)
| xsd_integer(sK2) ),
inference(resolve,[status(thm)],[c_50,c_22]) ).
cnf(c_62,negated_conjecture,
( cc(sK4)
| ~ rp(sK3,A)
| xsd_integer(sK2) ),
inference(copy,[status(thm)],[c_237]) ).
cnf(c_238,negated_conjecture,
( xsd_integer(sK2)
| rp(sK4,sK5)
| ~ rp(sK3,A)
| xsd_integer(sK2) ),
inference(resolve,[status(thm)],[c_52,c_22]) ).
cnf(c_63,negated_conjecture,
( rp(sK4,sK5)
| ~ rp(sK3,A)
| xsd_integer(sK2) ),
inference(copy,[status(thm)],[c_238]) ).
cnf(c_239,negated_conjecture,
( xsd_integer(sK2)
| rp(sK4,sK6)
| ~ rp(sK3,A)
| xsd_integer(sK2) ),
inference(resolve,[status(thm)],[c_54,c_22]) ).
cnf(c_64,negated_conjecture,
( rp(sK4,sK6)
| ~ rp(sK3,A)
| xsd_integer(sK2) ),
inference(copy,[status(thm)],[c_239]) ).
cnf(c_240,negated_conjecture,
( xsd_integer(sK2)
| sK6 != sK5
| ~ rp(sK3,A)
| xsd_integer(sK2) ),
inference(resolve,[status(thm)],[c_56,c_22]) ).
cnf(c_65,negated_conjecture,
( sK6 != sK5
| ~ rp(sK3,A)
| xsd_integer(sK2) ),
inference(copy,[status(thm)],[c_240]) ).
cnf(c_66,plain,
( B = A
| ~ rp(sK4,B)
| ~ rp(sK4,A)
| cc(sK3)
| xsd_integer(sK2) ),
inference(resolve,[status(thm)],[c_58,c_24]) ).
cnf(c_241,plain,
( cc(sK3)
| xsd_integer(sK2)
| A = sK6
| ~ rp(sK4,A)
| cc(sK3)
| xsd_integer(sK2) ),
inference(resolve,[status(thm)],[c_66,c_60]) ).
cnf(c_242,plain,
( cc(sK3)
| xsd_integer(sK2)
| sK6 = A
| ~ rp(sK4,A)
| cc(sK3)
| xsd_integer(sK2) ),
inference(copy,[status(thm)],[c_241]) ).
cnf(c_243,plain,
( cc(sK3)
| sK6 = A
| ~ rp(sK4,A)
| cc(sK3)
| xsd_integer(sK2) ),
inference(copy,[status(thm)],[c_242]) ).
cnf(c_76,plain,
( sK6 = A
| ~ rp(sK4,A)
| cc(sK3)
| xsd_integer(sK2) ),
inference(copy,[status(thm)],[c_243]) ).
cnf(c_244,plain,
( cc(sK3)
| xsd_integer(sK2)
| sK6 = sK5
| cc(sK3)
| xsd_integer(sK2) ),
inference(resolve,[status(thm)],[c_76,c_59]) ).
cnf(c_245,plain,
( cc(sK3)
| sK6 = sK5
| cc(sK3)
| xsd_integer(sK2) ),
inference(copy,[status(thm)],[c_244]) ).
cnf(c_82,plain,
( sK6 = sK5
| cc(sK3)
| xsd_integer(sK2) ),
inference(copy,[status(thm)],[c_245]) ).
cnf(c_85,plain,
( rp(sK3,sK0(sK3))
| sK6 = sK5
| xsd_integer(sK2) ),
inference(resolve,[status(thm)],[c_82,c_23]) ).
cnf(c_246,plain,
( rp(sK4,sK6)
| xsd_integer(sK2)
| sK6 = sK5
| xsd_integer(sK2) ),
inference(resolve,[status(thm)],[c_85,c_64]) ).
cnf(c_97,plain,
( rp(sK4,sK6)
| sK6 = sK5
| xsd_integer(sK2) ),
inference(copy,[status(thm)],[c_246]) ).
cnf(c_247,plain,
( rp(sK4,sK5)
| xsd_integer(sK2)
| sK6 = sK5
| xsd_integer(sK2) ),
inference(resolve,[status(thm)],[c_85,c_63]) ).
cnf(c_98,plain,
( rp(sK4,sK5)
| sK6 = sK5
| xsd_integer(sK2) ),
inference(copy,[status(thm)],[c_247]) ).
cnf(c_248,plain,
( cc(sK4)
| xsd_integer(sK2)
| sK6 = sK5
| xsd_integer(sK2) ),
inference(resolve,[status(thm)],[c_85,c_62]) ).
cnf(c_99,plain,
( cc(sK4)
| sK6 = sK5
| xsd_integer(sK2) ),
inference(copy,[status(thm)],[c_248]) ).
cnf(c_106,plain,
( sK6 = A
| ~ rp(sK4,A)
| ~ cc(sK4)
| sK6 = sK5
| xsd_integer(sK2) ),
inference(resolve,[status(thm)],[c_97,c_24]) ).
cnf(c_109,plain,
( ~ rp(sK4,sK5)
| ~ cc(sK4)
| sK6 = sK5
| xsd_integer(sK2) ),
inference(factor,[status(thm)],[c_106]) ).
cnf(c_249,plain,
( sK6 = sK5
| xsd_integer(sK2)
| ~ cc(sK4)
| sK6 = sK5
| xsd_integer(sK2) ),
inference(resolve,[status(thm)],[c_109,c_98]) ).
cnf(c_250,plain,
( sK6 = sK5
| ~ cc(sK4)
| sK6 = sK5
| xsd_integer(sK2) ),
inference(copy,[status(thm)],[c_249]) ).
cnf(c_114,plain,
( ~ cc(sK4)
| sK6 = sK5
| xsd_integer(sK2) ),
inference(copy,[status(thm)],[c_250]) ).
cnf(c_251,plain,
( sK6 = sK5
| xsd_integer(sK2)
| sK6 = sK5
| xsd_integer(sK2) ),
inference(resolve,[status(thm)],[c_114,c_99]) ).
cnf(c_252,plain,
( sK6 = sK5
| sK6 = sK5
| xsd_integer(sK2) ),
inference(copy,[status(thm)],[c_251]) ).
cnf(c_115,plain,
( sK6 = sK5
| xsd_integer(sK2) ),
inference(copy,[status(thm)],[c_252]) ).
cnf(c_123,plain,
( rp(sK4,sK6)
| ~ rp(sK3,A)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(resolve,[status(thm)],[c_115,c_38]) ).
cnf(c_124,plain,
( rp(sK4,sK5)
| ~ rp(sK3,A)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(resolve,[status(thm)],[c_115,c_36]) ).
cnf(c_125,plain,
( cc(sK4)
| ~ rp(sK3,A)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(resolve,[status(thm)],[c_115,c_34]) ).
cnf(c_126,plain,
( rp(sK4,sK6)
| cc(sK3)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(resolve,[status(thm)],[c_115,c_30]) ).
cnf(c_127,plain,
( rp(sK4,sK5)
| cc(sK3)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(resolve,[status(thm)],[c_115,c_28]) ).
cnf(c_128,plain,
( cc(sK4)
| cc(sK3)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(resolve,[status(thm)],[c_115,c_26]) ).
cnf(c_129,plain,
( ~ xsd_string(sK2)
| sK6 = sK5 ),
inference(resolve,[status(thm)],[c_115,c_21]) ).
cnf(c_136,plain,
( sK6 = A
| ~ rp(sK4,A)
| ~ cc(sK4)
| cc(sK3)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(resolve,[status(thm)],[c_126,c_24]) ).
cnf(c_139,plain,
( ~ rp(sK4,sK5)
| ~ cc(sK4)
| cc(sK3)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(factor,[status(thm)],[c_136]) ).
cnf(c_253,plain,
( cc(sK3)
| xsd_string(sK2)
| sK6 = sK5
| ~ cc(sK4)
| cc(sK3)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(resolve,[status(thm)],[c_139,c_127]) ).
cnf(c_254,plain,
( cc(sK3)
| xsd_string(sK2)
| ~ cc(sK4)
| cc(sK3)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(copy,[status(thm)],[c_253]) ).
cnf(c_255,plain,
( cc(sK3)
| ~ cc(sK4)
| cc(sK3)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(copy,[status(thm)],[c_254]) ).
cnf(c_151,plain,
( ~ cc(sK4)
| cc(sK3)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(copy,[status(thm)],[c_255]) ).
cnf(c_256,plain,
( cc(sK3)
| xsd_string(sK2)
| sK6 = sK5
| cc(sK3)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(resolve,[status(thm)],[c_151,c_128]) ).
cnf(c_257,plain,
( cc(sK3)
| xsd_string(sK2)
| cc(sK3)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(copy,[status(thm)],[c_256]) ).
cnf(c_258,plain,
( cc(sK3)
| cc(sK3)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(copy,[status(thm)],[c_257]) ).
cnf(c_152,plain,
( cc(sK3)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(copy,[status(thm)],[c_258]) ).
cnf(c_154,plain,
( rp(sK3,sK0(sK3))
| xsd_string(sK2)
| sK6 = sK5 ),
inference(resolve,[status(thm)],[c_152,c_23]) ).
cnf(c_259,plain,
( cc(sK4)
| xsd_string(sK2)
| sK6 = sK5
| xsd_string(sK2)
| sK6 = sK5 ),
inference(resolve,[status(thm)],[c_154,c_125]) ).
cnf(c_260,plain,
( cc(sK4)
| xsd_string(sK2)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(copy,[status(thm)],[c_259]) ).
cnf(c_178,plain,
( cc(sK4)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(copy,[status(thm)],[c_260]) ).
cnf(c_261,plain,
( rp(sK4,sK5)
| xsd_string(sK2)
| sK6 = sK5
| xsd_string(sK2)
| sK6 = sK5 ),
inference(resolve,[status(thm)],[c_154,c_124]) ).
cnf(c_262,plain,
( rp(sK4,sK5)
| xsd_string(sK2)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(copy,[status(thm)],[c_261]) ).
cnf(c_179,plain,
( rp(sK4,sK5)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(copy,[status(thm)],[c_262]) ).
cnf(c_263,plain,
( rp(sK4,sK6)
| xsd_string(sK2)
| sK6 = sK5
| xsd_string(sK2)
| sK6 = sK5 ),
inference(resolve,[status(thm)],[c_154,c_123]) ).
cnf(c_264,plain,
( rp(sK4,sK6)
| xsd_string(sK2)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(copy,[status(thm)],[c_263]) ).
cnf(c_180,plain,
( rp(sK4,sK6)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(copy,[status(thm)],[c_264]) ).
cnf(c_190,plain,
( sK6 = A
| ~ rp(sK4,A)
| ~ cc(sK4)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(resolve,[status(thm)],[c_180,c_24]) ).
cnf(c_193,plain,
( ~ rp(sK4,sK5)
| ~ cc(sK4)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(factor,[status(thm)],[c_190]) ).
cnf(c_265,plain,
( xsd_string(sK2)
| sK6 = sK5
| ~ cc(sK4)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(resolve,[status(thm)],[c_193,c_179]) ).
cnf(c_266,plain,
( xsd_string(sK2)
| ~ cc(sK4)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(copy,[status(thm)],[c_265]) ).
cnf(c_195,plain,
( ~ cc(sK4)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(copy,[status(thm)],[c_266]) ).
cnf(c_267,plain,
( xsd_string(sK2)
| sK6 = sK5
| xsd_string(sK2)
| sK6 = sK5 ),
inference(resolve,[status(thm)],[c_195,c_178]) ).
cnf(c_268,plain,
( xsd_string(sK2)
| xsd_string(sK2)
| sK6 = sK5 ),
inference(copy,[status(thm)],[c_267]) ).
cnf(c_196,plain,
( xsd_string(sK2)
| sK6 = sK5 ),
inference(copy,[status(thm)],[c_268]) ).
cnf(c_269,plain,
( sK6 = sK5
| sK6 = sK5 ),
inference(resolve,[status(thm)],[c_196,c_129]) ).
cnf(c_197,plain,
sK6 = sK5,
inference(copy,[status(thm)],[c_269]) ).
cnf(c_270,negated_conjecture,
( sK5 != sK5
| ~ rp(sK3,A)
| xsd_integer(sK2) ),
inference(paramod,[status(thm)],[c_197,c_65]) ).
cnf(c_199,negated_conjecture,
( ~ rp(sK3,A)
| xsd_integer(sK2) ),
inference(copy,[status(thm)],[c_270]) ).
cnf(c_271,negated_conjecture,
( sK5 != sK5
| cc(sK3)
| xsd_integer(sK2) ),
inference(paramod,[status(thm)],[c_197,c_61]) ).
cnf(c_200,negated_conjecture,
( cc(sK3)
| xsd_integer(sK2) ),
inference(copy,[status(thm)],[c_271]) ).
cnf(c_272,negated_conjecture,
( sK5 != sK5
| ~ rp(sK3,A)
| ~ xsd_integer(sK2)
| xsd_string(sK2) ),
inference(paramod,[status(thm)],[c_197,c_40]) ).
cnf(c_201,negated_conjecture,
( ~ rp(sK3,A)
| ~ xsd_integer(sK2)
| xsd_string(sK2) ),
inference(copy,[status(thm)],[c_272]) ).
cnf(c_273,negated_conjecture,
( sK5 != sK5
| cc(sK3)
| ~ xsd_integer(sK2)
| xsd_string(sK2) ),
inference(paramod,[status(thm)],[c_197,c_32]) ).
cnf(c_202,negated_conjecture,
( cc(sK3)
| ~ xsd_integer(sK2)
| xsd_string(sK2) ),
inference(copy,[status(thm)],[c_273]) ).
cnf(c_205,plain,
( rp(sK3,sK0(sK3))
| xsd_integer(sK2) ),
inference(resolve,[status(thm)],[c_200,c_23]) ).
cnf(c_274,plain,
( xsd_integer(sK2)
| xsd_integer(sK2) ),
inference(resolve,[status(thm)],[c_205,c_199]) ).
cnf(c_209,plain,
xsd_integer(sK2),
inference(copy,[status(thm)],[c_274]) ).
cnf(c_210,negated_conjecture,
( cc(sK3)
| xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_209,c_202]) ).
cnf(c_211,negated_conjecture,
( ~ rp(sK3,A)
| xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_209,c_201]) ).
cnf(c_212,plain,
~ xsd_string(sK2),
inference(resolve,[status(thm)],[c_209,c_21]) ).
cnf(c_214,negated_conjecture,
~ rp(sK3,A),
inference(resolve,[status(thm)],[c_212,c_211]) ).
cnf(c_215,negated_conjecture,
cc(sK3),
inference(resolve,[status(thm)],[c_212,c_210]) ).
cnf(c_275,negated_conjecture,
~ cc(sK3),
inference(resolve,[status(thm)],[c_23,c_214]) ).
cnf(c_216,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_215,c_275]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS142+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/10.37 % Computer : n019.cluster.edu
% 0.08/10.37 % Model : x86_64 x86_64
% 0.08/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.37 % Memory : 8046.5625MB
% 0.08/10.37 % OS : Linux 6.8.0-71-generic
% 0.08/10.37 % CPULimit : 300
% 0.08/10.37 % WCLimit : 300
% 0.08/10.37 % DateTime : Fri Sep 25 19:41:15 UTC 2026
% 0.08/10.37 % CPUTime :
% 0.08/10.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/10.37 % Process 3497199 was started by sandbox on n019,
% 0.08/10.37 % Fri Sep 25 19:41:15 2026
% 0.08/10.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/10.38
% 0.08/10.38 % From the command line: assign(max_seconds, 300).
% 0.13/10.40
% 0.13/10.40 % SZS status Theorem for theBenchmark
% 0.13/10.40
% 0.13/10.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/10.40 % Length of proof is 93.
% 0.13/10.40 % Level of proof is 30.
% 0.13/10.40 % Maximum clause weight is 20.000.
% 0.13/10.40 % Given clauses 121.
% 0.13/10.40
% 0.13/10.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------