%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS132+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 : n008.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 07:46:06 AM UTC 2026
% Result : Theorem 0.15s 0.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 12
% Syntax : Number of formulae : 142 ( 9 unt; 0 def)
% Number of atoms : 595 ( 0 equ)
% Maximal formula atoms : 38 ( 4 avg)
% Number of connectives : 708 ( 255 ~; 378 |; 58 &)
% ( 12 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 16 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-1 aty)
% Number of variables : 130 ( 9 sgn 70 !; 15 ?)
% 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] :
( cA(X)
<=> ? [Y] :
( cowlThing(Y)
& rq(X,Y) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cAorB(X)
<=> ? [Y] :
( cowlThing(Y)
& rs(X,Y) ) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X] :
( cB(X)
<=> ? [Y] :
( cowlThing(Y)
& rr(X,Y) ) ),
file('theBenchmark.p',axiom_4) ).
fof(axiom_5,axiom,
! [X] :
( cNothing(X)
=> ? [Y0] : rp(X,Y0) ),
file('theBenchmark.p',axiom_5) ).
fof(axiom_6,axiom,
! [X] :
( cNothing(X)
=> ~ ? [Y] : rp(X,Y) ),
file('theBenchmark.p',axiom_6) ).
fof(axiom_7,axiom,
! [X] :
( cnotA(X)
<=> ! [Y] :
( rq(X,Y)
=> cNothing(Y) ) ),
file('theBenchmark.p',axiom_7) ).
fof(axiom_8,axiom,
! [X] :
( cnotAorB(X)
<=> ! [Y] :
( rs(X,Y)
=> cNothing(Y) ) ),
file('theBenchmark.p',axiom_8) ).
fof(axiom_9,axiom,
! [X] :
( cnotAorB(X)
<=> ( cnotA(X)
& cnotB(X) ) ),
file('theBenchmark.p',axiom_9) ).
fof(axiom_10,axiom,
! [X] :
( cnotB(X)
<=> ! [Y] :
( rr(X,Y)
=> cNothing(Y) ) ),
file('theBenchmark.p',axiom_10) ).
fof(the_axiom,conjecture,
( ! [X] :
( cAorB(X)
<=> ( cA(X)
| cB(X) ) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('theBenchmark.p',the_axiom) ).
fof(the_axiom_neg,negated_conjecture,
~ ( ! [X] :
( cAorB(X)
<=> ( cA(X)
| cB(X) ) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(assume_negation,[status(cth)],[the_axiom]) ).
fof(nnf_3,plain,
! [X] :
( ( ! [Y] :
( ~ cowlThing(Y)
| ~ rq(X,Y) )
| cA(X) )
& ( ? [X0] :
( cowlThing(X0)
& rq(X,X0) )
| ~ cA(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ! [Y] :
( ~ cowlThing(Y)
| ~ rq(X,Y) )
| cA(X) )
& ( ( cowlThing(sK4(X))
& rq(X,sK4(X)) )
| ~ cA(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X0,sK4(X))],[nnf_3]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1] :
( ~ cowlThing(VAR_1)
| ~ rq(VAR_0,VAR_1)
| cA(VAR_0) )
& ! [VAR_0] :
( cowlThing(sK4(VAR_0))
| ~ cA(VAR_0) )
& ! [VAR_0] :
( rq(VAR_0,sK4(VAR_0))
| ~ cA(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_13,plain,
( ~ cowlThing(B)
| ~ rq(A,B)
| cA(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_15,plain,
cowlThing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
fof(nnf_4,plain,
! [X] :
( ( ! [Y] :
( ~ cowlThing(Y)
| ~ rs(X,Y) )
| cAorB(X) )
& ( ? [X0] :
( cowlThing(X0)
& rs(X,X0) )
| ~ cAorB(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_3]) ).
fof(sk_axiom_3_sk,plain,
! [X] :
( ( ! [Y] :
( ~ cowlThing(Y)
| ~ rs(X,Y) )
| cAorB(X) )
& ( ( cowlThing(sK6(X))
& rs(X,sK6(X)) )
| ~ cAorB(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6(X))],[nnf_4]) ).
fof(sk_axiom_3,plain,
( ! [VAR_0,VAR_1] :
( ~ cowlThing(VAR_1)
| ~ rs(VAR_0,VAR_1)
| cAorB(VAR_0) )
& ! [VAR_0] :
( cowlThing(sK6(VAR_0))
| ~ cAorB(VAR_0) )
& ! [VAR_0] :
( rs(VAR_0,sK6(VAR_0))
| ~ cAorB(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_3_sk]) ).
cnf(c_17,plain,
( ~ cowlThing(B)
| ~ rs(A,B)
| cAorB(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_3]) ).
fof(nnf_5,plain,
! [X] :
( ( ! [Y] :
( ~ cowlThing(Y)
| ~ rr(X,Y) )
| cB(X) )
& ( ? [X0] :
( cowlThing(X0)
& rr(X,X0) )
| ~ cB(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_4]) ).
fof(sk_axiom_4_sk,plain,
! [X] :
( ( ! [Y] :
( ~ cowlThing(Y)
| ~ rr(X,Y) )
| cB(X) )
& ( ( cowlThing(sK9(X))
& rr(X,sK9(X)) )
| ~ cB(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X0,sK9(X))],[nnf_5]) ).
fof(sk_axiom_4,plain,
( ! [VAR_0,VAR_1] :
( ~ cowlThing(VAR_1)
| ~ rr(VAR_0,VAR_1)
| cB(VAR_0) )
& ! [VAR_0] :
( cowlThing(sK9(VAR_0))
| ~ cB(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK9(VAR_0))
| ~ cB(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_4_sk]) ).
cnf(c_19,plain,
( ~ cowlThing(B)
| ~ rr(A,B)
| cB(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_4]) ).
fof(nnf_12,plain,
( ? [X] :
( ( ( ~ cA(X)
& ~ cB(X) )
| ~ cAorB(X) )
& ( cA(X)
| cB(X)
| cAorB(X) ) )
| ? [X0] :
( ( xsd_integer(X0)
| ~ xsd_string(X0) )
& ( ~ xsd_integer(X0)
| xsd_string(X0) ) )
| ? [X1] :
( cowlNothing(X1)
| ~ cowlThing(X1) ) ),
inference(fof_nnf,[status(thm)],[the_axiom_neg]) ).
fof(sk_the_axiom_neg_sk,plain,
( ( ( ( ~ cA(sK2)
& ~ cB(sK2) )
| ~ cAorB(sK2) )
& ( cA(sK2)
| cB(sK2)
| cAorB(sK2) ) )
| ( ( xsd_integer(sK1)
| ~ xsd_string(sK1) )
& ( ~ xsd_integer(sK1)
| xsd_string(sK1) ) )
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X1,sK0),skolemize(X0,sK1),skolemize(X,sK2)],[nnf_12]) ).
fof(sk_the_axiom_neg,plain,
( ( ~ cA(sK2)
| ~ cAorB(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( ~ cB(sK2)
| ~ cAorB(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( cA(sK2)
| cB(sK2)
| cAorB(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( ~ cA(sK2)
| ~ cAorB(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( ~ cB(sK2)
| ~ cAorB(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( cA(sK2)
| cB(sK2)
| cAorB(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ) ),
inference(cnf_transformation,[status(thm)],[sk_the_axiom_neg_sk]) ).
cnf(c_20,negated_conjecture,
( cA(sK2)
| cB(sK2)
| cAorB(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_21,negated_conjecture,
( ~ cB(sK2)
| ~ cAorB(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_22,negated_conjecture,
( ~ cA(sK2)
| ~ cAorB(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_23,negated_conjecture,
( cA(sK2)
| cB(sK2)
| cAorB(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_24,negated_conjecture,
( ~ cB(sK2)
| ~ cAorB(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_25,negated_conjecture,
( ~ cA(sK2)
| ~ cAorB(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_26,plain,
~ cowlNothing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_27,negated_conjecture,
( cA(sK2)
| cB(sK2)
| cAorB(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_20,c_15]) ).
cnf(c_28,negated_conjecture,
( ~ cB(sK2)
| ~ cAorB(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_21,c_15]) ).
cnf(c_29,negated_conjecture,
( ~ cA(sK2)
| ~ cAorB(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_22,c_15]) ).
cnf(c_30,negated_conjecture,
( cA(sK2)
| cB(sK2)
| cAorB(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_23,c_15]) ).
cnf(c_31,negated_conjecture,
( ~ cB(sK2)
| ~ cAorB(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_24,c_15]) ).
cnf(c_32,negated_conjecture,
( ~ cA(sK2)
| ~ cAorB(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_25,c_15]) ).
cnf(c_33,negated_conjecture,
( ~ cA(sK2)
| ~ cAorB(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_26,c_29]) ).
cnf(c_34,negated_conjecture,
( cA(sK2)
| cB(sK2)
| cAorB(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_26,c_30]) ).
cnf(c_35,negated_conjecture,
( ~ cB(sK2)
| ~ cAorB(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_26,c_31]) ).
cnf(c_36,negated_conjecture,
( ~ cA(sK2)
| ~ cAorB(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_26,c_32]) ).
cnf(c_37,negated_conjecture,
( ~ cB(sK2)
| ~ cAorB(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_26,c_28]) ).
cnf(c_38,negated_conjecture,
( cA(sK2)
| cB(sK2)
| cAorB(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_26,c_27]) ).
cnf(c_39,plain,
( ~ xsd_integer(A)
| ~ xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_40,plain,
( xsd_integer(A)
| xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
fof(nnf_8,plain,
! [X] :
( ( ? [Y] :
( ~ cNothing(Y)
& rq(X,Y) )
| cnotA(X) )
& ( ! [X0] :
( cNothing(X0)
| ~ rq(X,X0) )
| ~ cnotA(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_7]) ).
fof(sk_axiom_7_sk,plain,
! [X] :
( ( ( ~ cNothing(sK3(X))
& rq(X,sK3(X)) )
| cnotA(X) )
& ( ! [X0] :
( cNothing(X0)
| ~ rq(X,X0) )
| ~ cnotA(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(Y,sK3(X))],[nnf_8]) ).
fof(sk_axiom_7,plain,
( ! [VAR_0] :
( ~ cNothing(sK3(VAR_0))
| cnotA(VAR_0) )
& ! [VAR_0] :
( rq(VAR_0,sK3(VAR_0))
| cnotA(VAR_0) )
& ! [VAR_0,VAR_1] :
( cNothing(VAR_1)
| ~ rq(VAR_0,VAR_1)
| ~ cnotA(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_7_sk]) ).
cnf(c_41,plain,
( rq(A,sK3(A))
| cnotA(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_7]) ).
cnf(c_43,plain,
( ~ rq(A,B)
| cA(A) ),
inference(resolve,[status(thm)],[c_13,c_15]) ).
cnf(c_44,plain,
( cNothing(B)
| ~ rq(A,B)
| ~ cnotA(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_7]) ).
cnf(c_45,plain,
( rq(A,sK4(A))
| ~ cA(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_46,plain,
( cA(A)
| cnotA(A) ),
inference(resolve,[status(thm)],[c_41,c_43]) ).
cnf(c_47,plain,
( cNothing(sK4(A))
| ~ cnotA(A)
| ~ cA(A) ),
inference(resolve,[status(thm)],[c_45,c_44]) ).
cnf(c_50,negated_conjecture,
( cA(sK2)
| cB(sK2)
| cAorB(sK2)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_39,c_38]) ).
cnf(c_51,negated_conjecture,
( ~ cA(sK2)
| ~ cAorB(sK2)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_39,c_33]) ).
cnf(c_52,negated_conjecture,
( cA(sK2)
| cB(sK2)
| cAorB(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_40,c_34]) ).
cnf(c_53,negated_conjecture,
( ~ cA(sK2)
| ~ cAorB(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_40,c_36]) ).
fof(nnf_9,plain,
! [X] :
( ( ? [Y] :
( ~ cNothing(Y)
& rs(X,Y) )
| cnotAorB(X) )
& ( ! [X0] :
( cNothing(X0)
| ~ rs(X,X0) )
| ~ cnotAorB(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_8]) ).
fof(sk_axiom_8_sk,plain,
! [X] :
( ( ( ~ cNothing(sK5(X))
& rs(X,sK5(X)) )
| cnotAorB(X) )
& ( ! [X0] :
( cNothing(X0)
| ~ rs(X,X0) )
| ~ cnotAorB(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(Y,sK5(X))],[nnf_9]) ).
fof(sk_axiom_8,plain,
( ! [VAR_0] :
( ~ cNothing(sK5(VAR_0))
| cnotAorB(VAR_0) )
& ! [VAR_0] :
( rs(VAR_0,sK5(VAR_0))
| cnotAorB(VAR_0) )
& ! [VAR_0,VAR_1] :
( cNothing(VAR_1)
| ~ rs(VAR_0,VAR_1)
| ~ cnotAorB(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_8_sk]) ).
cnf(c_54,plain,
( rs(A,sK5(A))
| cnotAorB(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_8]) ).
cnf(c_56,plain,
( ~ rs(A,B)
| cAorB(A) ),
inference(resolve,[status(thm)],[c_17,c_15]) ).
cnf(c_59,plain,
( cNothing(B)
| ~ rs(A,B)
| ~ cnotAorB(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_8]) ).
cnf(c_60,plain,
( rs(A,sK6(A))
| ~ cAorB(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_3]) ).
cnf(c_61,plain,
( cAorB(A)
| cnotAorB(A) ),
inference(resolve,[status(thm)],[c_54,c_56]) ).
cnf(c_62,plain,
( cNothing(sK6(A))
| ~ cnotAorB(A)
| ~ cAorB(A) ),
inference(resolve,[status(thm)],[c_60,c_59]) ).
cnf(c_64,negated_conjecture,
( ~ cB(sK2)
| ~ cAorB(sK2)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_39,c_37]) ).
cnf(c_65,negated_conjecture,
( ~ cB(sK2)
| ~ cAorB(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_40,c_35]) ).
cnf(c_67,negated_conjecture,
( cNothing(sK4(sK2))
| ~ cnotA(sK2)
| cB(sK2)
| cAorB(sK2)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_50,c_47]) ).
cnf(c_68,negated_conjecture,
( cnotA(sK2)
| ~ cAorB(sK2)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_51,c_46]) ).
cnf(c_70,negated_conjecture,
( cNothing(sK4(sK2))
| ~ cnotA(sK2)
| cB(sK2)
| cAorB(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_52,c_47]) ).
cnf(c_71,negated_conjecture,
( cnotA(sK2)
| ~ cAorB(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_53,c_46]) ).
fof(nnf_6,plain,
! [X] :
( ? [Y0] : rp(X,Y0)
| ~ cNothing(X) ),
inference(fof_nnf,[status(thm)],[axiom_5]) ).
fof(sk_axiom_5,plain,
! [X] :
( rp(X,sK7(X))
| ~ cNothing(X) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(Y0,sK7(X))],[nnf_6]) ).
cnf(c_72,plain,
( rp(A,sK7(A))
| ~ cNothing(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_5]) ).
cnf(c_73,plain,
( ~ rp(A,B)
| ~ cNothing(A) ),
inference(clausify,[status(thm)],[axiom_6]) ).
cnf(c_74,plain,
( ~ cnotA(A)
| ~ cnotB(A)
| cnotAorB(A) ),
inference(clausify,[status(thm)],[axiom_9]) ).
cnf(c_75,plain,
( cnotA(A)
| ~ cnotAorB(A) ),
inference(clausify,[status(thm)],[axiom_9]) ).
cnf(c_78,negated_conjecture,
( cNothing(sK6(sK2))
| ~ cnotAorB(sK2)
| cNothing(sK4(sK2))
| ~ cnotA(sK2)
| cB(sK2)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_67,c_62]) ).
cnf(c_80,negated_conjecture,
( cnotAorB(sK2)
| cnotA(sK2)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_68,c_61]) ).
cnf(c_82,negated_conjecture,
( cNothing(sK6(sK2))
| ~ cnotAorB(sK2)
| cNothing(sK4(sK2))
| ~ cnotA(sK2)
| cB(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_70,c_62]) ).
cnf(c_84,negated_conjecture,
( cnotAorB(sK2)
| cnotA(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_71,c_61]) ).
cnf(c_88,negated_conjecture,
( ~ cnotB(sK2)
| cnotAorB(sK2)
| cnotAorB(sK2)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_80,c_74]) ).
cnf(c_90,negated_conjecture,
( ~ cnotB(sK2)
| cnotAorB(sK2)
| cnotAorB(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_84,c_74]) ).
fof(nnf_11,plain,
! [X] :
( ( ? [Y] :
( ~ cNothing(Y)
& rr(X,Y) )
| cnotB(X) )
& ( ! [X0] :
( cNothing(X0)
| ~ rr(X,X0) )
| ~ cnotB(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_10]) ).
fof(sk_axiom_10_sk,plain,
! [X] :
( ( ( ~ cNothing(sK8(X))
& rr(X,sK8(X)) )
| cnotB(X) )
& ( ! [X0] :
( cNothing(X0)
| ~ rr(X,X0) )
| ~ cnotB(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(Y,sK8(X))],[nnf_11]) ).
fof(sk_axiom_10,plain,
( ! [VAR_0] :
( ~ cNothing(sK8(VAR_0))
| cnotB(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK8(VAR_0))
| cnotB(VAR_0) )
& ! [VAR_0,VAR_1] :
( cNothing(VAR_1)
| ~ rr(VAR_0,VAR_1)
| ~ cnotB(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_10_sk]) ).
cnf(c_91,plain,
( rr(A,sK8(A))
| cnotB(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_10]) ).
cnf(c_92,plain,
( cNothing(B)
| ~ rr(A,B)
| ~ cnotB(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_10]) ).
cnf(c_93,plain,
( cnotB(A)
| ~ cnotAorB(A) ),
inference(clausify,[status(thm)],[axiom_9]) ).
cnf(c_94,plain,
( cNothing(B)
| ~ rr(A,B)
| ~ cnotAorB(A) ),
inference(resolve,[status(thm)],[c_93,c_92]) ).
cnf(c_96,negated_conjecture,
( cnotAorB(sK2)
| cnotAorB(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1)
| rr(sK2,sK8(sK2)) ),
inference(resolve,[status(thm)],[c_91,c_90]) ).
cnf(c_145,negated_conjecture,
( cnotAorB(sK2)
| cnotAorB(sK2)
| xsd_integer(sK1)
| rr(sK2,sK8(sK2)) ),
inference(copy,[status(thm)],[c_96]) ).
cnf(c_97,negated_conjecture,
( cnotAorB(sK2)
| xsd_integer(sK1)
| rr(sK2,sK8(sK2)) ),
inference(copy,[status(thm)],[c_145]) ).
cnf(c_99,negated_conjecture,
( cnotAorB(sK2)
| cnotAorB(sK2)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1)
| rr(sK2,sK8(sK2)) ),
inference(resolve,[status(thm)],[c_91,c_88]) ).
cnf(c_146,negated_conjecture,
( cnotAorB(sK2)
| cnotAorB(sK2)
| ~ xsd_integer(sK1)
| rr(sK2,sK8(sK2)) ),
inference(copy,[status(thm)],[c_99]) ).
cnf(c_100,negated_conjecture,
( cnotAorB(sK2)
| ~ xsd_integer(sK1)
| rr(sK2,sK8(sK2)) ),
inference(copy,[status(thm)],[c_146]) ).
cnf(c_102,plain,
( ~ cNothing(A)
| ~ cNothing(A) ),
inference(resolve,[status(thm)],[c_72,c_73]) ).
cnf(c_103,plain,
~ cNothing(A),
inference(copy,[status(thm)],[c_102]) ).
cnf(c_104,plain,
( rr(A,sK9(A))
| ~ cB(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_4]) ).
cnf(c_106,plain,
( ~ rr(A,B)
| cB(A) ),
inference(resolve,[status(thm)],[c_19,c_15]) ).
cnf(c_107,negated_conjecture,
( cnotAorB(sK2)
| ~ cB(sK2)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_64,c_61]) ).
cnf(c_108,negated_conjecture,
( cnotAorB(sK2)
| ~ cB(sK2)
| ~ xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_107]) ).
cnf(c_109,negated_conjecture,
( cnotAorB(sK2)
| ~ cB(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_65,c_61]) ).
cnf(c_110,negated_conjecture,
( cnotAorB(sK2)
| ~ cB(sK2)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_109]) ).
cnf(c_117,negated_conjecture,
( ~ cnotAorB(sK2)
| cNothing(sK6(sK2))
| ~ cnotAorB(sK2)
| cNothing(sK4(sK2))
| cB(sK2)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_78,c_75]) ).
cnf(c_147,negated_conjecture,
( ~ cnotAorB(sK2)
| cNothing(sK6(sK2))
| ~ cnotAorB(sK2)
| cNothing(sK4(sK2))
| cB(sK2)
| ~ xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_117]) ).
cnf(c_148,negated_conjecture,
( cNothing(sK6(sK2))
| ~ cnotAorB(sK2)
| cNothing(sK4(sK2))
| cB(sK2)
| ~ xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_147]) ).
cnf(c_149,negated_conjecture,
( cNothing(sK6(sK2))
| ~ cnotAorB(sK2)
| cB(sK2)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_103,c_148]) ).
cnf(c_118,negated_conjecture,
( ~ cnotAorB(sK2)
| cB(sK2)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_103,c_149]) ).
cnf(c_123,negated_conjecture,
( ~ cnotAorB(sK2)
| cNothing(sK6(sK2))
| ~ cnotAorB(sK2)
| cNothing(sK4(sK2))
| cB(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_82,c_75]) ).
cnf(c_150,negated_conjecture,
( ~ cnotAorB(sK2)
| cNothing(sK6(sK2))
| ~ cnotAorB(sK2)
| cNothing(sK4(sK2))
| cB(sK2)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_123]) ).
cnf(c_151,negated_conjecture,
( cNothing(sK6(sK2))
| ~ cnotAorB(sK2)
| cNothing(sK4(sK2))
| cB(sK2)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_150]) ).
cnf(c_152,negated_conjecture,
( cNothing(sK6(sK2))
| ~ cnotAorB(sK2)
| cB(sK2)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_103,c_151]) ).
cnf(c_124,negated_conjecture,
( ~ cnotAorB(sK2)
| cB(sK2)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_103,c_152]) ).
cnf(c_128,plain,
( ~ rr(A,B)
| ~ cnotAorB(A) ),
inference(resolve,[status(thm)],[c_103,c_94]) ).
cnf(c_129,plain,
( cnotAorB(sK2)
| xsd_integer(sK1)
| cB(sK2) ),
inference(resolve,[status(thm)],[c_106,c_97]) ).
cnf(c_153,negated_conjecture,
( cB(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1)
| cB(sK2) ),
inference(resolve,[status(thm)],[c_129,c_124]) ).
cnf(c_154,negated_conjecture,
( cB(sK2)
| xsd_integer(sK1)
| cB(sK2) ),
inference(copy,[status(thm)],[c_153]) ).
cnf(c_130,negated_conjecture,
( xsd_integer(sK1)
| cB(sK2) ),
inference(copy,[status(thm)],[c_154]) ).
cnf(c_155,negated_conjecture,
( cnotAorB(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_130,c_110]) ).
cnf(c_131,negated_conjecture,
( cnotAorB(sK2)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_155]) ).
cnf(c_132,plain,
( rr(sK2,sK9(sK2))
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_130,c_104]) ).
cnf(c_133,plain,
( ~ cnotAorB(sK2)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_132,c_128]) ).
cnf(c_156,plain,
( xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_133,c_131]) ).
cnf(c_135,plain,
xsd_integer(sK1),
inference(copy,[status(thm)],[c_156]) ).
cnf(c_136,negated_conjecture,
( ~ cnotAorB(sK2)
| cB(sK2) ),
inference(resolve,[status(thm)],[c_135,c_118]) ).
cnf(c_137,negated_conjecture,
( cnotAorB(sK2)
| ~ cB(sK2) ),
inference(resolve,[status(thm)],[c_135,c_108]) ).
cnf(c_138,negated_conjecture,
( cnotAorB(sK2)
| rr(sK2,sK8(sK2)) ),
inference(resolve,[status(thm)],[c_135,c_100]) ).
cnf(c_139,plain,
( cB(sK2)
| cnotAorB(sK2) ),
inference(resolve,[status(thm)],[c_138,c_106]) ).
cnf(c_157,negated_conjecture,
( cB(sK2)
| cB(sK2) ),
inference(resolve,[status(thm)],[c_139,c_136]) ).
cnf(c_140,negated_conjecture,
cB(sK2),
inference(copy,[status(thm)],[c_157]) ).
cnf(c_141,negated_conjecture,
cnotAorB(sK2),
inference(resolve,[status(thm)],[c_140,c_137]) ).
cnf(c_142,plain,
rr(sK2,sK9(sK2)),
inference(resolve,[status(thm)],[c_140,c_104]) ).
cnf(c_143,negated_conjecture,
~ rr(sK2,A),
inference(resolve,[status(thm)],[c_128,c_141]) ).
cnf(c_144,plain,
$false,
inference(resolve,[status(thm)],[c_143,c_142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS132+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n008.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 19:41:24 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.37 % Process 1706317 was started by sandbox on n008,
% 0.12/0.37 % Fri Sep 25 19:41:24 2026
% 0.12/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.38
% 0.15/0.38 % From the command line: assign(max_seconds, 300).
% 0.15/0.40
% 0.15/0.40 % SZS status Theorem for theBenchmark
% 0.15/0.40
% 0.15/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.15/0.40 % Length of proof is 105.
% 0.15/0.40 % Level of proof is 20.
% 0.15/0.40 % Maximum clause weight is 18.000.
% 0.15/0.40 % Given clauses 23.
% 0.15/0.40
% 0.15/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------