%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS175+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 : n017.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 07:46:15 AM UTC 2026
% Result : Theorem 0.16s 5.40s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 7
% Syntax : Number of formulae : 114 ( 11 unt; 0 def)
% Number of atoms : 552 ( 163 equ)
% Maximal formula atoms : 50 ( 4 avg)
% Number of connectives : 698 ( 260 ~; 406 |; 23 &)
% ( 8 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 32 ( 2 sgn 13 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cA_and_B_substitution_1,axiom,
! [A,B] :
( ( cA_and_B(A)
& A = B )
=> cA_and_B(B) ),
file('theBenchmark.p',cA_and_B_substitution_1) ).
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)
<=> X = ia ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cA_and_B(X)
<=> ( cB(X)
| cA(X) ) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X] :
( cB(X)
<=> X = ib ),
file('theBenchmark.p',axiom_4) ).
fof(the_axiom,conjecture,
( cowlThing(ib)
& cowlThing(ia)
& ! [X] :
( cA_and_B(X)
<=> ( X = ia
| X = ib ) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('theBenchmark.p',the_axiom) ).
fof(the_axiom_neg,negated_conjecture,
~ ( cowlThing(ib)
& cowlThing(ia)
& ! [X] :
( cA_and_B(X)
<=> ( X = ia
| X = ib ) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(assume_negation,[status(cth)],[the_axiom]) ).
cnf(c_15,plain,
( cA_and_B(A)
| ~ cA_and_B(B)
| A != B ),
inference(clausify,[status(thm)],[cA_and_B_substitution_1]) ).
cnf(c_21,plain,
cowlThing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_22,plain,
~ cowlNothing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_23,plain,
( ~ xsd_integer(A)
| ~ xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_24,plain,
( xsd_integer(A)
| xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_25,plain,
( ia = A
| ~ cA(A) ),
inference(clausify,[status(thm)],[axiom_2]) ).
cnf(c_26,plain,
( ia != A
| cA(A) ),
inference(clausify,[status(thm)],[axiom_2]) ).
cnf(c_27,plain,
( cB(A)
| cA(A)
| ~ cA_and_B(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
cnf(c_28,plain,
( ~ cA(A)
| cA_and_B(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
cnf(c_29,plain,
( ~ cB(A)
| cA_and_B(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
cnf(c_30,plain,
( ib = A
| ~ cB(A) ),
inference(clausify,[status(thm)],[axiom_4]) ).
cnf(c_31,plain,
( ib != A
| cB(A) ),
inference(clausify,[status(thm)],[axiom_4]) ).
fof(nnf_13,plain,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| ? [X] :
( ( ( ia != X
& ib != X )
| ~ cA_and_B(X) )
& ( ia = X
| ib = X
| cA_and_B(X) ) )
| ? [X1] :
( ( xsd_integer(X1)
| ~ xsd_string(X1) )
& ( ~ xsd_integer(X1)
| xsd_string(X1) ) )
| ? [X0] :
( cowlNothing(X0)
| ~ cowlThing(X0) ) ),
inference(fof_nnf,[status(thm)],[the_axiom_neg]) ).
fof(sk_the_axiom_neg_sk,plain,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| ( ( ( ia != sK2
& ib != sK2 )
| ~ cA_and_B(sK2) )
& ( ia = sK2
| ib = sK2
| cA_and_B(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(X0,sK0),skolemize(X1,sK1),skolemize(X,sK2)],[nnf_13]) ).
fof(sk_the_axiom_neg,plain,
( ( ~ cowlThing(ib)
| ~ cowlThing(ia)
| ia != sK2
| ~ cA_and_B(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( ~ cowlThing(ib)
| ~ cowlThing(ia)
| ib != sK2
| ~ cA_and_B(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( ~ cowlThing(ib)
| ~ cowlThing(ia)
| ia = sK2
| ib = sK2
| cA_and_B(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( ~ cowlThing(ib)
| ~ cowlThing(ia)
| ia != sK2
| ~ cA_and_B(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( ~ cowlThing(ib)
| ~ cowlThing(ia)
| ib != sK2
| ~ cA_and_B(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( ~ cowlThing(ib)
| ~ cowlThing(ia)
| ia = sK2
| ib = sK2
| cA_and_B(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ) ),
inference(cnf_transformation,[status(thm)],[sk_the_axiom_neg_sk]) ).
cnf(c_32,negated_conjecture,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| ia = sK2
| ib = sK2
| cA_and_B(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_87,negated_conjecture,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| ia = sK2
| sK2 = ib
| cA_and_B(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_88,negated_conjecture,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| sK2 = ia
| sK2 = ib
| cA_and_B(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(copy,[status(thm)],[c_87]) ).
cnf(c_89,negated_conjecture,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| sK2 = ia
| sK2 = ib
| cA_and_B(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_21,c_88]) ).
cnf(c_90,negated_conjecture,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| sK2 = ia
| sK2 = ib
| cA_and_B(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_22,c_89]) ).
cnf(c_91,negated_conjecture,
( ~ cowlThing(ib)
| sK2 = ia
| sK2 = ib
| cA_and_B(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_21,c_90]) ).
cnf(c_33,negated_conjecture,
( sK2 = ia
| sK2 = ib
| cA_and_B(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_21,c_91]) ).
cnf(c_34,negated_conjecture,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| ib != sK2
| ~ cA_and_B(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_92,negated_conjecture,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| sK2 != ib
| ~ cA_and_B(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(copy,[status(thm)],[c_34]) ).
cnf(c_93,negated_conjecture,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| sK2 != ib
| ~ cA_and_B(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_21,c_92]) ).
cnf(c_94,negated_conjecture,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| sK2 != ib
| ~ cA_and_B(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_22,c_93]) ).
cnf(c_95,negated_conjecture,
( ~ cowlThing(ib)
| sK2 != ib
| ~ cA_and_B(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_21,c_94]) ).
cnf(c_35,negated_conjecture,
( sK2 != ib
| ~ cA_and_B(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_21,c_95]) ).
cnf(c_36,negated_conjecture,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| ia != sK2
| ~ cA_and_B(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_96,negated_conjecture,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| sK2 != ia
| ~ cA_and_B(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(copy,[status(thm)],[c_36]) ).
cnf(c_97,negated_conjecture,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| sK2 != ia
| ~ cA_and_B(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_21,c_96]) ).
cnf(c_98,negated_conjecture,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| sK2 != ia
| ~ cA_and_B(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_22,c_97]) ).
cnf(c_99,negated_conjecture,
( ~ cowlThing(ib)
| sK2 != ia
| ~ cA_and_B(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_21,c_98]) ).
cnf(c_37,negated_conjecture,
( sK2 != ia
| ~ cA_and_B(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_21,c_99]) ).
cnf(c_38,negated_conjecture,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| ia = sK2
| ib = sK2
| cA_and_B(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_100,negated_conjecture,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| ia = sK2
| sK2 = ib
| cA_and_B(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(copy,[status(thm)],[c_38]) ).
cnf(c_101,negated_conjecture,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| sK2 = ia
| sK2 = ib
| cA_and_B(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(copy,[status(thm)],[c_100]) ).
cnf(c_102,negated_conjecture,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| sK2 = ia
| sK2 = ib
| cA_and_B(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_21,c_101]) ).
cnf(c_103,negated_conjecture,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| sK2 = ia
| sK2 = ib
| cA_and_B(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_22,c_102]) ).
cnf(c_104,negated_conjecture,
( ~ cowlThing(ib)
| sK2 = ia
| sK2 = ib
| cA_and_B(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_21,c_103]) ).
cnf(c_39,negated_conjecture,
( sK2 = ia
| sK2 = ib
| cA_and_B(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_21,c_104]) ).
cnf(c_40,negated_conjecture,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| ib != sK2
| ~ cA_and_B(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_105,negated_conjecture,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| sK2 != ib
| ~ cA_and_B(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(copy,[status(thm)],[c_40]) ).
cnf(c_106,negated_conjecture,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| sK2 != ib
| ~ cA_and_B(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_21,c_105]) ).
cnf(c_107,negated_conjecture,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| sK2 != ib
| ~ cA_and_B(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_22,c_106]) ).
cnf(c_108,negated_conjecture,
( ~ cowlThing(ib)
| sK2 != ib
| ~ cA_and_B(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_21,c_107]) ).
cnf(c_41,negated_conjecture,
( sK2 != ib
| ~ cA_and_B(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_21,c_108]) ).
cnf(c_42,negated_conjecture,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| ia != sK2
| ~ cA_and_B(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_109,negated_conjecture,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| sK2 != ia
| ~ cA_and_B(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(copy,[status(thm)],[c_42]) ).
cnf(c_110,negated_conjecture,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| sK2 != ia
| ~ cA_and_B(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_21,c_109]) ).
cnf(c_111,negated_conjecture,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| sK2 != ia
| ~ cA_and_B(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_22,c_110]) ).
cnf(c_112,negated_conjecture,
( ~ cowlThing(ib)
| sK2 != ia
| ~ cA_and_B(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_21,c_111]) ).
cnf(c_43,negated_conjecture,
( sK2 != ia
| ~ cA_and_B(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_21,c_112]) ).
cnf(c_45,plain,
cA(ia),
inference(xxres,[status(thm)],[c_26]) ).
cnf(c_46,plain,
cB(ib),
inference(xxres,[status(thm)],[c_31]) ).
cnf(c_113,negated_conjecture,
( xsd_integer(sK1)
| sK2 = ia
| sK2 = ib
| cA_and_B(sK2)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_39,c_24]) ).
cnf(c_47,negated_conjecture,
( sK2 = ia
| sK2 = ib
| cA_and_B(sK2)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_113]) ).
cnf(c_114,negated_conjecture,
( xsd_integer(sK1)
| sK2 != ib
| ~ cA_and_B(sK2)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_41,c_24]) ).
cnf(c_48,negated_conjecture,
( sK2 != ib
| ~ cA_and_B(sK2)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_114]) ).
cnf(c_115,negated_conjecture,
( xsd_integer(sK1)
| sK2 != ia
| ~ cA_and_B(sK2)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_43,c_24]) ).
cnf(c_49,negated_conjecture,
( sK2 != ia
| ~ cA_and_B(sK2)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_115]) ).
cnf(c_50,plain,
cA_and_B(ia),
inference(resolve,[status(thm)],[c_45,c_28]) ).
cnf(c_51,plain,
cA_and_B(ib),
inference(resolve,[status(thm)],[c_46,c_29]) ).
cnf(c_116,plain,
( cA_and_B(A)
| A != ib ),
inference(resolve,[status(thm)],[c_51,c_15]) ).
cnf(c_53,plain,
( cA_and_B(A)
| ib != A ),
inference(copy,[status(thm)],[c_116]) ).
cnf(c_117,negated_conjecture,
( sK2 = ia
| sK2 = ib
| cA_and_B(sK2)
| xsd_string(sK1)
| sK2 = ia
| sK2 = ib
| cA_and_B(sK2) ),
inference(resolve,[status(thm)],[c_47,c_33]) ).
cnf(c_118,negated_conjecture,
( sK2 = ia
| sK2 = ib
| xsd_string(sK1)
| sK2 = ia
| sK2 = ib
| cA_and_B(sK2) ),
inference(copy,[status(thm)],[c_117]) ).
cnf(c_119,negated_conjecture,
( sK2 = ia
| xsd_string(sK1)
| sK2 = ia
| sK2 = ib
| cA_and_B(sK2) ),
inference(copy,[status(thm)],[c_118]) ).
cnf(c_54,negated_conjecture,
( xsd_string(sK1)
| sK2 = ia
| sK2 = ib
| cA_and_B(sK2) ),
inference(copy,[status(thm)],[c_119]) ).
cnf(c_56,plain,
( ~ xsd_integer(sK1)
| sK2 = ia
| sK2 = ib
| cA_and_B(sK2) ),
inference(resolve,[status(thm)],[c_54,c_23]) ).
cnf(c_120,plain,
( sK2 = ia
| sK2 = ib
| cA_and_B(sK2)
| sK2 = ia
| sK2 = ib
| cA_and_B(sK2) ),
inference(resolve,[status(thm)],[c_56,c_47]) ).
cnf(c_121,plain,
( sK2 = ia
| sK2 = ib
| sK2 = ia
| sK2 = ib
| cA_and_B(sK2) ),
inference(copy,[status(thm)],[c_120]) ).
cnf(c_122,plain,
( sK2 = ia
| sK2 = ia
| sK2 = ib
| cA_and_B(sK2) ),
inference(copy,[status(thm)],[c_121]) ).
cnf(c_58,plain,
( sK2 = ia
| sK2 = ib
| cA_and_B(sK2) ),
inference(copy,[status(thm)],[c_122]) ).
cnf(c_59,plain,
( cB(sK2)
| cA(sK2)
| sK2 = ia
| sK2 = ib ),
inference(resolve,[status(thm)],[c_58,c_27]) ).
cnf(c_123,plain,
( ib = sK2
| cA(sK2)
| sK2 = ia
| sK2 = ib ),
inference(resolve,[status(thm)],[c_59,c_30]) ).
cnf(c_124,plain,
( sK2 = ib
| cA(sK2)
| sK2 = ia
| sK2 = ib ),
inference(copy,[status(thm)],[c_123]) ).
cnf(c_61,plain,
( cA(sK2)
| sK2 = ia
| sK2 = ib ),
inference(copy,[status(thm)],[c_124]) ).
cnf(c_125,plain,
( ia = sK2
| sK2 = ia
| sK2 = ib ),
inference(resolve,[status(thm)],[c_61,c_25]) ).
cnf(c_126,plain,
( sK2 = ia
| sK2 = ia
| sK2 = ib ),
inference(copy,[status(thm)],[c_125]) ).
cnf(c_62,plain,
( sK2 = ia
| sK2 = ib ),
inference(copy,[status(thm)],[c_126]) ).
cnf(c_127,plain,
( cA_and_B(A)
| A != ib ),
inference(copy,[status(thm)],[c_53]) ).
cnf(c_64,plain,
( cA_and_B(sK2)
| sK2 = ia ),
inference(resolve,[status(thm)],[c_62,c_127]) ).
cnf(c_128,plain,
( sK2 != ib
| ~ cA_and_B(ib)
| xsd_integer(sK1)
| sK2 = ia ),
inference(paramod,[status(thm)],[c_62,c_48]) ).
cnf(c_67,plain,
( sK2 != ib
| xsd_integer(sK1)
| sK2 = ia ),
inference(resolve,[status(thm)],[c_51,c_128]) ).
cnf(c_129,plain,
( sK2 = ia
| xsd_integer(sK1)
| sK2 = ia ),
inference(resolve,[status(thm)],[c_67,c_62]) ).
cnf(c_74,plain,
( xsd_integer(sK1)
| sK2 = ia ),
inference(copy,[status(thm)],[c_129]) ).
cnf(c_75,plain,
( sK2 != ib
| ~ cA_and_B(sK2)
| xsd_string(sK1)
| sK2 = ia ),
inference(resolve,[status(thm)],[c_74,c_35]) ).
cnf(c_130,plain,
( sK2 = ia
| sK2 != ib
| xsd_string(sK1)
| sK2 = ia ),
inference(resolve,[status(thm)],[c_75,c_64]) ).
cnf(c_78,plain,
( sK2 != ib
| xsd_string(sK1)
| sK2 = ia ),
inference(copy,[status(thm)],[c_130]) ).
cnf(c_131,plain,
( sK2 = ia
| xsd_string(sK1)
| sK2 = ia ),
inference(resolve,[status(thm)],[c_78,c_62]) ).
cnf(c_79,plain,
( xsd_string(sK1)
| sK2 = ia ),
inference(copy,[status(thm)],[c_131]) ).
cnf(c_80,plain,
( ~ xsd_integer(sK1)
| sK2 = ia ),
inference(resolve,[status(thm)],[c_79,c_23]) ).
cnf(c_132,plain,
( sK2 = ia
| sK2 = ia ),
inference(resolve,[status(thm)],[c_80,c_74]) ).
cnf(c_82,plain,
sK2 = ia,
inference(copy,[status(thm)],[c_132]) ).
cnf(c_133,negated_conjecture,
( sK2 != ia
| ~ cA_and_B(ia)
| xsd_integer(sK1) ),
inference(paramod,[status(thm)],[c_82,c_49]) ).
cnf(c_134,negated_conjecture,
( ia != ia
| ~ cA_and_B(ia)
| xsd_integer(sK1) ),
inference(paramod,[status(thm)],[c_82,c_133]) ).
cnf(c_135,negated_conjecture,
( ~ cA_and_B(ia)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_134]) ).
cnf(c_83,negated_conjecture,
xsd_integer(sK1),
inference(resolve,[status(thm)],[c_50,c_135]) ).
cnf(c_136,negated_conjecture,
( sK2 != ia
| ~ cA_and_B(ia)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(paramod,[status(thm)],[c_82,c_37]) ).
cnf(c_137,negated_conjecture,
( ia != ia
| ~ cA_and_B(ia)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(paramod,[status(thm)],[c_82,c_136]) ).
cnf(c_138,negated_conjecture,
( ~ cA_and_B(ia)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(copy,[status(thm)],[c_137]) ).
cnf(c_139,negated_conjecture,
( ~ cA_and_B(ia)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_83,c_138]) ).
cnf(c_84,negated_conjecture,
xsd_string(sK1),
inference(resolve,[status(thm)],[c_50,c_139]) ).
cnf(c_140,plain,
~ xsd_string(sK1),
inference(resolve,[status(thm)],[c_23,c_83]) ).
cnf(c_86,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_84,c_140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS175+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n017.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Fri Sep 25 19:37:53 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.38 % Process 2991401 was started by sandbox on n017,
% 0.11/5.38 % Fri Sep 25 19:37:53 2026
% 0.11/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/5.39
% 0.11/5.39 % From the command line: assign(max_seconds, 300).
% 0.16/5.40
% 0.16/5.40 % SZS status Theorem for theBenchmark
% 0.16/5.40
% 0.16/5.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/5.40 % Length of proof is 56.
% 0.16/5.40 % Level of proof is 19.
% 0.16/5.40 % Maximum clause weight is 12.000.
% 0.16/5.40 % Given clauses 57.
% 0.16/5.40
% 0.16/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------