%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS143+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 0.12s 0.59s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 5
% Syntax : Number of formulae : 80 ( 11 unt; 0 def)
% Number of atoms : 310 ( 23 equ)
% Maximal formula atoms : 46 ( 3 avg)
% Number of connectives : 355 ( 125 ~; 193 |; 27 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 63 ( 20 sgn 26 !; 9 ?)
% 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] : rp(X,Y0) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cc(X)
=> ! [Y0,Y1] :
( ( rp(X,Y1)
& rp(X,Y0) )
=> Y0 = Y1 ) ),
file('theBenchmark.p',axiom_3) ).
fof(the_axiom,conjecture,
( ! [X] :
( cc(X)
=> ( ! [Y0,Y1] :
( ( rp(X,Y1)
& rp(X,Y0) )
=> Y0 = Y1 )
& ? [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 )
& ? [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_20,plain,
cowlThing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_21,plain,
~ cowlNothing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_22,plain,
( ~ xsd_integer(A)
| ~ xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_23,plain,
( xsd_integer(A)
| xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
fof(nnf_10,plain,
! [X] :
( ? [Y0] : rp(X,Y0)
| ~ cc(X) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2,plain,
! [X] :
( rp(X,sK0(X))
| ~ cc(X) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Y0,sK0(X))],[nnf_10]) ).
cnf(c_24,plain,
( rp(A,sK0(A))
| ~ cc(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_25,plain,
( C = B
| ~ rp(A,C)
| ~ rp(A,B)
| ~ cc(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(nnf_12,plain,
( ? [X] :
( ( ? [Y0,Y1] :
( Y1 != Y0
& rp(X,Y1)
& rp(X,Y0) )
| ! [X2] : ~ rp(X,X2) )
& cc(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,
( ( ( ( sK5 != sK4
& rp(sK3,sK5)
& rp(sK3,sK4) )
| ! [X2] : ~ rp(sK3,X2) )
& 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]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X,sK3),skolemize(Y0,sK4),skolemize(Y1,sK5)],[nnf_12]) ).
fof(sk_the_axiom_neg,plain,
( ! [VAR_0] :
( sK5 != sK4
| ~ rp(sK3,VAR_0)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) )
& ! [VAR_0] :
( rp(sK3,sK5)
| ~ rp(sK3,VAR_0)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) )
& ! [VAR_0] :
( rp(sK3,sK4)
| ~ rp(sK3,VAR_0)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) )
& ( cc(sK3)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) )
& ! [VAR_0] :
( sK5 != sK4
| ~ rp(sK3,VAR_0)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) )
& ! [VAR_0] :
( rp(sK3,sK5)
| ~ rp(sK3,VAR_0)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) )
& ! [VAR_0] :
( rp(sK3,sK4)
| ~ rp(sK3,VAR_0)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) )
& ( cc(sK3)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) ) ),
inference(cnf_transformation,[status(thm)],[sk_the_axiom_neg_sk]) ).
cnf(c_26,negated_conjecture,
( cc(sK3)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_111,negated_conjecture,
( cc(sK3)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1) ),
inference(resolve,[status(thm)],[c_20,c_26]) ).
cnf(c_27,negated_conjecture,
( cc(sK3)
| ~ xsd_integer(sK2)
| xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_21,c_111]) ).
cnf(c_28,negated_conjecture,
( rp(sK3,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_112,negated_conjecture,
( rp(sK3,sK4)
| ~ rp(sK3,A)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1) ),
inference(resolve,[status(thm)],[c_20,c_28]) ).
cnf(c_29,negated_conjecture,
( rp(sK3,sK4)
| ~ rp(sK3,A)
| ~ xsd_integer(sK2)
| xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_21,c_112]) ).
cnf(c_30,negated_conjecture,
( rp(sK3,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_113,negated_conjecture,
( rp(sK3,sK5)
| ~ rp(sK3,A)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1) ),
inference(resolve,[status(thm)],[c_20,c_30]) ).
cnf(c_31,negated_conjecture,
( rp(sK3,sK5)
| ~ rp(sK3,A)
| ~ xsd_integer(sK2)
| xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_21,c_113]) ).
cnf(c_32,negated_conjecture,
( sK5 != 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_114,negated_conjecture,
( sK5 != sK4
| ~ rp(sK3,A)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK1) ),
inference(resolve,[status(thm)],[c_20,c_32]) ).
cnf(c_33,negated_conjecture,
( sK5 != sK4
| ~ rp(sK3,A)
| ~ xsd_integer(sK2)
| xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_21,c_114]) ).
cnf(c_34,negated_conjecture,
( cc(sK3)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1)
| ~ cowlThing(sK1) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_115,negated_conjecture,
( cc(sK3)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1) ),
inference(resolve,[status(thm)],[c_20,c_34]) ).
cnf(c_35,negated_conjecture,
( cc(sK3)
| xsd_integer(sK2)
| ~ xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_21,c_115]) ).
cnf(c_36,negated_conjecture,
( rp(sK3,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_116,negated_conjecture,
( rp(sK3,sK4)
| ~ rp(sK3,A)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1) ),
inference(resolve,[status(thm)],[c_20,c_36]) ).
cnf(c_37,negated_conjecture,
( rp(sK3,sK4)
| ~ rp(sK3,A)
| xsd_integer(sK2)
| ~ xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_21,c_116]) ).
cnf(c_38,negated_conjecture,
( rp(sK3,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_117,negated_conjecture,
( rp(sK3,sK5)
| ~ rp(sK3,A)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1) ),
inference(resolve,[status(thm)],[c_20,c_38]) ).
cnf(c_39,negated_conjecture,
( rp(sK3,sK5)
| ~ rp(sK3,A)
| xsd_integer(sK2)
| ~ xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_21,c_117]) ).
cnf(c_40,negated_conjecture,
( sK5 != 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_118,negated_conjecture,
( sK5 != sK4
| ~ rp(sK3,A)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK1) ),
inference(resolve,[status(thm)],[c_20,c_40]) ).
cnf(c_41,negated_conjecture,
( sK5 != sK4
| ~ rp(sK3,A)
| xsd_integer(sK2)
| ~ xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_21,c_118]) ).
cnf(c_119,negated_conjecture,
( xsd_string(sK2)
| cc(sK3)
| xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_27,c_23]) ).
cnf(c_44,negated_conjecture,
( cc(sK3)
| xsd_string(sK2) ),
inference(copy,[status(thm)],[c_119]) ).
cnf(c_120,negated_conjecture,
( xsd_integer(sK2)
| cc(sK3)
| xsd_integer(sK2) ),
inference(resolve,[status(thm)],[c_35,c_23]) ).
cnf(c_45,negated_conjecture,
( cc(sK3)
| xsd_integer(sK2) ),
inference(copy,[status(thm)],[c_120]) ).
cnf(c_46,plain,
( ~ xsd_integer(sK2)
| cc(sK3) ),
inference(resolve,[status(thm)],[c_44,c_22]) ).
cnf(c_121,plain,
( cc(sK3)
| cc(sK3) ),
inference(resolve,[status(thm)],[c_46,c_45]) ).
cnf(c_53,plain,
cc(sK3),
inference(copy,[status(thm)],[c_121]) ).
cnf(c_54,plain,
rp(sK3,sK0(sK3)),
inference(resolve,[status(thm)],[c_53,c_24]) ).
cnf(c_56,plain,
( sK5 != sK4
| xsd_integer(sK2)
| ~ xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_54,c_41]) ).
cnf(c_57,plain,
( rp(sK3,sK5)
| xsd_integer(sK2)
| ~ xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_54,c_39]) ).
cnf(c_58,plain,
( rp(sK3,sK4)
| xsd_integer(sK2)
| ~ xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_54,c_37]) ).
cnf(c_59,plain,
( sK5 != sK4
| ~ xsd_integer(sK2)
| xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_54,c_33]) ).
cnf(c_60,plain,
( rp(sK3,sK5)
| ~ xsd_integer(sK2)
| xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_54,c_31]) ).
cnf(c_61,plain,
( rp(sK3,sK4)
| ~ xsd_integer(sK2)
| xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_54,c_29]) ).
cnf(c_122,plain,
( xsd_integer(sK2)
| sK5 != sK4
| xsd_integer(sK2) ),
inference(resolve,[status(thm)],[c_56,c_23]) ).
cnf(c_65,plain,
( sK5 != sK4
| xsd_integer(sK2) ),
inference(copy,[status(thm)],[c_122]) ).
cnf(c_123,plain,
( xsd_integer(sK2)
| rp(sK3,sK5)
| xsd_integer(sK2) ),
inference(resolve,[status(thm)],[c_57,c_23]) ).
cnf(c_66,plain,
( rp(sK3,sK5)
| xsd_integer(sK2) ),
inference(copy,[status(thm)],[c_123]) ).
cnf(c_124,plain,
( xsd_integer(sK2)
| rp(sK3,sK4)
| xsd_integer(sK2) ),
inference(resolve,[status(thm)],[c_58,c_23]) ).
cnf(c_67,plain,
( rp(sK3,sK4)
| xsd_integer(sK2) ),
inference(copy,[status(thm)],[c_124]) ).
cnf(c_125,plain,
( xsd_string(sK2)
| sK5 != sK4
| xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_59,c_23]) ).
cnf(c_68,plain,
( sK5 != sK4
| xsd_string(sK2) ),
inference(copy,[status(thm)],[c_125]) ).
cnf(c_126,plain,
( rp(sK3,sK5)
| rp(sK3,sK5)
| xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_60,c_66]) ).
cnf(c_78,plain,
( rp(sK3,sK5)
| xsd_string(sK2) ),
inference(copy,[status(thm)],[c_126]) ).
cnf(c_79,plain,
( ~ xsd_integer(sK2)
| rp(sK3,sK5) ),
inference(resolve,[status(thm)],[c_78,c_22]) ).
cnf(c_127,plain,
( rp(sK3,sK4)
| rp(sK3,sK4)
| xsd_string(sK2) ),
inference(resolve,[status(thm)],[c_61,c_67]) ).
cnf(c_84,plain,
( rp(sK3,sK4)
| xsd_string(sK2) ),
inference(copy,[status(thm)],[c_127]) ).
cnf(c_128,plain,
( rp(sK3,sK5)
| rp(sK3,sK5) ),
inference(resolve,[status(thm)],[c_79,c_66]) ).
cnf(c_89,plain,
rp(sK3,sK5),
inference(copy,[status(thm)],[c_128]) ).
cnf(c_129,plain,
( sK5 = A
| ~ rp(sK3,A)
| ~ cc(sK3) ),
inference(resolve,[status(thm)],[c_89,c_25]) ).
cnf(c_91,plain,
( sK5 = A
| ~ rp(sK3,A) ),
inference(resolve,[status(thm)],[c_53,c_129]) ).
cnf(c_94,plain,
( ~ xsd_integer(sK2)
| rp(sK3,sK4) ),
inference(resolve,[status(thm)],[c_84,c_22]) ).
cnf(c_130,plain,
( rp(sK3,sK4)
| rp(sK3,sK4) ),
inference(resolve,[status(thm)],[c_94,c_67]) ).
cnf(c_100,plain,
rp(sK3,sK4),
inference(copy,[status(thm)],[c_130]) ).
cnf(c_105,plain,
sK5 = sK4,
inference(resolve,[status(thm)],[c_91,c_100]) ).
cnf(c_106,plain,
xsd_string(sK2),
inference(resolve,[status(thm)],[c_105,c_68]) ).
cnf(c_107,plain,
xsd_integer(sK2),
inference(resolve,[status(thm)],[c_105,c_65]) ).
cnf(c_131,plain,
~ xsd_integer(sK2),
inference(resolve,[status(thm)],[c_106,c_22]) ).
cnf(c_110,plain,
$false,
inference(resolve,[status(thm)],[c_107,c_131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS143+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.57 % Computer : n002.cluster.edu
% 0.12/0.57 % Model : x86_64 x86_64
% 0.12/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.57 % Memory : 8046.5625MB
% 0.12/0.57 % OS : Linux 6.8.0-71-generic
% 0.12/0.57 % CPULimit : 300
% 0.12/0.57 % WCLimit : 300
% 0.12/0.57 % DateTime : Fri Sep 25 19:43:37 UTC 2026
% 0.12/0.57 % CPUTime :
% 0.12/0.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.57 % Process 3974356 was started by sandbox2 on n002,
% 0.12/0.57 % Fri Sep 25 19:43:37 2026
% 0.12/0.57 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.58
% 0.12/0.58 % From the command line: assign(max_seconds, 300).
% 0.12/0.59
% 0.12/0.59 % SZS status Theorem for theBenchmark
% 0.12/0.59
% 0.12/0.59 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.12/0.59 % Length of proof is 53.
% 0.12/0.59 % Level of proof is 15.
% 0.12/0.59 % Maximum clause weight is 16.000.
% 0.12/0.59 % Given clauses 50.
% 0.12/0.59
% 0.12/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------