%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS172+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 07:46:15 AM UTC 2026
% Result : Theorem 0.13s 0.43s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 9
% Syntax : Number of formulae : 80 ( 10 unt; 0 def)
% Number of atoms : 271 ( 28 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 283 ( 92 ~; 164 |; 16 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 45 ( 4 sgn 22 !; 4 ?)
% 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] :
( cd(X)
<=> rq(X,iv) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cd(X)
<=> rp(X,iv) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X,Y,Z] :
( ( rp(X,Z)
& rp(X,Y) )
=> Y = Z ),
file('theBenchmark.p',axiom_4) ).
fof(axiom_5,axiom,
! [X,Y] :
( rp(X,Y)
=> cd(X) ),
file('theBenchmark.p',axiom_5) ).
fof(axiom_6,axiom,
! [X,Y,Z] :
( ( rq(X,Z)
& rq(X,Y) )
=> Y = Z ),
file('theBenchmark.p',axiom_6) ).
fof(axiom_7,axiom,
! [X,Y] :
( rq(X,Y)
=> cd(X) ),
file('theBenchmark.p',axiom_7) ).
fof(the_axiom,conjecture,
( ! [X,Y] :
( rq(X,Y)
<=> rp(X,Y) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('theBenchmark.p',the_axiom) ).
fof(the_axiom_neg,negated_conjecture,
~ ( ! [X,Y] :
( rq(X,Y)
<=> rp(X,Y) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(assume_negation,[status(cth)],[the_axiom]) ).
cnf(c_28,plain,
cowlThing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_29,plain,
~ cowlNothing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_30,plain,
( ~ xsd_integer(A)
| ~ xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_31,plain,
( xsd_integer(A)
| xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_32,plain,
( rq(A,iv)
| ~ cd(A) ),
inference(clausify,[status(thm)],[axiom_2]) ).
cnf(c_34,plain,
( rp(A,iv)
| ~ cd(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
cnf(c_36,plain,
( C = B
| ~ rp(A,C)
| ~ rp(A,B) ),
inference(clausify,[status(thm)],[axiom_4]) ).
cnf(c_37,plain,
( cd(A)
| ~ rp(A,B) ),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_38,plain,
( C = B
| ~ rq(A,C)
| ~ rq(A,B) ),
inference(clausify,[status(thm)],[axiom_6]) ).
cnf(c_39,plain,
( cd(A)
| ~ rq(A,B) ),
inference(clausify,[status(thm)],[axiom_7]) ).
fof(nnf_18,plain,
( ? [X,Y] :
( ( ~ rp(X,Y)
| ~ rq(X,Y) )
& ( rp(X,Y)
| rq(X,Y) ) )
| ? [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,
( ( ( ~ rp(sK2,sK3)
| ~ rq(sK2,sK3) )
& ( rp(sK2,sK3)
| rq(sK2,sK3) ) )
| ( ( 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,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X,sK2),skolemize(Y,sK3)],[nnf_18]) ).
fof(sk_the_axiom_neg,plain,
( ( ~ rp(sK2,sK3)
| ~ rq(sK2,sK3)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( rp(sK2,sK3)
| rq(sK2,sK3)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( ~ rp(sK2,sK3)
| ~ rq(sK2,sK3)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( rp(sK2,sK3)
| rq(sK2,sK3)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ) ),
inference(cnf_transformation,[status(thm)],[sk_the_axiom_neg_sk]) ).
cnf(c_40,negated_conjecture,
( rp(sK2,sK3)
| rq(sK2,sK3)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_84,negated_conjecture,
( rp(sK2,sK3)
| rq(sK2,sK3)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_28,c_40]) ).
cnf(c_41,negated_conjecture,
( rp(sK2,sK3)
| rq(sK2,sK3)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_29,c_84]) ).
cnf(c_42,negated_conjecture,
( ~ rp(sK2,sK3)
| ~ rq(sK2,sK3)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_85,negated_conjecture,
( ~ rp(sK2,sK3)
| ~ rq(sK2,sK3)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_28,c_42]) ).
cnf(c_43,negated_conjecture,
( ~ rp(sK2,sK3)
| ~ rq(sK2,sK3)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_29,c_85]) ).
cnf(c_44,negated_conjecture,
( rp(sK2,sK3)
| rq(sK2,sK3)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_86,negated_conjecture,
( rp(sK2,sK3)
| rq(sK2,sK3)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_28,c_44]) ).
cnf(c_45,negated_conjecture,
( rp(sK2,sK3)
| rq(sK2,sK3)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_29,c_86]) ).
cnf(c_46,negated_conjecture,
( ~ rp(sK2,sK3)
| ~ rq(sK2,sK3)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_87,negated_conjecture,
( ~ rp(sK2,sK3)
| ~ rq(sK2,sK3)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_28,c_46]) ).
cnf(c_47,negated_conjecture,
( ~ rp(sK2,sK3)
| ~ rq(sK2,sK3)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_29,c_87]) ).
cnf(c_88,negated_conjecture,
( xsd_integer(sK1)
| rp(sK2,sK3)
| rq(sK2,sK3)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_45,c_31]) ).
cnf(c_49,negated_conjecture,
( rp(sK2,sK3)
| rq(sK2,sK3)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_88]) ).
cnf(c_89,negated_conjecture,
( xsd_integer(sK1)
| ~ rp(sK2,sK3)
| ~ rq(sK2,sK3)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_47,c_31]) ).
cnf(c_50,negated_conjecture,
( ~ rp(sK2,sK3)
| ~ rq(sK2,sK3)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_89]) ).
cnf(c_51,plain,
( cd(sK2)
| rp(sK2,sK3)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_49,c_39]) ).
cnf(c_52,plain,
( sK3 = A
| ~ rq(sK2,A)
| rp(sK2,sK3)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_49,c_38]) ).
cnf(c_90,plain,
( cd(sK2)
| cd(sK2)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_51,c_37]) ).
cnf(c_55,plain,
( cd(sK2)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_90]) ).
cnf(c_56,plain,
( rp(sK2,sK3)
| rq(sK2,sK3)
| xsd_string(sK1)
| cd(sK2) ),
inference(resolve,[status(thm)],[c_55,c_41]) ).
cnf(c_57,plain,
( ~ xsd_string(sK1)
| cd(sK2) ),
inference(resolve,[status(thm)],[c_55,c_30]) ).
cnf(c_91,plain,
( cd(sK2)
| rp(sK2,sK3)
| xsd_string(sK1)
| cd(sK2) ),
inference(resolve,[status(thm)],[c_56,c_39]) ).
cnf(c_59,plain,
( rp(sK2,sK3)
| xsd_string(sK1)
| cd(sK2) ),
inference(copy,[status(thm)],[c_91]) ).
cnf(c_92,plain,
( cd(sK2)
| xsd_string(sK1)
| cd(sK2) ),
inference(resolve,[status(thm)],[c_59,c_37]) ).
cnf(c_60,plain,
( xsd_string(sK1)
| cd(sK2) ),
inference(copy,[status(thm)],[c_92]) ).
cnf(c_93,plain,
( cd(sK2)
| cd(sK2) ),
inference(resolve,[status(thm)],[c_60,c_57]) ).
cnf(c_61,plain,
cd(sK2),
inference(copy,[status(thm)],[c_93]) ).
cnf(c_62,plain,
rp(sK2,iv),
inference(resolve,[status(thm)],[c_61,c_34]) ).
cnf(c_63,plain,
rq(sK2,iv),
inference(resolve,[status(thm)],[c_61,c_32]) ).
cnf(c_65,plain,
( iv = A
| ~ rp(sK2,A) ),
inference(resolve,[status(thm)],[c_62,c_36]) ).
cnf(c_68,plain,
( sK3 = iv
| rp(sK2,sK3)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_63,c_52]) ).
cnf(c_69,plain,
( iv = A
| ~ rq(sK2,A) ),
inference(resolve,[status(thm)],[c_63,c_38]) ).
cnf(c_94,plain,
( iv = sK3
| sK3 = iv
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_68,c_65]) ).
cnf(c_95,plain,
( sK3 = iv
| sK3 = iv
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_94]) ).
cnf(c_72,plain,
( sK3 = iv
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_95]) ).
cnf(c_74,plain,
( rp(sK2,sK3)
| rq(sK2,sK3)
| xsd_string(sK1)
| sK3 = iv ),
inference(resolve,[status(thm)],[c_72,c_41]) ).
cnf(c_75,plain,
( ~ xsd_string(sK1)
| sK3 = iv ),
inference(resolve,[status(thm)],[c_72,c_30]) ).
cnf(c_96,plain,
( iv = sK3
| rp(sK2,sK3)
| xsd_string(sK1)
| sK3 = iv ),
inference(resolve,[status(thm)],[c_74,c_69]) ).
cnf(c_97,plain,
( sK3 = iv
| rp(sK2,sK3)
| xsd_string(sK1)
| sK3 = iv ),
inference(copy,[status(thm)],[c_96]) ).
cnf(c_77,plain,
( rp(sK2,sK3)
| xsd_string(sK1)
| sK3 = iv ),
inference(copy,[status(thm)],[c_97]) ).
cnf(c_98,plain,
( iv = sK3
| xsd_string(sK1)
| sK3 = iv ),
inference(resolve,[status(thm)],[c_77,c_65]) ).
cnf(c_99,plain,
( sK3 = iv
| xsd_string(sK1)
| sK3 = iv ),
inference(copy,[status(thm)],[c_98]) ).
cnf(c_79,plain,
( xsd_string(sK1)
| sK3 = iv ),
inference(copy,[status(thm)],[c_99]) ).
cnf(c_100,plain,
( sK3 = iv
| sK3 = iv ),
inference(resolve,[status(thm)],[c_79,c_75]) ).
cnf(c_80,plain,
sK3 = iv,
inference(copy,[status(thm)],[c_100]) ).
cnf(c_101,negated_conjecture,
( ~ rp(sK2,sK3)
| ~ rq(sK2,iv)
| xsd_integer(sK1) ),
inference(paramod,[status(thm)],[c_80,c_50]) ).
cnf(c_102,negated_conjecture,
( ~ rp(sK2,iv)
| ~ rq(sK2,iv)
| xsd_integer(sK1) ),
inference(paramod,[status(thm)],[c_80,c_101]) ).
cnf(c_103,negated_conjecture,
( ~ rp(sK2,iv)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_63,c_102]) ).
cnf(c_81,negated_conjecture,
xsd_integer(sK1),
inference(resolve,[status(thm)],[c_62,c_103]) ).
cnf(c_104,negated_conjecture,
( ~ rp(sK2,sK3)
| ~ rq(sK2,iv)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(paramod,[status(thm)],[c_80,c_43]) ).
cnf(c_105,negated_conjecture,
( ~ rp(sK2,iv)
| ~ rq(sK2,iv)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(paramod,[status(thm)],[c_80,c_104]) ).
cnf(c_106,negated_conjecture,
( ~ rp(sK2,iv)
| ~ rq(sK2,iv)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_81,c_105]) ).
cnf(c_107,negated_conjecture,
( ~ rp(sK2,iv)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_63,c_106]) ).
cnf(c_82,negated_conjecture,
xsd_string(sK1),
inference(resolve,[status(thm)],[c_62,c_107]) ).
cnf(c_108,plain,
~ xsd_string(sK1),
inference(resolve,[status(thm)],[c_81,c_30]) ).
cnf(c_83,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_82,c_108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS172+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 19:42:35 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 3499726 was started by sandbox on n019,
% 0.13/0.36 % Fri Sep 25 19:42:35 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.43
% 0.13/0.43 % SZS status Theorem for theBenchmark
% 0.13/0.43
% 0.13/0.43 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.13/0.43 % Length of proof is 51.
% 0.13/0.43 % Level of proof is 19.
% 0.13/0.43 % Maximum clause weight is 16.000.
% 0.13/0.43 % Given clauses 53.
% 0.13/0.43
% 0.13/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------