%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS148+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 : n001.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 07:46:09 AM UTC 2026
% Result : Theorem 22.42s 3.73s
% Output : CNFRefutation 22.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 10 unt; 0 def)
% Number of atoms : 166 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 237 ( 111 ~; 103 |; 18 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 17 ( 2 sgn 8 !; 2 ?)
% 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_25,axiom,
! [X] :
( cC140(X)
<=> ( cC138(X)
& cTOP(X) ) ),
file('theBenchmark.p',axiom_25) ).
fof(axiom_71,axiom,
! [X] :
( cTEST(X)
<=> ( cC116(X)
& cC140(X) ) ),
file('theBenchmark.p',axiom_71) ).
fof(the_axiom,conjecture,
( cC140(iV5475)
& cC116(iV5475)
& cowlThing(iV5475)
& cC138(iV5475)
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('theBenchmark.p',the_axiom) ).
fof(the_axiom_neg,negated_conjecture,
~ ( cC140(iV5475)
& cC116(iV5475)
& cowlThing(iV5475)
& cC138(iV5475)
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(assume_negation,[status(cth)],[the_axiom]) ).
fof(nnf_77,plain,
( ~ cC140(iV5475)
| ~ cC116(iV5475)
| ~ cowlThing(iV5475)
| ~ cC138(iV5475)
| ? [X] :
( ( xsd_integer(X)
| ~ xsd_string(X) )
& ( ~ xsd_integer(X)
| xsd_string(X) ) )
| ? [X0] :
( cowlNothing(X0)
| ~ cowlThing(X0) ) ),
inference(fof_nnf,[status(thm)],[the_axiom_neg]) ).
fof(sk_the_axiom_neg_sk,plain,
( ~ cC140(iV5475)
| ~ cC116(iV5475)
| ~ cowlThing(iV5475)
| ~ cC138(iV5475)
| ( ( 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]),skolemize(X0,sK0),skolemize(X,sK1)],[nnf_77]) ).
fof(sk_the_axiom_neg,plain,
( ( ~ cC140(iV5475)
| ~ cC116(iV5475)
| ~ cowlThing(iV5475)
| ~ cC138(iV5475)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( ~ cC140(iV5475)
| ~ cC116(iV5475)
| ~ cowlThing(iV5475)
| ~ cC138(iV5475)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ) ),
inference(cnf_transformation,[status(thm)],[sk_the_axiom_neg_sk]) ).
cnf(c_78,negated_conjecture,
( ~ cC140(iV5475)
| ~ cC116(iV5475)
| ~ cowlThing(iV5475)
| ~ cC138(iV5475)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_79,plain,
~ cowlNothing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_80,negated_conjecture,
( ~ cC140(iV5475)
| ~ cC116(iV5475)
| ~ cowlThing(iV5475)
| ~ cC138(iV5475)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_81,negated_conjecture,
( ~ cC140(iV5475)
| ~ cC116(iV5475)
| ~ cowlThing(iV5475)
| ~ cC138(iV5475)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| ~ cowlThing(sK0) ),
inference(resolve,[status(thm)],[c_78,c_79]) ).
cnf(c_82,negated_conjecture,
( ~ cC140(iV5475)
| ~ cC116(iV5475)
| ~ cowlThing(iV5475)
| ~ cC138(iV5475)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| ~ cowlThing(sK0) ),
inference(resolve,[status(thm)],[c_80,c_79]) ).
cnf(c_83,plain,
( xsd_integer(A)
| xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_84,plain,
( ~ xsd_integer(A)
| ~ xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_836,negated_conjecture,
( ~ cC140(iV5475)
| ~ cC116(iV5475)
| ~ cowlThing(iV5475)
| ~ cC138(iV5475)
| ~ xsd_integer(sK1)
| ~ cowlThing(sK0)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_84,c_81]) ).
cnf(c_837,negated_conjecture,
( ~ cC140(iV5475)
| ~ cC116(iV5475)
| ~ cowlThing(iV5475)
| ~ cC138(iV5475)
| ~ cowlThing(sK0)
| ~ xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_836]) ).
cnf(c_838,negated_conjecture,
( ~ cC140(iV5475)
| ~ cC116(iV5475)
| ~ cowlThing(iV5475)
| ~ cC138(iV5475)
| xsd_integer(sK1)
| ~ cowlThing(sK0)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_83,c_82]) ).
cnf(c_839,negated_conjecture,
( ~ cC140(iV5475)
| ~ cC116(iV5475)
| ~ cowlThing(iV5475)
| ~ cC138(iV5475)
| ~ cowlThing(sK0)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_838]) ).
cnf(c_840,plain,
cowlThing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_878,plain,
( cC138(A)
| ~ cC140(A) ),
inference(clausify,[status(thm)],[axiom_25]) ).
cnf(c_951,plain,
( cC140(A)
| ~ cTEST(A) ),
inference(clausify,[status(thm)],[axiom_71]) ).
cnf(c_952,plain,
( cC116(A)
| ~ cTEST(A) ),
inference(clausify,[status(thm)],[axiom_71]) ).
fof(axiom_72,axiom,
cTEST(iV5475),
file('theBenchmark.p',axiom_72) ).
cnf(c_954,plain,
cTEST(iV5475),
inference(clausify,[status(thm)],[axiom_72]) ).
cnf(c_2339,negated_conjecture,
( ~ cC140(iV5475)
| ~ cC116(iV5475)
| ~ cowlThing(iV5475)
| ~ cC138(iV5475)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_840,c_839]) ).
cnf(c_1976,negated_conjecture,
( ~ cC140(iV5475)
| ~ cC116(iV5475)
| ~ cC138(iV5475)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_840,c_2339]) ).
cnf(c_2340,negated_conjecture,
( ~ cC140(iV5475)
| ~ cC116(iV5475)
| ~ cowlThing(iV5475)
| ~ cC138(iV5475)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_840,c_837]) ).
cnf(c_1977,negated_conjecture,
( ~ cC140(iV5475)
| ~ cC116(iV5475)
| ~ cC138(iV5475)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_840,c_2340]) ).
cnf(c_1986,plain,
cC116(iV5475),
inference(resolve,[status(thm)],[c_954,c_952]) ).
cnf(c_1987,plain,
cC140(iV5475),
inference(resolve,[status(thm)],[c_954,c_951]) ).
cnf(c_2341,negated_conjecture,
( ~ cC140(iV5475)
| ~ cC138(iV5475)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_1986,c_1977]) ).
cnf(c_1988,negated_conjecture,
( ~ cC138(iV5475)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_1987,c_2341]) ).
cnf(c_2342,negated_conjecture,
( ~ cC140(iV5475)
| ~ cC138(iV5475)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_1986,c_1976]) ).
cnf(c_1989,negated_conjecture,
( ~ cC138(iV5475)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_1987,c_2342]) ).
cnf(c_2336,plain,
cC138(iV5475),
inference(resolve,[status(thm)],[c_1987,c_878]) ).
cnf(c_2337,negated_conjecture,
xsd_integer(sK1),
inference(resolve,[status(thm)],[c_2336,c_1989]) ).
cnf(c_2343,negated_conjecture,
~ cC138(iV5475),
inference(resolve,[status(thm)],[c_2337,c_1988]) ).
cnf(c_2338,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2336,c_2343]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KRS148+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n001.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Fri Sep 25 19:46:57 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.42 % Process 4061881 was started by sandbox2 on n001,
% 0.17/0.42 % Fri Sep 25 19:46:57 2026
% 0.17/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 22.42/3.73
% 22.42/3.73 % given #500 (I,wt=12): 1281 -cC56(A) | cC50(B) | -rR1(B,A). [resolve(134,b,131,c)].
% 22.42/3.73
% 22.42/3.73 % given #1000 (I,wt=18): 1803 -cC96(A) | cC50(B) | -rR1(B,f38(A)). [resolve(158,b,131,c)].
% 22.42/3.73
% 22.42/3.73 % SZS status Theorem for theBenchmark
% 22.42/3.73
% 22.42/3.73 % Proof 1 at 3.14 (+ 0.06) seconds.
% 22.42/3.73 % Length of proof is 30.
% 22.42/3.73 % Level of proof is 8.
% 22.42/3.73 % Maximum clause weight is 17.000.
% 22.42/3.73 % Given clauses 1175.
% 22.42/3.73
% 22.42/3.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------