%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS156+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 07:46:10 AM UTC 2026
% Result : Theorem 0.27s 0.56s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 15 unt; 0 def)
% Number of atoms : 167 ( 0 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 217 ( 96 ~; 96 |; 19 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 18 ( 2 sgn 9 !; 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] :
( cC116(X)
<=> ( cC114xcomp(X)
& cTOP(X) ) ),
file('theBenchmark.p',axiom_25) ).
fof(axiom_49,axiom,
! [X] :
( cC140(X)
<=> ( cC138(X)
& cTOP(X) ) ),
file('theBenchmark.p',axiom_49) ).
fof(axiom_127,axiom,
! [X] :
( cTEST(X)
<=> ( cC116(X)
& cC140(X) ) ),
file('theBenchmark.p',axiom_127) ).
fof(the_axiom,conjecture,
( cC138(iV5475)
& cowlThing(iV5475)
& cC140(iV5475)
& cC116(iV5475)
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('theBenchmark.p',the_axiom) ).
fof(the_axiom_neg,negated_conjecture,
~ ( cC138(iV5475)
& cowlThing(iV5475)
& cC140(iV5475)
& cC116(iV5475)
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(assume_negation,[status(cth)],[the_axiom]) ).
cnf(c_138,plain,
cowlThing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_139,plain,
~ cowlNothing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_140,plain,
( ~ xsd_integer(A)
| ~ xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_141,plain,
( xsd_integer(A)
| xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_199,plain,
( ~ cC114xcomp(A)
| ~ cTOP(A)
| cC116(A) ),
inference(clausify,[status(thm)],[axiom_25]) ).
cnf(c_260,plain,
( cC138(A)
| ~ cC140(A) ),
inference(clausify,[status(thm)],[axiom_49]) ).
cnf(c_457,plain,
( cC140(A)
| ~ cTEST(A) ),
inference(clausify,[status(thm)],[axiom_127]) ).
fof(axiom_128,axiom,
cTOP(iV5475),
file('theBenchmark.p',axiom_128) ).
cnf(c_460,plain,
cTOP(iV5475),
inference(clausify,[status(thm)],[axiom_128]) ).
fof(axiom_130,axiom,
cC114xcomp(iV5475),
file('theBenchmark.p',axiom_130) ).
cnf(c_461,plain,
cC114xcomp(iV5475),
inference(clausify,[status(thm)],[axiom_130]) ).
fof(axiom_131,axiom,
cTEST(iV5475),
file('theBenchmark.p',axiom_131) ).
cnf(c_462,plain,
cTEST(iV5475),
inference(clausify,[status(thm)],[axiom_131]) ).
fof(nnf_133,plain,
( ~ cC138(iV5475)
| ~ cowlThing(iV5475)
| ~ cC140(iV5475)
| ~ cC116(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,
( ~ cC138(iV5475)
| ~ cowlThing(iV5475)
| ~ cC140(iV5475)
| ~ cC116(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_133]) ).
fof(sk_the_axiom_neg,plain,
( ( ~ cC138(iV5475)
| ~ cowlThing(iV5475)
| ~ cC140(iV5475)
| ~ cC116(iV5475)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( ~ cC138(iV5475)
| ~ cowlThing(iV5475)
| ~ cC140(iV5475)
| ~ cC116(iV5475)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ) ),
inference(cnf_transformation,[status(thm)],[sk_the_axiom_neg_sk]) ).
cnf(c_474,negated_conjecture,
( ~ cC138(iV5475)
| ~ cowlThing(iV5475)
| ~ cC140(iV5475)
| ~ cC116(iV5475)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_493,negated_conjecture,
( ~ cC138(iV5475)
| ~ cowlThing(iV5475)
| ~ cC140(iV5475)
| ~ cC116(iV5475)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_138,c_474]) ).
cnf(c_494,negated_conjecture,
( ~ cC138(iV5475)
| ~ cowlThing(iV5475)
| ~ cC140(iV5475)
| ~ cC116(iV5475)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_139,c_493]) ).
cnf(c_475,negated_conjecture,
( ~ cC138(iV5475)
| ~ cC140(iV5475)
| ~ cC116(iV5475)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_138,c_494]) ).
cnf(c_476,negated_conjecture,
( ~ cC138(iV5475)
| ~ cowlThing(iV5475)
| ~ cC140(iV5475)
| ~ cC116(iV5475)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_495,negated_conjecture,
( ~ cC138(iV5475)
| ~ cowlThing(iV5475)
| ~ cC140(iV5475)
| ~ cC116(iV5475)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_138,c_476]) ).
cnf(c_496,negated_conjecture,
( ~ cC138(iV5475)
| ~ cowlThing(iV5475)
| ~ cC140(iV5475)
| ~ cC116(iV5475)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_139,c_495]) ).
cnf(c_477,negated_conjecture,
( ~ cC138(iV5475)
| ~ cC140(iV5475)
| ~ cC116(iV5475)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_138,c_496]) ).
cnf(c_497,plain,
( ~ cC114xcomp(iV5475)
| cC116(iV5475) ),
inference(resolve,[status(thm)],[c_199,c_460]) ).
cnf(c_478,plain,
cC116(iV5475),
inference(resolve,[status(thm)],[c_461,c_497]) ).
cnf(c_479,negated_conjecture,
( ~ cC138(iV5475)
| ~ cC140(iV5475)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_478,c_477]) ).
cnf(c_480,negated_conjecture,
( ~ cC138(iV5475)
| ~ cC140(iV5475)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_478,c_475]) ).
cnf(c_498,negated_conjecture,
( xsd_integer(sK1)
| ~ cC138(iV5475)
| ~ cC140(iV5475)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_479,c_141]) ).
cnf(c_482,negated_conjecture,
( ~ cC138(iV5475)
| ~ cC140(iV5475)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_498]) ).
cnf(c_483,plain,
cC140(iV5475),
inference(resolve,[status(thm)],[c_462,c_457]) ).
cnf(c_484,negated_conjecture,
( ~ cC138(iV5475)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_483,c_482]) ).
cnf(c_485,negated_conjecture,
( ~ cC138(iV5475)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_483,c_480]) ).
cnf(c_486,plain,
cC138(iV5475),
inference(resolve,[status(thm)],[c_483,c_260]) ).
cnf(c_487,negated_conjecture,
( ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_486,c_485]) ).
cnf(c_488,negated_conjecture,
xsd_integer(sK1),
inference(resolve,[status(thm)],[c_486,c_484]) ).
cnf(c_489,negated_conjecture,
xsd_string(sK1),
inference(resolve,[status(thm)],[c_488,c_487]) ).
cnf(c_499,negated_conjecture,
~ xsd_integer(sK1),
inference(resolve,[status(thm)],[c_489,c_140]) ).
cnf(c_492,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_488,c_499]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KRS156+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n001.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 19:47:11 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 4062457 was started by sandbox2 on n001,
% 0.17/0.44 % Fri Sep 25 19:47:11 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.48
% 0.17/0.48 % From the command line: assign(max_seconds, 300).
% 0.17/0.48
% 0.17/0.48 % SInE: 143 to sos, 2 to usable, of 145 axioms (tolerance 2.00, depth 0 fixpoint).
% 0.27/0.56
% 0.27/0.56 % SZS status Theorem for theBenchmark
% 0.27/0.56
% 0.27/0.56 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.27/0.56 % Length of proof is 32.
% 0.27/0.56 % Level of proof is 8.
% 0.27/0.56 % Maximum clause weight is 107.000.
% 0.27/0.56 % Given clauses 50.
% 0.27/0.56
% 0.27/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------