%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS169+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 : n005.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 07:46:14 AM UTC 2026
% Result : Theorem 0.11s 0.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 8 unt; 0 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 186 ( 87 ~; 81 |; 14 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 16 ( 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_5,axiom,
! [X,Y] :
( rhasLeader(X,Y)
<=> rhasHead(X,Y) ),
file('theBenchmark.p',axiom_5) ).
fof(the_axiom,conjecture,
( cowlThing(iY)
& rhasHead(iX,iY)
& cowlThing(iX)
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('theBenchmark.p',the_axiom) ).
fof(the_axiom_neg,negated_conjecture,
~ ( cowlThing(iY)
& rhasHead(iX,iY)
& cowlThing(iX)
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(assume_negation,[status(cth)],[the_axiom]) ).
fof(nnf_4,plain,
( ~ cowlThing(iY)
| ~ rhasHead(iX,iY)
| ~ cowlThing(iX)
| ? [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,
( ~ cowlThing(iY)
| ~ rhasHead(iX,iY)
| ~ cowlThing(iX)
| ( ( 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_4]) ).
fof(sk_the_axiom_neg,plain,
( ( ~ cowlThing(iY)
| ~ rhasHead(iX,iY)
| ~ cowlThing(iX)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( ~ cowlThing(iY)
| ~ rhasHead(iX,iY)
| ~ cowlThing(iX)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ) ),
inference(cnf_transformation,[status(thm)],[sk_the_axiom_neg_sk]) ).
cnf(c_5,negated_conjecture,
( ~ cowlThing(iY)
| ~ rhasHead(iX,iY)
| ~ cowlThing(iX)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_6,plain,
~ cowlNothing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_7,negated_conjecture,
( ~ cowlThing(iY)
| ~ rhasHead(iX,iY)
| ~ cowlThing(iX)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_8,negated_conjecture,
( ~ cowlThing(iY)
| ~ rhasHead(iX,iY)
| ~ cowlThing(iX)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| ~ cowlThing(sK0) ),
inference(resolve,[status(thm)],[c_5,c_6]) ).
cnf(c_9,negated_conjecture,
( ~ cowlThing(iY)
| ~ rhasHead(iX,iY)
| ~ cowlThing(iX)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| ~ cowlThing(sK0) ),
inference(resolve,[status(thm)],[c_7,c_6]) ).
cnf(c_10,plain,
( xsd_integer(A)
| xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_11,plain,
( ~ xsd_integer(A)
| ~ xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_12,plain,
( rhasHead(A,B)
| ~ rhasLeader(A,B) ),
inference(clausify,[status(thm)],[axiom_5]) ).
fof(axiom_3,axiom,
rhasLeader(iX,iY),
file('theBenchmark.p',axiom_3) ).
cnf(c_13,plain,
rhasLeader(iX,iY),
inference(clausify,[status(thm)],[axiom_3]) ).
cnf(c_15,negated_conjecture,
( ~ cowlThing(iY)
| ~ rhasHead(iX,iY)
| ~ cowlThing(iX)
| xsd_integer(sK1)
| ~ cowlThing(sK0)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_10,c_9]) ).
cnf(c_16,plain,
rhasHead(iX,iY),
inference(resolve,[status(thm)],[c_12,c_13]) ).
cnf(c_17,negated_conjecture,
( ~ cowlThing(iY)
| ~ rhasHead(iX,iY)
| ~ cowlThing(iX)
| ~ xsd_integer(sK1)
| ~ cowlThing(sK0)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_11,c_8]) ).
cnf(c_18,negated_conjecture,
( ~ cowlThing(iY)
| ~ cowlThing(iX)
| ~ xsd_integer(sK1)
| ~ cowlThing(sK0)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_17,c_16]) ).
cnf(c_19,negated_conjecture,
( ~ cowlThing(iY)
| ~ cowlThing(iX)
| ~ cowlThing(sK0)
| ~ xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_18]) ).
cnf(c_20,negated_conjecture,
( ~ cowlThing(iY)
| ~ cowlThing(iX)
| xsd_integer(sK1)
| ~ cowlThing(sK0)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_15,c_16]) ).
cnf(c_21,negated_conjecture,
( ~ cowlThing(iY)
| ~ cowlThing(iX)
| ~ cowlThing(sK0)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_20]) ).
cnf(c_22,plain,
cowlThing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_25,negated_conjecture,
( ~ cowlThing(iY)
| ~ cowlThing(iX)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_22,c_21]) ).
cnf(c_26,negated_conjecture,
( ~ cowlThing(iY)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_22,c_25]) ).
cnf(c_23,negated_conjecture,
xsd_integer(sK1),
inference(resolve,[status(thm)],[c_22,c_26]) ).
cnf(c_27,negated_conjecture,
( ~ cowlThing(iY)
| ~ cowlThing(iX)
| ~ cowlThing(sK0) ),
inference(resolve,[status(thm)],[c_23,c_19]) ).
cnf(c_28,negated_conjecture,
( ~ cowlThing(iY)
| ~ cowlThing(iX) ),
inference(resolve,[status(thm)],[c_22,c_27]) ).
cnf(c_29,negated_conjecture,
~ cowlThing(iY),
inference(resolve,[status(thm)],[c_22,c_28]) ).
cnf(c_24,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_22,c_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS169+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n005.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Fri Sep 25 19:41:49 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 8648 was started by sandbox on n005,
% 0.11/0.38 % Fri Sep 25 19:41:49 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 0.11/0.40
% 0.11/0.40 % SZS status Theorem for theBenchmark
% 0.11/0.40
% 0.11/0.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.40 % Length of proof is 23.
% 0.11/0.40 % Level of proof is 7.
% 0.11/0.40 % Maximum clause weight is 8.000.
% 0.11/0.40 % Given clauses 0.
% 0.11/0.40
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------