%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS134+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 : n003.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 07:46:06 AM UTC 2026
% Result : Theorem 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 40 ( 5 unt; 0 def)
% Number of atoms : 167 ( 0 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 208 ( 81 ~; 101 |; 18 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 22 ( 3 sgn 12 !; 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,Y] :
( rprop(X,Y)
=> cA(Y) ),
file('theBenchmark.p',axiom_2) ).
fof(the_axiom,conjecture,
( ! [X] :
( cowlThing(X)
=> ! [Y] :
( rprop(X,Y)
=> cA(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] :
( cowlThing(X)
=> ! [Y] :
( rprop(X,Y)
=> cA(Y) ) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(assume_negation,[status(cth)],[the_axiom]) ).
cnf(c_6,plain,
~ cowlNothing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
fof(nnf_4,plain,
( ? [X] :
( ? [Y] :
( ~ cA(Y)
& rprop(X,Y) )
& cowlThing(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,
( ( ~ cA(sK3)
& rprop(sK2,sK3)
& cowlThing(sK2) )
| ( ( 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_4]) ).
fof(sk_the_axiom_neg,plain,
( ( ~ cA(sK3)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( rprop(sK2,sK3)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( cowlThing(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( ~ cA(sK3)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( rprop(sK2,sK3)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( cowlThing(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ) ),
inference(cnf_transformation,[status(thm)],[sk_the_axiom_neg_sk]) ).
cnf(c_7,negated_conjecture,
( rprop(sK2,sK3)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_8,negated_conjecture,
( ~ cA(sK3)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_10,negated_conjecture,
( rprop(sK2,sK3)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_11,negated_conjecture,
( ~ cA(sK3)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_12,negated_conjecture,
( ~ cA(sK3)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| ~ cowlThing(sK0) ),
inference(resolve,[status(thm)],[c_8,c_6]) ).
cnf(c_14,negated_conjecture,
( rprop(sK2,sK3)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| ~ cowlThing(sK0) ),
inference(resolve,[status(thm)],[c_10,c_6]) ).
cnf(c_15,negated_conjecture,
( ~ cA(sK3)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| ~ cowlThing(sK0) ),
inference(resolve,[status(thm)],[c_11,c_6]) ).
cnf(c_16,negated_conjecture,
( rprop(sK2,sK3)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| ~ cowlThing(sK0) ),
inference(resolve,[status(thm)],[c_7,c_6]) ).
cnf(c_18,plain,
( xsd_integer(A)
| xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_19,plain,
( ~ xsd_integer(A)
| ~ xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_20,plain,
cowlThing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_21,negated_conjecture,
( rprop(sK2,sK3)
| xsd_integer(sK1)
| ~ cowlThing(sK0)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_18,c_14]) ).
cnf(c_22,negated_conjecture,
( ~ cA(sK3)
| xsd_integer(sK1)
| ~ cowlThing(sK0)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_18,c_15]) ).
cnf(c_23,negated_conjecture,
( rprop(sK2,sK3)
| ~ xsd_integer(sK1)
| ~ cowlThing(sK0)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_19,c_16]) ).
cnf(c_24,negated_conjecture,
( ~ cA(sK3)
| ~ xsd_integer(sK1)
| ~ cowlThing(sK0)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_19,c_12]) ).
cnf(c_25,plain,
( cA(B)
| ~ rprop(A,B) ),
inference(clausify,[status(thm)],[axiom_2]) ).
cnf(c_26,negated_conjecture,
( rprop(sK2,sK3)
| xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_20,c_21]) ).
cnf(c_27,negated_conjecture,
( rprop(sK2,sK3)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_20,c_23]) ).
cnf(c_28,negated_conjecture,
( ~ cA(sK3)
| xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_20,c_22]) ).
cnf(c_29,negated_conjecture,
( xsd_integer(sK1)
| xsd_integer(sK1)
| cA(sK3) ),
inference(resolve,[status(thm)],[c_25,c_26]) ).
cnf(c_30,negated_conjecture,
( ~ xsd_integer(sK1)
| ~ xsd_integer(sK1)
| cA(sK3) ),
inference(resolve,[status(thm)],[c_25,c_27]) ).
cnf(c_31,negated_conjecture,
( ~ cA(sK3)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_20,c_24]) ).
cnf(c_32,negated_conjecture,
( ~ xsd_integer(sK1)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_31,c_30]) ).
cnf(c_36,negated_conjecture,
( ~ xsd_integer(sK1)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_37,negated_conjecture,
( ~ xsd_integer(sK1)
| ~ xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_36]) ).
cnf(c_33,negated_conjecture,
~ xsd_integer(sK1),
inference(copy,[status(thm)],[c_37]) ).
cnf(c_34,negated_conjecture,
( xsd_integer(sK1)
| xsd_integer(sK1)
| xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_28,c_29]) ).
cnf(c_38,negated_conjecture,
( xsd_integer(sK1)
| xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_34]) ).
cnf(c_39,negated_conjecture,
( xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_38]) ).
cnf(c_40,negated_conjecture,
xsd_integer(sK1),
inference(copy,[status(thm)],[c_39]) ).
cnf(c_35,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_33,c_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS134+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n003.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 19:42:55 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 918769 was started by sandbox on n003,
% 0.11/0.36 % Fri Sep 25 19:42:55 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 0.11/0.38
% 0.11/0.38 % SZS status Theorem for theBenchmark
% 0.11/0.38
% 0.11/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.38 % Length of proof is 31.
% 0.11/0.38 % Level of proof is 8.
% 0.11/0.38 % Maximum clause weight is 2.000.
% 0.11/0.38 % Given clauses 0.
% 0.11/0.38
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------