%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS163+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 : n017.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 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 12 unt; 0 def)
% Number of atoms : 135 ( 23 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 161 ( 65 ~; 76 |; 16 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 19 ( 2 sgn 9 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cA_substitution_1,axiom,
! [A,B] :
( ( cA(A)
& A = B )
=> cA(B) ),
file('theBenchmark.p',cA_substitution_1) ).
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_6,axiom,
! [X] :
~ ( cA(X)
& cB(X) ),
file('theBenchmark.p',axiom_6) ).
fof(the_axiom,conjecture,
( ia != ib
& cowlThing(ib)
& cowlThing(ia)
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('theBenchmark.p',the_axiom) ).
fof(the_axiom_neg,negated_conjecture,
~ ( ia != ib
& cowlThing(ib)
& cowlThing(ia)
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(assume_negation,[status(cth)],[the_axiom]) ).
cnf(c_11,plain,
( cA(A)
| ~ cA(B)
| A != B ),
inference(clausify,[status(thm)],[cA_substitution_1]) ).
cnf(c_17,plain,
cowlThing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_18,plain,
~ cowlNothing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_19,plain,
( ~ xsd_integer(A)
| ~ xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_20,plain,
( xsd_integer(A)
| xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
fof(axiom_2,axiom,
cA(ia),
file('theBenchmark.p',axiom_2) ).
cnf(c_21,plain,
cA(ia),
inference(clausify,[status(thm)],[axiom_2]) ).
fof(axiom_4,axiom,
cB(ib),
file('theBenchmark.p',axiom_4) ).
cnf(c_22,plain,
cB(ib),
inference(clausify,[status(thm)],[axiom_4]) ).
cnf(c_23,plain,
( ~ cA(A)
| ~ cB(A) ),
inference(clausify,[status(thm)],[axiom_6]) ).
fof(nnf_10,plain,
( ib = ia
| ~ cowlThing(ib)
| ~ cowlThing(ia)
| ? [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,
( ib = ia
| ~ cowlThing(ib)
| ~ cowlThing(ia)
| ( ( 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_10]) ).
fof(sk_the_axiom_neg,plain,
( ( ib = ia
| ~ cowlThing(ib)
| ~ cowlThing(ia)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( ib = ia
| ~ cowlThing(ib)
| ~ cowlThing(ia)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ) ),
inference(cnf_transformation,[status(thm)],[sk_the_axiom_neg_sk]) ).
cnf(c_24,negated_conjecture,
( ib = ia
| ~ cowlThing(ib)
| ~ cowlThing(ia)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_39,negated_conjecture,
( ib = ia
| ~ cowlThing(ib)
| ~ cowlThing(ia)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_17,c_24]) ).
cnf(c_40,negated_conjecture,
( ib = ia
| ~ cowlThing(ib)
| ~ cowlThing(ia)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_18,c_39]) ).
cnf(c_41,negated_conjecture,
( ib = ia
| ~ cowlThing(ib)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_17,c_40]) ).
cnf(c_25,negated_conjecture,
( ib = ia
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_17,c_41]) ).
cnf(c_26,negated_conjecture,
( ib = ia
| ~ cowlThing(ib)
| ~ cowlThing(ia)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_42,negated_conjecture,
( ib = ia
| ~ cowlThing(ib)
| ~ cowlThing(ia)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_17,c_26]) ).
cnf(c_43,negated_conjecture,
( ib = ia
| ~ cowlThing(ib)
| ~ cowlThing(ia)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_18,c_42]) ).
cnf(c_44,negated_conjecture,
( ib = ia
| ~ cowlThing(ib)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_17,c_43]) ).
cnf(c_27,negated_conjecture,
( ib = ia
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_17,c_44]) ).
cnf(c_31,plain,
~ cA(ib),
inference(resolve,[status(thm)],[c_23,c_22]) ).
cnf(c_45,negated_conjecture,
( xsd_integer(sK1)
| ib = ia
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_27,c_20]) ).
cnf(c_33,negated_conjecture,
( ib = ia
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_45]) ).
cnf(c_46,plain,
( cA(A)
| A != ia ),
inference(resolve,[status(thm)],[c_11,c_21]) ).
cnf(c_34,plain,
ib != ia,
inference(resolve,[status(thm)],[c_46,c_31]) ).
cnf(c_35,negated_conjecture,
xsd_integer(sK1),
inference(resolve,[status(thm)],[c_34,c_33]) ).
cnf(c_47,negated_conjecture,
( ib = ia
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_35,c_25]) ).
cnf(c_36,negated_conjecture,
xsd_string(sK1),
inference(resolve,[status(thm)],[c_34,c_47]) ).
cnf(c_48,plain,
~ xsd_string(sK1),
inference(resolve,[status(thm)],[c_19,c_35]) ).
cnf(c_38,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_36,c_48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS163+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 19:37:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2990639 was started by sandbox2 on n017,
% 0.10/0.37 % Fri Sep 25 19:37:33 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.39
% 0.10/0.39 % SZS status Theorem for theBenchmark
% 0.10/0.39
% 0.10/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.39 % Length of proof is 23.
% 0.10/0.39 % Level of proof is 6.
% 0.10/0.39 % Maximum clause weight is 7.000.
% 0.10/0.39 % Given clauses 18.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------