%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS166+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 : n006.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 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 6 unt; 0 def)
% Number of atoms : 192 ( 0 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 233 ( 89 ~; 123 |; 14 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 19 ( 2 sgn 10 !; 3 ?)
% 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] :
( cAutomobile(X)
=> cCar(X) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cCar(X)
=> cAutomobile(X) ),
file('theBenchmark.p',axiom_3) ).
fof(the_axiom,conjecture,
( ! [X] :
( cCar(X)
<=> cAutomobile(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('theBenchmark.p',the_axiom) ).
fof(the_axiom_neg,negated_conjecture,
~ ( ! [X] :
( cCar(X)
<=> cAutomobile(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(assume_negation,[status(cth)],[the_axiom]) ).
fof(nnf_5,plain,
( ? [X] :
( ( ~ cAutomobile(X)
| ~ cCar(X) )
& ( cAutomobile(X)
| cCar(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,
( ( ( ~ cAutomobile(sK2)
| ~ cCar(sK2) )
& ( cAutomobile(sK2)
| cCar(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]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X,sK2)],[nnf_5]) ).
fof(sk_the_axiom_neg,plain,
( ( ~ cAutomobile(sK2)
| ~ cCar(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( cAutomobile(sK2)
| cCar(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( ~ cAutomobile(sK2)
| ~ cCar(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( cAutomobile(sK2)
| cCar(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ) ),
inference(cnf_transformation,[status(thm)],[sk_the_axiom_neg_sk]) ).
cnf(c_6,negated_conjecture,
( cAutomobile(sK2)
| cCar(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_7,plain,
cowlThing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_8,negated_conjecture,
( ~ cAutomobile(sK2)
| ~ cCar(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_9,negated_conjecture,
( cAutomobile(sK2)
| cCar(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_10,negated_conjecture,
( ~ cAutomobile(sK2)
| ~ cCar(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_11,plain,
~ cowlNothing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_12,negated_conjecture,
( cAutomobile(sK2)
| cCar(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_6,c_7]) ).
cnf(c_13,negated_conjecture,
( ~ cAutomobile(sK2)
| ~ cCar(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_8,c_7]) ).
cnf(c_14,negated_conjecture,
( cAutomobile(sK2)
| cCar(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_9,c_7]) ).
cnf(c_15,negated_conjecture,
( ~ cAutomobile(sK2)
| ~ cCar(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_10,c_7]) ).
cnf(c_16,negated_conjecture,
( ~ cAutomobile(sK2)
| ~ cCar(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_11,c_13]) ).
cnf(c_17,negated_conjecture,
( cAutomobile(sK2)
| cCar(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_11,c_14]) ).
cnf(c_18,negated_conjecture,
( ~ cAutomobile(sK2)
| ~ cCar(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_11,c_15]) ).
cnf(c_19,negated_conjecture,
( cAutomobile(sK2)
| cCar(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_11,c_12]) ).
cnf(c_20,plain,
( ~ xsd_integer(A)
| ~ xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_21,plain,
( xsd_integer(A)
| xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_22,negated_conjecture,
( cAutomobile(sK2)
| cCar(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_21,c_17]) ).
cnf(c_23,negated_conjecture,
( ~ cAutomobile(sK2)
| ~ cCar(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_21,c_18]) ).
cnf(c_24,negated_conjecture,
( ~ cAutomobile(sK2)
| ~ cCar(sK2)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_20,c_16]) ).
cnf(c_25,negated_conjecture,
( cAutomobile(sK2)
| cCar(sK2)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_20,c_19]) ).
cnf(c_26,plain,
( cAutomobile(A)
| ~ cCar(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
cnf(c_27,plain,
( cCar(A)
| ~ cAutomobile(A) ),
inference(clausify,[status(thm)],[axiom_2]) ).
cnf(c_28,negated_conjecture,
( cCar(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1)
| cCar(sK2) ),
inference(resolve,[status(thm)],[c_27,c_22]) ).
cnf(c_39,negated_conjecture,
( cCar(sK2)
| xsd_integer(sK1)
| cCar(sK2) ),
inference(copy,[status(thm)],[c_28]) ).
cnf(c_29,negated_conjecture,
( xsd_integer(sK1)
| cCar(sK2) ),
inference(copy,[status(thm)],[c_39]) ).
cnf(c_30,negated_conjecture,
( cCar(sK2)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1)
| cCar(sK2) ),
inference(resolve,[status(thm)],[c_27,c_25]) ).
cnf(c_40,negated_conjecture,
( cCar(sK2)
| ~ xsd_integer(sK1)
| cCar(sK2) ),
inference(copy,[status(thm)],[c_30]) ).
cnf(c_31,negated_conjecture,
( ~ xsd_integer(sK1)
| cCar(sK2) ),
inference(copy,[status(thm)],[c_40]) ).
cnf(c_32,negated_conjecture,
( ~ cCar(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1)
| ~ cCar(sK2) ),
inference(resolve,[status(thm)],[c_26,c_23]) ).
cnf(c_41,negated_conjecture,
( ~ cCar(sK2)
| xsd_integer(sK1)
| ~ cCar(sK2) ),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_33,negated_conjecture,
( xsd_integer(sK1)
| ~ cCar(sK2) ),
inference(copy,[status(thm)],[c_41]) ).
cnf(c_34,negated_conjecture,
( ~ cCar(sK2)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1)
| ~ cCar(sK2) ),
inference(resolve,[status(thm)],[c_26,c_24]) ).
cnf(c_42,negated_conjecture,
( ~ cCar(sK2)
| ~ xsd_integer(sK1)
| ~ cCar(sK2) ),
inference(copy,[status(thm)],[c_34]) ).
cnf(c_35,negated_conjecture,
( ~ xsd_integer(sK1)
| ~ cCar(sK2) ),
inference(copy,[status(thm)],[c_42]) ).
cnf(c_43,negated_conjecture,
( cCar(sK2)
| cCar(sK2) ),
inference(resolve,[status(thm)],[c_31,c_29]) ).
cnf(c_36,negated_conjecture,
cCar(sK2),
inference(copy,[status(thm)],[c_43]) ).
cnf(c_37,negated_conjecture,
~ xsd_integer(sK1),
inference(resolve,[status(thm)],[c_36,c_35]) ).
cnf(c_44,negated_conjecture,
xsd_integer(sK1),
inference(resolve,[status(thm)],[c_36,c_33]) ).
cnf(c_38,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_37,c_44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS166+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n006.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 19:41:56 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3578479 was started by sandbox2 on n006,
% 0.09/0.37 % Fri Sep 25 19:41:56 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.39
% 0.09/0.39 % SZS status Theorem for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.39 % Length of proof is 38.
% 0.09/0.39 % Level of proof is 9.
% 0.09/0.39 % Maximum clause weight is 4.000.
% 0.09/0.39 % Given clauses 2.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------