%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS171+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 : n012.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 07:46:15 AM UTC 2026
% Result : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% 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 : 234 ( 90 ~; 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; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 26 ( 2 sgn 14 !; 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] :
( rhasHead(X,Y)
=> rhasLeader(X,Y) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X,Y] :
( rhasLeader(X,Y)
=> rhasHead(X,Y) ),
file('theBenchmark.p',axiom_3) ).
fof(the_axiom,conjecture,
( ! [X,Y] :
( rhasLeader(X,Y)
<=> rhasHead(X,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,Y] :
( rhasLeader(X,Y)
<=> rhasHead(X,Y) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(assume_negation,[status(cth)],[the_axiom]) ).
fof(nnf_5,plain,
( ? [X,Y] :
( ( ~ rhasHead(X,Y)
| ~ rhasLeader(X,Y) )
& ( rhasHead(X,Y)
| rhasLeader(X,Y) ) )
| ? [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,
( ( ( ~ rhasHead(sK2,sK3)
| ~ rhasLeader(sK2,sK3) )
& ( rhasHead(sK2,sK3)
| rhasLeader(sK2,sK3) ) )
| ( ( 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_5]) ).
fof(sk_the_axiom_neg,plain,
( ( ~ rhasHead(sK2,sK3)
| ~ rhasLeader(sK2,sK3)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( rhasHead(sK2,sK3)
| rhasLeader(sK2,sK3)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( ~ rhasHead(sK2,sK3)
| ~ rhasLeader(sK2,sK3)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( rhasHead(sK2,sK3)
| rhasLeader(sK2,sK3)
| ~ 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,
( rhasHead(sK2,sK3)
| rhasLeader(sK2,sK3)
| ~ 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,
( ~ rhasHead(sK2,sK3)
| ~ rhasLeader(sK2,sK3)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_9,negated_conjecture,
( rhasHead(sK2,sK3)
| rhasLeader(sK2,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,
( ~ rhasHead(sK2,sK3)
| ~ rhasLeader(sK2,sK3)
| 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,
( rhasHead(sK2,sK3)
| rhasLeader(sK2,sK3)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_6,c_7]) ).
cnf(c_13,negated_conjecture,
( ~ rhasHead(sK2,sK3)
| ~ rhasLeader(sK2,sK3)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_8,c_7]) ).
cnf(c_14,negated_conjecture,
( rhasHead(sK2,sK3)
| rhasLeader(sK2,sK3)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_9,c_7]) ).
cnf(c_15,negated_conjecture,
( ~ rhasHead(sK2,sK3)
| ~ rhasLeader(sK2,sK3)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_10,c_7]) ).
cnf(c_16,negated_conjecture,
( ~ rhasHead(sK2,sK3)
| ~ rhasLeader(sK2,sK3)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_11,c_13]) ).
cnf(c_17,negated_conjecture,
( rhasHead(sK2,sK3)
| rhasLeader(sK2,sK3)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_11,c_14]) ).
cnf(c_18,negated_conjecture,
( ~ rhasHead(sK2,sK3)
| ~ rhasLeader(sK2,sK3)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_11,c_15]) ).
cnf(c_19,negated_conjecture,
( rhasHead(sK2,sK3)
| rhasLeader(sK2,sK3)
| ~ 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,
( rhasHead(sK2,sK3)
| rhasLeader(sK2,sK3)
| xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_21,c_17]) ).
cnf(c_23,negated_conjecture,
( ~ rhasHead(sK2,sK3)
| ~ rhasLeader(sK2,sK3)
| xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_21,c_18]) ).
cnf(c_24,negated_conjecture,
( ~ rhasHead(sK2,sK3)
| ~ rhasLeader(sK2,sK3)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_20,c_16]) ).
cnf(c_25,negated_conjecture,
( rhasHead(sK2,sK3)
| rhasLeader(sK2,sK3)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_20,c_19]) ).
cnf(c_26,plain,
( rhasHead(A,B)
| ~ rhasLeader(A,B) ),
inference(clausify,[status(thm)],[axiom_3]) ).
cnf(c_27,plain,
( rhasLeader(A,B)
| ~ rhasHead(A,B) ),
inference(clausify,[status(thm)],[axiom_2]) ).
cnf(c_28,negated_conjecture,
( rhasLeader(sK2,sK3)
| xsd_integer(sK1)
| xsd_integer(sK1)
| rhasLeader(sK2,sK3) ),
inference(resolve,[status(thm)],[c_27,c_22]) ).
cnf(c_39,negated_conjecture,
( rhasLeader(sK2,sK3)
| xsd_integer(sK1)
| rhasLeader(sK2,sK3) ),
inference(copy,[status(thm)],[c_28]) ).
cnf(c_29,negated_conjecture,
( xsd_integer(sK1)
| rhasLeader(sK2,sK3) ),
inference(copy,[status(thm)],[c_39]) ).
cnf(c_30,negated_conjecture,
( rhasLeader(sK2,sK3)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1)
| rhasLeader(sK2,sK3) ),
inference(resolve,[status(thm)],[c_27,c_25]) ).
cnf(c_40,negated_conjecture,
( rhasLeader(sK2,sK3)
| ~ xsd_integer(sK1)
| rhasLeader(sK2,sK3) ),
inference(copy,[status(thm)],[c_30]) ).
cnf(c_31,negated_conjecture,
( ~ xsd_integer(sK1)
| rhasLeader(sK2,sK3) ),
inference(copy,[status(thm)],[c_40]) ).
cnf(c_32,negated_conjecture,
( ~ rhasLeader(sK2,sK3)
| xsd_integer(sK1)
| xsd_integer(sK1)
| ~ rhasLeader(sK2,sK3) ),
inference(resolve,[status(thm)],[c_26,c_23]) ).
cnf(c_41,negated_conjecture,
( ~ rhasLeader(sK2,sK3)
| xsd_integer(sK1)
| ~ rhasLeader(sK2,sK3) ),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_33,negated_conjecture,
( xsd_integer(sK1)
| ~ rhasLeader(sK2,sK3) ),
inference(copy,[status(thm)],[c_41]) ).
cnf(c_34,negated_conjecture,
( ~ rhasLeader(sK2,sK3)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1)
| ~ rhasLeader(sK2,sK3) ),
inference(resolve,[status(thm)],[c_26,c_24]) ).
cnf(c_42,negated_conjecture,
( ~ rhasLeader(sK2,sK3)
| ~ xsd_integer(sK1)
| ~ rhasLeader(sK2,sK3) ),
inference(copy,[status(thm)],[c_34]) ).
cnf(c_35,negated_conjecture,
( ~ xsd_integer(sK1)
| ~ rhasLeader(sK2,sK3) ),
inference(copy,[status(thm)],[c_42]) ).
cnf(c_43,negated_conjecture,
( xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_33,c_29]) ).
cnf(c_36,negated_conjecture,
xsd_integer(sK1),
inference(copy,[status(thm)],[c_43]) ).
cnf(c_37,negated_conjecture,
~ rhasLeader(sK2,sK3),
inference(resolve,[status(thm)],[c_36,c_35]) ).
cnf(c_44,negated_conjecture,
~ xsd_integer(sK1),
inference(resolve,[status(thm)],[c_37,c_31]) ).
cnf(c_38,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_36,c_44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS171+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n012.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 19:42:06 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 2821050 was started by sandbox2 on n012,
% 0.08/0.35 % Fri Sep 25 19:42:06 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 0.12/0.36
% 0.12/0.36 % SZS status Theorem for theBenchmark
% 0.12/0.36
% 0.12/0.36 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.36 % Length of proof is 38.
% 0.12/0.36 % Level of proof is 9.
% 0.12/0.36 % Maximum clause weight is 5.000.
% 0.12/0.36 % Given clauses 3.
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------