%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS160+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 : n016.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 07:46:11 AM UTC 2026
% Result : Theorem 0.15s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 12 unt; 0 def)
% Number of atoms : 207 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 301 ( 142 ~; 136 |; 18 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 22 ( 2 sgn 8 !; 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] :
( cC10(X)
<=> ( cC2(X)
& cC4(X) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cC12(X)
<=> ? [Y] :
( cC10(Y)
& rR1(X,Y) ) ),
file('theBenchmark.p',axiom_3) ).
fof(the_axiom,conjecture,
( cowlThing(iV21081)
& cC10(iV21081)
& cC12(iV21080)
& cowlThing(iV21080)
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('theBenchmark.p',the_axiom) ).
fof(the_axiom_neg,negated_conjecture,
~ ( cowlThing(iV21081)
& cC10(iV21081)
& cC12(iV21080)
& cowlThing(iV21080)
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(assume_negation,[status(cth)],[the_axiom]) ).
fof(nnf_15,plain,
( ~ cowlThing(iV21081)
| ~ cC10(iV21081)
| ~ cC12(iV21080)
| ~ cowlThing(iV21080)
| ? [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(iV21081)
| ~ cC10(iV21081)
| ~ cC12(iV21080)
| ~ cowlThing(iV21080)
| ( ( 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_15]) ).
fof(sk_the_axiom_neg,plain,
( ( ~ cowlThing(iV21081)
| ~ cC10(iV21081)
| ~ cC12(iV21080)
| ~ cowlThing(iV21080)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( ~ cowlThing(iV21081)
| ~ cC10(iV21081)
| ~ cC12(iV21080)
| ~ cowlThing(iV21080)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ) ),
inference(cnf_transformation,[status(thm)],[sk_the_axiom_neg_sk]) ).
cnf(c_16,negated_conjecture,
( ~ cowlThing(iV21081)
| ~ cC10(iV21081)
| ~ cC12(iV21080)
| ~ cowlThing(iV21080)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_17,plain,
~ cowlNothing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_18,negated_conjecture,
( ~ cowlThing(iV21081)
| ~ cC10(iV21081)
| ~ cC12(iV21080)
| ~ cowlThing(iV21080)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_19,negated_conjecture,
( ~ cowlThing(iV21081)
| ~ cC10(iV21081)
| ~ cC12(iV21080)
| ~ cowlThing(iV21080)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| ~ cowlThing(sK0) ),
inference(resolve,[status(thm)],[c_16,c_17]) ).
cnf(c_20,negated_conjecture,
( ~ cowlThing(iV21081)
| ~ cC10(iV21081)
| ~ cC12(iV21080)
| ~ cowlThing(iV21080)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| ~ cowlThing(sK0) ),
inference(resolve,[status(thm)],[c_18,c_17]) ).
cnf(c_21,plain,
( xsd_integer(A)
| xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_22,plain,
( ~ xsd_integer(A)
| ~ xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_23,plain,
( ~ cC2(A)
| ~ cC4(A)
| cC10(A) ),
inference(clausify,[status(thm)],[axiom_2]) ).
cnf(c_26,negated_conjecture,
( ~ cowlThing(iV21081)
| ~ cC10(iV21081)
| ~ cC12(iV21080)
| ~ cowlThing(iV21080)
| xsd_integer(sK1)
| ~ cowlThing(sK0)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_21,c_20]) ).
cnf(c_27,negated_conjecture,
( ~ cowlThing(iV21081)
| ~ cC10(iV21081)
| ~ cC12(iV21080)
| ~ cowlThing(iV21080)
| ~ xsd_integer(sK1)
| ~ cowlThing(sK0)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_22,c_19]) ).
cnf(c_29,plain,
( ~ cC10(B)
| ~ rR1(A,B)
| cC12(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
cnf(c_31,plain,
( ~ cC2(B)
| ~ cC4(B)
| ~ rR1(A,B)
| cC12(A) ),
inference(resolve,[status(thm)],[c_29,c_23]) ).
cnf(c_32,negated_conjecture,
( ~ cowlThing(iV21081)
| ~ cC12(iV21080)
| ~ cowlThing(iV21080)
| ~ xsd_integer(sK1)
| ~ cowlThing(sK0)
| ~ xsd_integer(sK1)
| ~ cC2(iV21081)
| ~ cC4(iV21081) ),
inference(resolve,[status(thm)],[c_23,c_27]) ).
cnf(c_33,negated_conjecture,
( ~ cowlThing(iV21081)
| ~ cC12(iV21080)
| ~ cowlThing(iV21080)
| xsd_integer(sK1)
| ~ cowlThing(sK0)
| xsd_integer(sK1)
| ~ cC2(iV21081)
| ~ cC4(iV21081) ),
inference(resolve,[status(thm)],[c_23,c_26]) ).
fof(axiom_18,axiom,
cC4(iV21081),
file('theBenchmark.p',axiom_18) ).
cnf(c_34,plain,
cC4(iV21081),
inference(clausify,[status(thm)],[axiom_18]) ).
cnf(c_40,negated_conjecture,
( ~ cowlThing(iV21081)
| ~ cC12(iV21080)
| ~ cowlThing(iV21080)
| xsd_integer(sK1)
| ~ cowlThing(sK0)
| xsd_integer(sK1)
| ~ cC2(iV21081) ),
inference(resolve,[status(thm)],[c_34,c_33]) ).
cnf(c_41,negated_conjecture,
( ~ cowlThing(iV21081)
| ~ cC12(iV21080)
| ~ cowlThing(iV21080)
| ~ xsd_integer(sK1)
| ~ cowlThing(sK0)
| ~ xsd_integer(sK1)
| ~ cC2(iV21081) ),
inference(resolve,[status(thm)],[c_34,c_32]) ).
cnf(c_42,plain,
( ~ cC2(iV21081)
| ~ rR1(A,iV21081)
| cC12(A) ),
inference(resolve,[status(thm)],[c_34,c_31]) ).
fof(axiom_20,axiom,
cC2(iV21081),
file('theBenchmark.p',axiom_20) ).
cnf(c_44,plain,
cC2(iV21081),
inference(clausify,[status(thm)],[axiom_20]) ).
fof(axiom_17,axiom,
rR1(iV21080,iV21081),
file('theBenchmark.p',axiom_17) ).
cnf(c_46,plain,
rR1(iV21080,iV21081),
inference(clausify,[status(thm)],[axiom_17]) ).
cnf(c_50,plain,
( ~ rR1(A,iV21081)
| cC12(A) ),
inference(resolve,[status(thm)],[c_44,c_42]) ).
cnf(c_58,plain,
cC12(iV21080),
inference(resolve,[status(thm)],[c_46,c_50]) ).
cnf(c_65,negated_conjecture,
( ~ cowlThing(iV21081)
| ~ cC12(iV21080)
| ~ cowlThing(iV21080)
| xsd_integer(sK1)
| ~ cowlThing(sK0)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_44,c_40]) ).
cnf(c_66,negated_conjecture,
( ~ cowlThing(iV21081)
| ~ cC12(iV21080)
| ~ cowlThing(iV21080)
| ~ xsd_integer(sK1)
| ~ cowlThing(sK0)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_44,c_41]) ).
cnf(c_129,negated_conjecture,
( ~ cowlThing(iV21081)
| ~ cowlThing(iV21080)
| ~ xsd_integer(sK1)
| ~ cowlThing(sK0)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_66,c_58]) ).
cnf(c_130,negated_conjecture,
( ~ cowlThing(iV21081)
| ~ cowlThing(iV21080)
| ~ cowlThing(sK0)
| ~ xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_129]) ).
cnf(c_131,negated_conjecture,
( ~ cowlThing(iV21081)
| ~ cowlThing(iV21080)
| xsd_integer(sK1)
| ~ cowlThing(sK0)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_65,c_58]) ).
cnf(c_132,negated_conjecture,
( ~ cowlThing(iV21081)
| ~ cowlThing(iV21080)
| ~ cowlThing(sK0)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_131]) ).
cnf(c_139,plain,
cowlThing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_148,negated_conjecture,
( ~ cowlThing(iV21081)
| ~ cowlThing(iV21080)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_139,c_132]) ).
cnf(c_149,negated_conjecture,
( ~ cowlThing(iV21081)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_139,c_148]) ).
cnf(c_146,negated_conjecture,
xsd_integer(sK1),
inference(resolve,[status(thm)],[c_139,c_149]) ).
cnf(c_150,negated_conjecture,
( ~ cowlThing(iV21081)
| ~ cowlThing(iV21080)
| ~ cowlThing(sK0) ),
inference(resolve,[status(thm)],[c_146,c_130]) ).
cnf(c_151,negated_conjecture,
( ~ cowlThing(iV21081)
| ~ cowlThing(iV21080) ),
inference(resolve,[status(thm)],[c_139,c_150]) ).
cnf(c_152,negated_conjecture,
~ cowlThing(iV21081),
inference(resolve,[status(thm)],[c_139,c_151]) ).
cnf(c_147,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_139,c_152]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS160+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n016.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 19:46:45 UTC 2026
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.37 % Process 3132680 was started by sandbox on n016,
% 0.15/0.37 % Fri Sep 25 19:46:45 2026
% 0.15/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.38
% 0.15/0.38 % From the command line: assign(max_seconds, 300).
% 0.15/0.39
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39
% 0.15/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.15/0.39 % Length of proof is 36.
% 0.15/0.39 % Level of proof is 10.
% 0.15/0.39 % Maximum clause weight is 8.000.
% 0.15/0.39 % Given clauses 0.
% 0.15/0.39
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------