%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KRS131+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 01:53:07 PM UTC 2026
% Result : Theorem 4.14s 1.02s
% Output : Proof 4.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 7
% Syntax : Number of formulae : 84 ( 4 unt; 0 def)
% Number of atoms : 307 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 312 ( 89 ~; 185 |; 28 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-1 aty)
% Number of variables : 59 ( 5 sgn 31 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,conjecture,
( ! [X] :
( cnotA(X)
<=> ~ cA(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_axiom) ).
fof(f6_neg,negated_conjecture,
~ ( ! [X] :
( cnotA(X)
<=> ~ cA(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_nnf,plain,
( ? [X] :
( ( ~ cA(X)
& ~ cnotA(X) )
| ( cA(X)
& cnotA(X) ) )
| ? [X] :
( ( ~ xsd_integer(X)
& ~ xsd_string(X) )
| ( xsd_integer(X)
& xsd_string(X) ) )
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_sk,plain,
( ( ~ cA(sk5)
& ~ cnotA(sk5) )
| ( cA(sk5)
& cnotA(sk5) )
| ( ~ xsd_integer(sk4)
& ~ xsd_string(sk4) )
| ( xsd_integer(sk4)
& xsd_string(sk4) )
| cowlNothing(sk3)
| ~ cowlThing(sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4,sk5])],[f6_nnf]) ).
cnf(c18,plain,
( ~ cnotA(sk5)
| cA(sk5)
| ~ xsd_integer(sk4)
| xsd_string(sk4)
| cowlNothing(sk3)
| ~ cowlThing(sk3) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
fof(f0,axiom,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
fof(f0_nnf,plain,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
cowlThing(X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p30,plain,
( ~ cnotA(sk5)
| cA(sk5)
| ~ xsd_integer(sk4)
| xsd_string(sk4)
| cowlNothing(sk3) ),
inference(resolution,[status(thm)],[c18,c0]) ).
fof(f1,axiom,
! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f1_nnf,plain,
! [X] :
( ( xsd_integer(X)
| xsd_string(X) )
& ( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] :
( ( xsd_integer(X)
| xsd_string(X) )
& ( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c3,plain,
( xsd_integer(X0)
| xsd_string(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p35,plain,
( xsd_string(sk4)
| ~ cnotA(sk5)
| cA(sk5)
| xsd_string(sk4)
| cowlNothing(sk3) ),
inference(resolution,[status(thm)],[p30,c3]) ).
cnf(p38,plain,
( ~ cnotA(sk5)
| cA(sk5)
| xsd_string(sk4)
| cowlNothing(sk3) ),
inference(factoring,[status(thm)],[p35]) ).
fof(f5,axiom,
! [X] :
( cnotA(X)
<=> ! [Y] :
( rq(X,Y)
=> cNothing(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(f5_nnf,plain,
! [X] :
( ( ? [Y] :
( ~ cNothing(Y)
& rq(X,Y) )
| cnotA(X) )
& ( ! [Y] :
( cNothing(Y)
| ~ rq(X,Y) )
| ~ cnotA(X) ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y] :
( ( ( ~ cNothing(sk2(X))
& rq(X,sk2(X)) )
| cnotA(X) )
& ( cNothing(Y)
| ~ rq(X,Y)
| ~ cnotA(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f5_nnf]) ).
cnf(c10,plain,
( rq(X0,sk2(X0))
| cnotA(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f2,axiom,
! [X] :
( cA(X)
<=> ? [Y] :
( cowlThing(Y)
& rq(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f2_nnf,plain,
! [X] :
( ( ! [Y] :
( ~ cowlThing(Y)
| ~ rq(X,Y) )
| cA(X) )
& ( ? [Y] :
( cowlThing(Y)
& rq(X,Y) )
| ~ cA(X) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] :
( ( ~ cowlThing(Y)
| ~ rq(X,Y)
| cA(X) )
& ( ( cowlThing(sk0(X))
& rq(X,sk0(X)) )
| ~ cA(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f2_nnf]) ).
cnf(c6,plain,
( ~ cowlThing(X1)
| ~ rq(X0,X1)
| cA(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p28,plain,
( ~ cowlThing(sk2(X0))
| cA(X0)
| cnotA(X0) ),
inference(resolution,[status(thm)],[c10,c6]) ).
cnf(p33,plain,
( cA(X0)
| cnotA(X0) ),
inference(resolution,[status(thm)],[p28,c0]) ).
cnf(p39,plain,
( cA(sk5)
| cA(sk5)
| xsd_string(sk4)
| cowlNothing(sk3) ),
inference(resolution,[status(thm)],[p38,p33]) ).
cnf(p40,plain,
( cA(sk5)
| xsd_string(sk4)
| cowlNothing(sk3) ),
inference(factoring,[status(thm)],[p39]) ).
cnf(c17,plain,
( ~ cA(sk5)
| cnotA(sk5)
| ~ xsd_integer(sk4)
| xsd_string(sk4)
| cowlNothing(sk3)
| ~ cowlThing(sk3) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p29,plain,
( ~ cA(sk5)
| cnotA(sk5)
| ~ xsd_integer(sk4)
| xsd_string(sk4)
| cowlNothing(sk3) ),
inference(resolution,[status(thm)],[c17,c0]) ).
cnf(p34,plain,
( xsd_string(sk4)
| ~ cA(sk5)
| cnotA(sk5)
| xsd_string(sk4)
| cowlNothing(sk3) ),
inference(resolution,[status(thm)],[p29,c3]) ).
cnf(p37,plain,
( ~ cA(sk5)
| cnotA(sk5)
| xsd_string(sk4)
| cowlNothing(sk3) ),
inference(factoring,[status(thm)],[p34]) ).
cnf(p42,plain,
( cnotA(sk5)
| xsd_string(sk4)
| cowlNothing(sk3)
| xsd_string(sk4)
| cowlNothing(sk3) ),
inference(resolution,[status(thm)],[p40,p37]) ).
cnf(p43,plain,
( cnotA(sk5)
| xsd_string(sk4)
| xsd_string(sk4)
| cowlNothing(sk3) ),
inference(factoring,[status(thm)],[p42]) ).
cnf(p45,plain,
( cnotA(sk5)
| xsd_string(sk4)
| cowlNothing(sk3) ),
inference(factoring,[status(thm)],[p43]) ).
cnf(c9,plain,
( cNothing(X1)
| ~ rq(X0,X1)
| ~ cnotA(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p46,plain,
( cNothing(X0)
| ~ rq(sk5,X0)
| xsd_string(sk4)
| cowlNothing(sk3) ),
inference(resolution,[status(thm)],[p45,c9]) ).
cnf(c4,plain,
( rq(X0,sk0(X0))
| ~ cA(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p41,plain,
( rq(sk5,sk0(sk5))
| xsd_string(sk4)
| cowlNothing(sk3) ),
inference(resolution,[status(thm)],[p40,c4]) ).
cnf(p47,plain,
( xsd_string(sk4)
| cowlNothing(sk3)
| cNothing(sk0(sk5))
| xsd_string(sk4)
| cowlNothing(sk3) ),
inference(resolution,[status(thm)],[p46,p41]) ).
cnf(p48,plain,
( xsd_string(sk4)
| cNothing(sk0(sk5))
| xsd_string(sk4)
| cowlNothing(sk3) ),
inference(factoring,[status(thm)],[p47]) ).
cnf(p50,plain,
( cNothing(sk0(sk5))
| xsd_string(sk4)
| cowlNothing(sk3) ),
inference(factoring,[status(thm)],[p48]) ).
fof(f4,axiom,
! [X] :
( cNothing(X)
=> ? [Y0] : rp(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
fof(f4_nnf,plain,
! [X] :
( ? [Y0] : rp(X,Y0)
| ~ cNothing(X) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X] :
( rp(X,sk1(X))
| ~ cNothing(X) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f4_nnf]) ).
cnf(c8,plain,
( rp(X0,sk1(X0))
| ~ cNothing(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p52,plain,
( rp(sk0(sk5),sk1(sk0(sk5)))
| xsd_string(sk4)
| cowlNothing(sk3) ),
inference(resolution,[status(thm)],[p50,c8]) ).
fof(f3,axiom,
! [X] :
( cNothing(X)
=> ~ ? [Y] : rp(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f3_nnf,plain,
! [X] :
( ! [Y] : ~ rp(X,Y)
| ~ cNothing(X) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] :
( ~ rp(X,Y)
| ~ cNothing(X) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c7,plain,
( ~ rp(X0,X1)
| ~ cNothing(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p51,plain,
( ~ rp(sk0(sk5),X0)
| xsd_string(sk4)
| cowlNothing(sk3) ),
inference(resolution,[status(thm)],[p50,c7]) ).
cnf(p53,plain,
( xsd_string(sk4)
| cowlNothing(sk3)
| xsd_string(sk4)
| cowlNothing(sk3) ),
inference(resolution,[status(thm)],[p52,p51]) ).
cnf(p54,plain,
( xsd_string(sk4)
| xsd_string(sk4)
| cowlNothing(sk3) ),
inference(factoring,[status(thm)],[p53]) ).
cnf(p56,plain,
( xsd_string(sk4)
| cowlNothing(sk3) ),
inference(factoring,[status(thm)],[p54]) ).
cnf(c22,plain,
( ~ cnotA(sk5)
| cA(sk5)
| ~ xsd_string(sk4)
| xsd_integer(sk4)
| cowlNothing(sk3)
| ~ cowlThing(sk3) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p32,plain,
( ~ cnotA(sk5)
| cA(sk5)
| ~ xsd_string(sk4)
| xsd_integer(sk4)
| cowlNothing(sk3) ),
inference(resolution,[status(thm)],[c22,c0]) ).
cnf(p59,plain,
( ~ cnotA(sk5)
| cA(sk5)
| xsd_integer(sk4)
| cowlNothing(sk3)
| cowlNothing(sk3) ),
inference(resolution,[status(thm)],[p56,p32]) ).
cnf(p61,plain,
( ~ cnotA(sk5)
| cA(sk5)
| xsd_integer(sk4)
| cowlNothing(sk3) ),
inference(factoring,[status(thm)],[p59]) ).
cnf(p62,plain,
( cA(sk5)
| cA(sk5)
| xsd_integer(sk4)
| cowlNothing(sk3) ),
inference(resolution,[status(thm)],[p61,p33]) ).
cnf(p63,plain,
( cA(sk5)
| xsd_integer(sk4)
| cowlNothing(sk3) ),
inference(factoring,[status(thm)],[p62]) ).
cnf(c21,plain,
( ~ cA(sk5)
| cnotA(sk5)
| ~ xsd_string(sk4)
| xsd_integer(sk4)
| cowlNothing(sk3)
| ~ cowlThing(sk3) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p31,plain,
( ~ cA(sk5)
| cnotA(sk5)
| ~ xsd_string(sk4)
| xsd_integer(sk4)
| cowlNothing(sk3) ),
inference(resolution,[status(thm)],[c21,c0]) ).
cnf(p58,plain,
( ~ cA(sk5)
| cnotA(sk5)
| xsd_integer(sk4)
| cowlNothing(sk3)
| cowlNothing(sk3) ),
inference(resolution,[status(thm)],[p56,p31]) ).
cnf(p60,plain,
( ~ cA(sk5)
| cnotA(sk5)
| xsd_integer(sk4)
| cowlNothing(sk3) ),
inference(factoring,[status(thm)],[p58]) ).
cnf(p65,plain,
( cnotA(sk5)
| xsd_integer(sk4)
| cowlNothing(sk3)
| xsd_integer(sk4)
| cowlNothing(sk3) ),
inference(resolution,[status(thm)],[p63,p60]) ).
cnf(p66,plain,
( cnotA(sk5)
| xsd_integer(sk4)
| xsd_integer(sk4)
| cowlNothing(sk3) ),
inference(factoring,[status(thm)],[p65]) ).
cnf(p68,plain,
( cnotA(sk5)
| xsd_integer(sk4)
| cowlNothing(sk3) ),
inference(factoring,[status(thm)],[p66]) ).
cnf(p69,plain,
( cNothing(X0)
| ~ rq(sk5,X0)
| xsd_integer(sk4)
| cowlNothing(sk3) ),
inference(resolution,[status(thm)],[p68,c9]) ).
cnf(p64,plain,
( rq(sk5,sk0(sk5))
| xsd_integer(sk4)
| cowlNothing(sk3) ),
inference(resolution,[status(thm)],[p63,c4]) ).
cnf(p70,plain,
( xsd_integer(sk4)
| cowlNothing(sk3)
| cNothing(sk0(sk5))
| xsd_integer(sk4)
| cowlNothing(sk3) ),
inference(resolution,[status(thm)],[p69,p64]) ).
cnf(p71,plain,
( xsd_integer(sk4)
| cNothing(sk0(sk5))
| xsd_integer(sk4)
| cowlNothing(sk3) ),
inference(factoring,[status(thm)],[p70]) ).
cnf(p73,plain,
( cNothing(sk0(sk5))
| xsd_integer(sk4)
| cowlNothing(sk3) ),
inference(factoring,[status(thm)],[p71]) ).
cnf(p75,plain,
( rp(sk0(sk5),sk1(sk0(sk5)))
| xsd_integer(sk4)
| cowlNothing(sk3) ),
inference(resolution,[status(thm)],[p73,c8]) ).
cnf(p74,plain,
( ~ rp(sk0(sk5),X0)
| xsd_integer(sk4)
| cowlNothing(sk3) ),
inference(resolution,[status(thm)],[p73,c7]) ).
cnf(p76,plain,
( xsd_integer(sk4)
| cowlNothing(sk3)
| xsd_integer(sk4)
| cowlNothing(sk3) ),
inference(resolution,[status(thm)],[p75,p74]) ).
cnf(p77,plain,
( xsd_integer(sk4)
| xsd_integer(sk4)
| cowlNothing(sk3) ),
inference(factoring,[status(thm)],[p76]) ).
cnf(p79,plain,
( xsd_integer(sk4)
| cowlNothing(sk3) ),
inference(factoring,[status(thm)],[p77]) ).
cnf(c2,plain,
( ~ xsd_integer(X0)
| ~ xsd_string(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p57,plain,
( ~ xsd_integer(sk4)
| cowlNothing(sk3) ),
inference(resolution,[status(thm)],[p56,c2]) ).
cnf(p80,plain,
( cowlNothing(sk3)
| cowlNothing(sk3) ),
inference(resolution,[status(thm)],[p79,p57]) ).
cnf(p81,plain,
cowlNothing(sk3),
inference(factoring,[status(thm)],[p80]) ).
cnf(c1,plain,
~ cowlNothing(X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p82,plain,
$false,
inference(resolution,[status(thm)],[p81,c1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS131+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n003.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 : Wed Sep 23 19:30:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.14/1.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.14/1.02 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------