%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KRS167+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 01:53:23 PM UTC 2026
% Result : Theorem 4.47s 1.12s
% Output : Proof 4.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 5
% Syntax : Number of formulae : 86 ( 7 unt; 0 def)
% Number of atoms : 324 ( 26 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 342 ( 104 ~; 190 |; 39 &)
% ( 7 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-1 aty)
% Number of variables : 74 ( 8 sgn 32 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,conjecture,
( ! [X] :
( cc1(X)
<=> cc2(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',the_axiom) ).
fof(f12_neg,negated_conjecture,
~ ( ! [X] :
( cc1(X)
<=> cc2(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f12_nnf,plain,
( ? [X] :
( ( cc2(X)
& ~ cc1(X) )
| ( ~ cc2(X)
& cc1(X) ) )
| ? [X] :
( ( ~ xsd_integer(X)
& ~ xsd_string(X) )
| ( xsd_integer(X)
& xsd_string(X) ) )
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(nnf_transformation,[status(thm)],[f12_neg]) ).
fof(f12_sk,plain,
( ( cc2(sk8)
& ~ cc1(sk8) )
| ( ~ cc2(sk8)
& cc1(sk8) )
| ( ~ xsd_integer(sk7)
& ~ xsd_string(sk7) )
| ( xsd_integer(sk7)
& xsd_string(sk7) )
| cowlNothing(sk6)
| ~ cowlThing(sk6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk6,sk7,sk8])],[f12_nnf]) ).
cnf(c31,plain,
( cc2(sk8)
| cc1(sk8)
| ~ xsd_string(sk7)
| xsd_integer(sk7)
| cowlNothing(sk6)
| ~ cowlThing(sk6) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
fof(f8,axiom,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).
fof(f8_nnf,plain,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
cowlThing(X0),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p40,plain,
( cc2(sk8)
| cc1(sk8)
| ~ xsd_string(sk7)
| xsd_integer(sk7)
| cowlNothing(sk6) ),
inference(resolution,[status(thm)],[c31,c8]) ).
fof(f9,axiom,
! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
fof(f9_nnf,plain,
! [X] :
( ( xsd_integer(X)
| xsd_string(X) )
& ( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X] :
( ( xsd_integer(X)
| xsd_string(X) )
& ( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c11,plain,
( xsd_integer(X0)
| xsd_string(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p42,plain,
( xsd_integer(sk7)
| cc2(sk8)
| cc1(sk8)
| xsd_integer(sk7)
| cowlNothing(sk6) ),
inference(resolution,[status(thm)],[p40,c11]) ).
cnf(p44,plain,
( cc2(sk8)
| cc1(sk8)
| xsd_integer(sk7)
| cowlNothing(sk6) ),
inference(factoring,[status(thm)],[p42]) ).
cnf(c27,plain,
( cc2(sk8)
| cc1(sk8)
| ~ xsd_integer(sk7)
| xsd_string(sk7)
| cowlNothing(sk6)
| ~ cowlThing(sk6) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p38,plain,
( cc2(sk8)
| cc1(sk8)
| ~ xsd_integer(sk7)
| xsd_string(sk7)
| cowlNothing(sk6) ),
inference(resolution,[status(thm)],[c27,c8]) ).
cnf(p46,plain,
( cc2(sk8)
| cc1(sk8)
| xsd_string(sk7)
| cowlNothing(sk6)
| cc2(sk8)
| cc1(sk8)
| cowlNothing(sk6) ),
inference(resolution,[status(thm)],[p44,p38]) ).
cnf(p47,plain,
( cc2(sk8)
| cc1(sk8)
| xsd_string(sk7)
| cc2(sk8)
| cc1(sk8)
| cowlNothing(sk6) ),
inference(factoring,[status(thm)],[p46]) ).
cnf(p50,plain,
( cc2(sk8)
| xsd_string(sk7)
| cc2(sk8)
| cc1(sk8)
| cowlNothing(sk6) ),
inference(factoring,[status(thm)],[p47]) ).
cnf(p52,plain,
( xsd_string(sk7)
| cc2(sk8)
| cc1(sk8)
| cowlNothing(sk6) ),
inference(factoring,[status(thm)],[p50]) ).
cnf(c10,plain,
( ~ xsd_integer(X0)
| ~ xsd_string(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p53,plain,
( ~ xsd_integer(sk7)
| cc2(sk8)
| cc1(sk8)
| cowlNothing(sk6) ),
inference(resolution,[status(thm)],[p52,c10]) ).
cnf(p54,plain,
( cc2(sk8)
| cc1(sk8)
| cowlNothing(sk6)
| cc2(sk8)
| cc1(sk8)
| cowlNothing(sk6) ),
inference(resolution,[status(thm)],[p53,p44]) ).
cnf(p55,plain,
( cc2(sk8)
| cc1(sk8)
| cc2(sk8)
| cc1(sk8)
| cowlNothing(sk6) ),
inference(factoring,[status(thm)],[p54]) ).
cnf(p58,plain,
( cc2(sk8)
| cc2(sk8)
| cc1(sk8)
| cowlNothing(sk6) ),
inference(factoring,[status(thm)],[p55]) ).
cnf(p60,plain,
( cc2(sk8)
| cc1(sk8)
| cowlNothing(sk6) ),
inference(factoring,[status(thm)],[p58]) ).
cnf(c9,plain,
~ cowlNothing(X0),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p61,plain,
( cc2(sk8)
| cc1(sk8) ),
inference(resolution,[status(thm)],[p60,c9]) ).
fof(f11,axiom,
! [X] :
( cc2(X)
<=> ( ! [Y0,Y1] :
( ( rp(X,Y1)
& rp(X,Y0) )
=> Y0 = Y1 )
& ? [Y0] : rp(X,Y0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
fof(f11_nnf,plain,
! [X] :
( ( ? [Y0,Y1] :
( Y0 != Y1
& rp(X,Y1)
& rp(X,Y0) )
| ! [Y0] : ~ rp(X,Y0)
| cc2(X) )
& ( ( ! [Y0,Y1] :
( Y0 = Y1
| ~ rp(X,Y1)
| ~ rp(X,Y0) )
& ? [Y0] : rp(X,Y0) )
| ~ cc2(X) ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y0,Y1] :
( ( ( sk4(X) != sk5(X)
& rp(X,sk5(X))
& rp(X,sk4(X)) )
| ~ rp(X,Y0)
| cc2(X) )
& ( ( ( Y0 = Y1
| ~ rp(X,Y1)
| ~ rp(X,Y0) )
& rp(X,sk3(X)) )
| ~ cc2(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4,sk5])],[f11_nnf]) ).
cnf(c17,plain,
( rp(X0,sk3(X0))
| ~ cc2(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p62,plain,
( rp(sk8,sk3(sk8))
| cc1(sk8) ),
inference(resolution,[status(thm)],[p61,c17]) ).
fof(f10,axiom,
! [X] :
( cc1(X)
<=> ( ! [Y0,Y1] :
( ( rp(X,Y1)
& rp(X,Y0) )
=> Y0 = Y1 )
& ? [Y0] : rp(X,Y0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f10_nnf,plain,
! [X] :
( ( ? [Y0,Y1] :
( Y0 != Y1
& rp(X,Y1)
& rp(X,Y0) )
| ! [Y0] : ~ rp(X,Y0)
| cc1(X) )
& ( ( ! [Y0,Y1] :
( Y0 = Y1
| ~ rp(X,Y1)
| ~ rp(X,Y0) )
& ? [Y0] : rp(X,Y0) )
| ~ cc1(X) ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y0,Y1] :
( ( ( sk1(X) != sk2(X)
& rp(X,sk2(X))
& rp(X,sk1(X)) )
| ~ rp(X,Y0)
| cc1(X) )
& ( ( ( Y0 = Y1
| ~ rp(X,Y1)
| ~ rp(X,Y0) )
& rp(X,sk0(X)) )
| ~ cc1(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f10_nnf]) ).
cnf(c14,plain,
( rp(X0,sk1(X0))
| ~ rp(X0,X1)
| cc1(X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p64,plain,
( rp(sk8,sk1(sk8))
| cc1(sk8)
| cc1(sk8) ),
inference(resolution,[status(thm)],[p62,c14]) ).
cnf(p68,plain,
( rp(sk8,sk1(sk8))
| cc1(sk8) ),
inference(factoring,[status(thm)],[p64]) ).
cnf(c18,plain,
( X1 = X2
| ~ rp(X0,X2)
| ~ rp(X0,X1)
| ~ cc2(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p63,plain,
( X0 = X1
| ~ rp(sk8,X1)
| ~ rp(sk8,X0)
| cc1(sk8) ),
inference(resolution,[status(thm)],[p61,c18]) ).
cnf(p72,plain,
( sk1(sk8) = X0
| ~ rp(sk8,X0)
| cc1(sk8)
| cc1(sk8) ),
inference(resolution,[status(thm)],[p68,p63]) ).
cnf(p76,plain,
( sk1(sk8) = X0
| ~ rp(sk8,X0)
| cc1(sk8) ),
inference(factoring,[status(thm)],[p72]) ).
cnf(c15,plain,
( rp(X0,sk2(X0))
| ~ rp(X0,X1)
| cc1(X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p65,plain,
( rp(sk8,sk2(sk8))
| cc1(sk8)
| cc1(sk8) ),
inference(resolution,[status(thm)],[p62,c15]) ).
cnf(p69,plain,
( rp(sk8,sk2(sk8))
| cc1(sk8) ),
inference(factoring,[status(thm)],[p65]) ).
cnf(p81,plain,
( cc1(sk8)
| sk1(sk8) = sk2(sk8)
| cc1(sk8) ),
inference(resolution,[status(thm)],[p76,p69]) ).
cnf(p97,plain,
( sk1(sk8) = sk2(sk8)
| cc1(sk8) ),
inference(factoring,[status(thm)],[p81]) ).
cnf(c16,plain,
( sk1(X0) != sk2(X0)
| ~ rp(X0,X1)
| cc1(X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p66,plain,
( sk1(sk8) != sk2(sk8)
| cc1(sk8)
| cc1(sk8) ),
inference(resolution,[status(thm)],[p62,c16]) ).
cnf(p70,plain,
( sk1(sk8) != sk2(sk8)
| cc1(sk8) ),
inference(factoring,[status(thm)],[p66]) ).
cnf(p126,plain,
( cc1(sk8)
| cc1(sk8) ),
inference(resolution,[status(thm)],[p97,p70]) ).
cnf(p141,plain,
cc1(sk8),
inference(factoring,[status(thm)],[p126]) ).
cnf(c12,plain,
( rp(X0,sk0(X0))
| ~ cc1(X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p142,plain,
rp(sk8,sk0(sk8)),
inference(resolution,[status(thm)],[p141,c12]) ).
cnf(c19,plain,
( rp(X0,sk4(X0))
| ~ rp(X0,X1)
| cc2(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p144,plain,
( rp(sk8,sk4(sk8))
| cc2(sk8) ),
inference(resolution,[status(thm)],[p142,c19]) ).
cnf(c13,plain,
( X1 = X2
| ~ rp(X0,X2)
| ~ rp(X0,X1)
| ~ cc1(X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p143,plain,
( X0 = X1
| ~ rp(sk8,X1)
| ~ rp(sk8,X0) ),
inference(resolution,[status(thm)],[p141,c13]) ).
cnf(p148,plain,
( sk4(sk8) = X0
| ~ rp(sk8,X0)
| cc2(sk8) ),
inference(resolution,[status(thm)],[p144,p143]) ).
cnf(c20,plain,
( rp(X0,sk5(X0))
| ~ rp(X0,X1)
| cc2(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p145,plain,
( rp(sk8,sk5(sk8))
| cc2(sk8) ),
inference(resolution,[status(thm)],[p142,c20]) ).
cnf(p153,plain,
( cc2(sk8)
| sk4(sk8) = sk5(sk8)
| cc2(sk8) ),
inference(resolution,[status(thm)],[p148,p145]) ).
cnf(p176,plain,
( sk4(sk8) = sk5(sk8)
| cc2(sk8) ),
inference(factoring,[status(thm)],[p153]) ).
cnf(c21,plain,
( sk4(X0) != sk5(X0)
| ~ rp(X0,X1)
| cc2(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p146,plain,
( sk4(sk8) != sk5(sk8)
| cc2(sk8) ),
inference(resolution,[status(thm)],[p142,c21]) ).
cnf(p195,plain,
( cc2(sk8)
| cc2(sk8) ),
inference(resolution,[status(thm)],[p176,p146]) ).
cnf(p204,plain,
cc2(sk8),
inference(factoring,[status(thm)],[p195]) ).
cnf(c32,plain,
( ~ cc1(sk8)
| ~ cc2(sk8)
| ~ xsd_string(sk7)
| xsd_integer(sk7)
| cowlNothing(sk6)
| ~ cowlThing(sk6) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p41,plain,
( ~ cc1(sk8)
| ~ cc2(sk8)
| ~ xsd_string(sk7)
| xsd_integer(sk7)
| cowlNothing(sk6) ),
inference(resolution,[status(thm)],[c32,c8]) ).
cnf(p43,plain,
( xsd_integer(sk7)
| ~ cc1(sk8)
| ~ cc2(sk8)
| xsd_integer(sk7)
| cowlNothing(sk6) ),
inference(resolution,[status(thm)],[p41,c11]) ).
cnf(p45,plain,
( ~ cc1(sk8)
| ~ cc2(sk8)
| xsd_integer(sk7)
| cowlNothing(sk6) ),
inference(factoring,[status(thm)],[p43]) ).
cnf(p206,plain,
( ~ cc1(sk8)
| xsd_integer(sk7)
| cowlNothing(sk6) ),
inference(resolution,[status(thm)],[p204,p45]) ).
cnf(p209,plain,
( xsd_integer(sk7)
| cowlNothing(sk6) ),
inference(resolution,[status(thm)],[p206,p141]) ).
cnf(c28,plain,
( ~ cc1(sk8)
| ~ cc2(sk8)
| ~ xsd_integer(sk7)
| xsd_string(sk7)
| cowlNothing(sk6)
| ~ cowlThing(sk6) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p39,plain,
( ~ cc1(sk8)
| ~ cc2(sk8)
| ~ xsd_integer(sk7)
| xsd_string(sk7)
| cowlNothing(sk6) ),
inference(resolution,[status(thm)],[c28,c8]) ).
cnf(p211,plain,
( ~ cc1(sk8)
| ~ cc2(sk8)
| xsd_string(sk7)
| cowlNothing(sk6)
| cowlNothing(sk6) ),
inference(resolution,[status(thm)],[p209,p39]) ).
cnf(p212,plain,
( ~ cc1(sk8)
| ~ cc2(sk8)
| xsd_string(sk7)
| cowlNothing(sk6) ),
inference(factoring,[status(thm)],[p211]) ).
cnf(p213,plain,
( ~ cc1(sk8)
| xsd_string(sk7)
| cowlNothing(sk6) ),
inference(resolution,[status(thm)],[p212,p204]) ).
cnf(p214,plain,
( xsd_string(sk7)
| cowlNothing(sk6) ),
inference(resolution,[status(thm)],[p213,p141]) ).
cnf(p215,plain,
( ~ xsd_integer(sk7)
| cowlNothing(sk6) ),
inference(resolution,[status(thm)],[p214,c10]) ).
cnf(p216,plain,
( cowlNothing(sk6)
| cowlNothing(sk6) ),
inference(resolution,[status(thm)],[p215,p209]) ).
cnf(p217,plain,
cowlNothing(sk6),
inference(factoring,[status(thm)],[p216]) ).
cnf(p218,plain,
$false,
inference(resolution,[status(thm)],[p217,c9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS167+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n008.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 : Wed Sep 23 19:35:27 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.47/1.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.47/1.12 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------