%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KRS010-1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 01:52:54 PM UTC 2026
% Result : Unsatisfiable 2.81s 1.75s
% Output : Proof 2.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 99 ( 19 unt; 0 def)
% Number of atoms : 271 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 302 ( 130 ~; 172 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 71 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f30,axiom,
( ~ d(X2)
| ~ d(X3)
| ~ r(X1,X2)
| ~ r(X1,X3)
| equalish(X3,X2)
| f(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_31) ).
fof(f30_nnf,plain,
! [X1,X3,X2] :
( ~ d(X2)
| ~ d(X3)
| ~ r(X1,X2)
| ~ r(X1,X3)
| equalish(X3,X2)
| f(X1) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [X1,X3,X2] :
( ~ d(X2)
| ~ d(X3)
| ~ r(X1,X2)
| ~ r(X1,X3)
| equalish(X3,X2)
| f(X1) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
( ~ d(X2)
| ~ d(X1)
| ~ r(X0,X2)
| ~ r(X0,X1)
| equalish(X1,X2)
| f(X0) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(f23,axiom,
( ~ r3least(X1)
| r(X1,u2r3(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_24) ).
fof(f23_nnf,plain,
! [X1] :
( ~ r3least(X1)
| r(X1,u2r3(X1)) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [X1] :
( ~ r3least(X1)
| r(X1,u2r3(X1)) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( ~ r3least(X0)
| r(X0,u2r3(X0)) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(f6,axiom,
( ~ e(X1)
| r3least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
fof(f6_nnf,plain,
! [X1] :
( ~ e(X1)
| r3least(X1) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X1] :
( ~ e(X1)
| r3least(X1) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( ~ e(X0)
| r3least(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(f0,negated_conjecture,
e(exist),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
fof(f0_nnf,plain,
e(exist),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
e(exist),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(p31,plain,
r3least(exist),
inference(resolution,[status(thm)],[c6,c0]) ).
cnf(p51,plain,
r(exist,u2r3(exist)),
inference(resolution,[status(thm)],[c23,p31]) ).
cnf(p73,plain,
( ~ d(X0)
| ~ d(u2r3(exist))
| ~ r(exist,X0)
| equalish(u2r3(exist),X0)
| f(exist) ),
inference(resolution,[status(thm)],[c30,p51]) ).
cnf(f22,axiom,
( ~ r3least(X1)
| r(X1,u2r2(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_23) ).
fof(f22_nnf,plain,
! [X1] :
( ~ r3least(X1)
| r(X1,u2r2(X1)) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [X1] :
( ~ r3least(X1)
| r(X1,u2r2(X1)) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( ~ r3least(X0)
| r(X0,u2r2(X0)) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p44,plain,
r(exist,u2r2(exist)),
inference(resolution,[status(thm)],[c22,p31]) ).
cnf(p96,plain,
( ~ d(u2r2(exist))
| ~ d(u2r3(exist))
| equalish(u2r3(exist),u2r2(exist))
| f(exist) ),
inference(resolution,[status(thm)],[p73,p44]) ).
cnf(f7,axiom,
( ~ r(X1,X2)
| ~ e(X1)
| a(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
fof(f7_nnf,plain,
! [X2,X1] :
( ~ r(X1,X2)
| ~ e(X1)
| a(X2) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X2,X1] :
( ~ r(X1,X2)
| ~ e(X1)
| a(X2) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ r(X1,X0)
| ~ e(X1)
| a(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p39,plain,
( ~ r(exist,X0)
| a(X0) ),
inference(resolution,[status(thm)],[c7,c0]) ).
cnf(p54,plain,
a(u2r3(exist)),
inference(resolution,[status(thm)],[p51,p39]) ).
cnf(f2,axiom,
( ~ a(X1)
| d(X1)
| c(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
fof(f2_nnf,plain,
! [X1] :
( ~ a(X1)
| d(X1)
| c(X1) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X1] :
( ~ a(X1)
| d(X1)
| c(X1) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ a(X0)
| d(X0)
| c(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p57,plain,
( d(u2r3(exist))
| c(u2r3(exist)) ),
inference(resolution,[status(thm)],[p54,c2]) ).
cnf(p102,plain,
( c(u2r3(exist))
| ~ d(u2r2(exist))
| equalish(u2r3(exist),u2r2(exist))
| f(exist) ),
inference(resolution,[status(thm)],[p96,p57]) ).
cnf(p47,plain,
a(u2r2(exist)),
inference(resolution,[status(thm)],[p44,p39]) ).
cnf(p49,plain,
( d(u2r2(exist))
| c(u2r2(exist)) ),
inference(resolution,[status(thm)],[p47,c2]) ).
cnf(p111,plain,
( c(u2r2(exist))
| c(u2r3(exist))
| equalish(u2r3(exist),u2r2(exist))
| f(exist) ),
inference(resolution,[status(thm)],[p102,p49]) ).
cnf(f20,axiom,
( ~ equalish(u2r3(X1),u2r2(X1))
| ~ r3least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_21) ).
fof(f20_nnf,plain,
! [X1] :
( ~ equalish(u2r3(X1),u2r2(X1))
| ~ r3least(X1) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [X1] :
( ~ equalish(u2r3(X1),u2r2(X1))
| ~ r3least(X1) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( ~ equalish(u2r3(X0),u2r2(X0))
| ~ r3least(X0) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p62,plain,
~ equalish(u2r3(exist),u2r2(exist)),
inference(resolution,[status(thm)],[c20,p31]) ).
cnf(p115,plain,
( c(u2r2(exist))
| c(u2r3(exist))
| f(exist) ),
inference(resolution,[status(thm)],[p111,p62]) ).
cnf(f5,axiom,
( ~ c(X3)
| ~ c(X4)
| ~ r(X1,X3)
| ~ r(X1,X4)
| ~ e(X1)
| equalish(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
fof(f5_nnf,plain,
! [X4,X3,X1] :
( ~ c(X3)
| ~ c(X4)
| ~ r(X1,X3)
| ~ r(X1,X4)
| ~ e(X1)
| equalish(X4,X3) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X4,X3,X1] :
( ~ c(X3)
| ~ c(X4)
| ~ r(X1,X3)
| ~ r(X1,X4)
| ~ e(X1)
| equalish(X4,X3) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ c(X1)
| ~ c(X0)
| ~ r(X2,X1)
| ~ r(X2,X0)
| ~ e(X2)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p34,plain,
( ~ c(X1)
| ~ c(X0)
| ~ r(exist,X1)
| ~ r(exist,X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c5,c0]) ).
cnf(p52,plain,
( ~ c(X0)
| ~ c(u2r3(exist))
| ~ r(exist,X0)
| equalish(u2r3(exist),X0) ),
inference(resolution,[status(thm)],[p51,p34]) ).
cnf(f21,axiom,
( ~ r3least(X1)
| r(X1,u2r1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_22) ).
fof(f21_nnf,plain,
! [X1] :
( ~ r3least(X1)
| r(X1,u2r1(X1)) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [X1] :
( ~ r3least(X1)
| r(X1,u2r1(X1)) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( ~ r3least(X0)
| r(X0,u2r1(X0)) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p38,plain,
r(exist,u2r1(exist)),
inference(resolution,[status(thm)],[c21,p31]) ).
cnf(p58,plain,
( ~ c(u2r1(exist))
| ~ c(u2r3(exist))
| equalish(u2r3(exist),u2r1(exist)) ),
inference(resolution,[status(thm)],[p52,p38]) ).
cnf(p118,plain,
( ~ c(u2r1(exist))
| equalish(u2r3(exist),u2r1(exist))
| c(u2r2(exist))
| f(exist) ),
inference(resolution,[status(thm)],[p115,p58]) ).
cnf(p72,plain,
( ~ d(X0)
| ~ d(u2r2(exist))
| ~ r(exist,X0)
| equalish(u2r2(exist),X0)
| f(exist) ),
inference(resolution,[status(thm)],[c30,p44]) ).
cnf(p89,plain,
( ~ d(u2r1(exist))
| ~ d(u2r2(exist))
| equalish(u2r2(exist),u2r1(exist))
| f(exist) ),
inference(resolution,[status(thm)],[p72,p38]) ).
cnf(p92,plain,
( c(u2r2(exist))
| ~ d(u2r1(exist))
| equalish(u2r2(exist),u2r1(exist))
| f(exist) ),
inference(resolution,[status(thm)],[p89,p49]) ).
cnf(p42,plain,
a(u2r1(exist)),
inference(resolution,[status(thm)],[p39,p38]) ).
cnf(p43,plain,
( d(u2r1(exist))
| c(u2r1(exist)) ),
inference(resolution,[status(thm)],[p42,c2]) ).
cnf(p99,plain,
( c(u2r1(exist))
| c(u2r2(exist))
| equalish(u2r2(exist),u2r1(exist))
| f(exist) ),
inference(resolution,[status(thm)],[p92,p43]) ).
cnf(f18,axiom,
( ~ equalish(u2r2(X1),u2r1(X1))
| ~ r3least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_19) ).
fof(f18_nnf,plain,
! [X1] :
( ~ equalish(u2r2(X1),u2r1(X1))
| ~ r3least(X1) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X1] :
( ~ equalish(u2r2(X1),u2r1(X1))
| ~ r3least(X1) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( ~ equalish(u2r2(X0),u2r1(X0))
| ~ r3least(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p60,plain,
~ equalish(u2r2(exist),u2r1(exist)),
inference(resolution,[status(thm)],[c18,p31]) ).
cnf(p107,plain,
( c(u2r1(exist))
| c(u2r2(exist))
| f(exist) ),
inference(resolution,[status(thm)],[p99,p60]) ).
cnf(p120,plain,
( c(u2r2(exist))
| f(exist)
| equalish(u2r3(exist),u2r1(exist))
| c(u2r2(exist))
| f(exist) ),
inference(resolution,[status(thm)],[p118,p107]) ).
cnf(p124,plain,
( c(u2r2(exist))
| equalish(u2r3(exist),u2r1(exist))
| c(u2r2(exist))
| f(exist) ),
inference(factoring,[status(thm)],[p120]) ).
cnf(p126,plain,
( equalish(u2r3(exist),u2r1(exist))
| c(u2r2(exist))
| f(exist) ),
inference(factoring,[status(thm)],[p124]) ).
cnf(f19,axiom,
( ~ equalish(u2r3(X1),u2r1(X1))
| ~ r3least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_20) ).
fof(f19_nnf,plain,
! [X1] :
( ~ equalish(u2r3(X1),u2r1(X1))
| ~ r3least(X1) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X1] :
( ~ equalish(u2r3(X1),u2r1(X1))
| ~ r3least(X1) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( ~ equalish(u2r3(X0),u2r1(X0))
| ~ r3least(X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p61,plain,
~ equalish(u2r3(exist),u2r1(exist)),
inference(resolution,[status(thm)],[c19,p31]) ).
cnf(p127,plain,
( c(u2r2(exist))
| f(exist) ),
inference(resolution,[status(thm)],[p126,p61]) ).
cnf(p95,plain,
( ~ d(u2r1(exist))
| ~ d(u2r3(exist))
| equalish(u2r3(exist),u2r1(exist))
| f(exist) ),
inference(resolution,[status(thm)],[p73,p38]) ).
cnf(p100,plain,
( c(u2r3(exist))
| ~ d(u2r1(exist))
| equalish(u2r3(exist),u2r1(exist))
| f(exist) ),
inference(resolution,[status(thm)],[p95,p57]) ).
cnf(p110,plain,
( c(u2r1(exist))
| c(u2r3(exist))
| equalish(u2r3(exist),u2r1(exist))
| f(exist) ),
inference(resolution,[status(thm)],[p100,p43]) ).
cnf(p112,plain,
( c(u2r1(exist))
| c(u2r3(exist))
| f(exist) ),
inference(resolution,[status(thm)],[p110,p61]) ).
cnf(p59,plain,
( ~ c(u2r2(exist))
| ~ c(u2r3(exist))
| equalish(u2r3(exist),u2r2(exist)) ),
inference(resolution,[status(thm)],[p52,p44]) ).
cnf(p114,plain,
( ~ c(u2r2(exist))
| equalish(u2r3(exist),u2r2(exist))
| c(u2r1(exist))
| f(exist) ),
inference(resolution,[status(thm)],[p112,p59]) ).
cnf(p131,plain,
( equalish(u2r3(exist),u2r2(exist))
| c(u2r1(exist))
| f(exist)
| f(exist) ),
inference(resolution,[status(thm)],[p127,p114]) ).
cnf(p133,plain,
( equalish(u2r3(exist),u2r2(exist))
| c(u2r1(exist))
| f(exist) ),
inference(factoring,[status(thm)],[p131]) ).
cnf(p134,plain,
( c(u2r1(exist))
| f(exist) ),
inference(resolution,[status(thm)],[p133,p62]) ).
cnf(p45,plain,
( ~ c(X0)
| ~ c(u2r2(exist))
| ~ r(exist,X0)
| equalish(u2r2(exist),X0) ),
inference(resolution,[status(thm)],[p44,p34]) ).
cnf(p50,plain,
( ~ c(u2r1(exist))
| ~ c(u2r2(exist))
| equalish(u2r2(exist),u2r1(exist)) ),
inference(resolution,[status(thm)],[p45,p38]) ).
cnf(p129,plain,
( ~ c(u2r1(exist))
| equalish(u2r2(exist),u2r1(exist))
| f(exist) ),
inference(resolution,[status(thm)],[p127,p50]) ).
cnf(p138,plain,
( equalish(u2r2(exist),u2r1(exist))
| f(exist)
| f(exist) ),
inference(resolution,[status(thm)],[p134,p129]) ).
cnf(p140,plain,
( equalish(u2r2(exist),u2r1(exist))
| f(exist) ),
inference(factoring,[status(thm)],[p138]) ).
cnf(p141,plain,
f(exist),
inference(resolution,[status(thm)],[p140,p60]) ).
cnf(f1,negated_conjecture,
~ f(exist),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
fof(f1_nnf,plain,
~ f(exist),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
~ f(exist),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ f(exist),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p142,plain,
$false,
inference(resolution,[status(thm)],[p141,c1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS010-1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.98 % Computer : n006.cluster.edu
% 0.11/0.98 % Model : x86_64 x86_64
% 0.11/0.98 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.98 % Memory : 8046.5625MB
% 0.11/0.98 % OS : Linux 6.8.0-71-generic
% 0.11/0.98 % CPULimit : 300
% 0.11/0.98 % WCLimit : 300
% 0.11/0.98 % DateTime : Wed Sep 23 19:14:23 UTC 2026
% 0.11/0.99 % CPUTime :
% 0.11/0.99 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.81/1.75 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.81/1.75 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------