%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KRS002-1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 01:52:53 PM UTC 2026
% Result : Unsatisfiable 4.01s 1.09s
% Output : Proof 4.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 53 ( 13 unt; 0 def)
% Number of atoms : 110 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 119 ( 62 ~; 57 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 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 : 57 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f14,axiom,
( ~ r(X1,X2)
| ~ e(X1)
| d(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_15) ).
fof(f14_nnf,plain,
! [X2,X1] :
( ~ r(X1,X2)
| ~ e(X1)
| d(X2) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X2,X1] :
( ~ r(X1,X2)
| ~ e(X1)
| d(X2) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( ~ r(X1,X0)
| ~ e(X1)
| d(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(f0,negated_conjecture,
e(exist),
file('/export/starexec/sandbox/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(p23,plain,
( ~ r(exist,X0)
| d(X0) ),
inference(resolution,[status(thm)],[c14,c0]) ).
cnf(f13,axiom,
( ~ e(X1)
| r(X1,u4r2(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_14) ).
fof(f13_nnf,plain,
! [X1] :
( ~ e(X1)
| r(X1,u4r2(X1)) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X1] :
( ~ e(X1)
| r(X1,u4r2(X1)) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( ~ e(X0)
| r(X0,u4r2(X0)) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p21,plain,
r(exist,u4r2(exist)),
inference(resolution,[status(thm)],[c13,c0]) ).
cnf(p24,plain,
d(u4r2(exist)),
inference(resolution,[status(thm)],[p23,p21]) ).
cnf(f7,axiom,
( ~ d(X1)
| s1most(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8) ).
fof(f7_nnf,plain,
! [X1] :
( ~ d(X1)
| s1most(X1) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X1] :
( ~ d(X1)
| s1most(X1) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ d(X0)
| s1most(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p25,plain,
s1most(u4r2(exist)),
inference(resolution,[status(thm)],[p24,c7]) ).
cnf(f9,axiom,
( ~ s(X1,X2)
| ~ s(X1,X3)
| ~ s1most(X1)
| equalish(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_10) ).
fof(f9_nnf,plain,
! [X3,X2,X1] :
( ~ s(X1,X2)
| ~ s(X1,X3)
| ~ s1most(X1)
| equalish(X3,X2) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X3,X2,X1] :
( ~ s(X1,X2)
| ~ s(X1,X3)
| ~ s1most(X1)
| equalish(X3,X2) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( ~ s(X2,X1)
| ~ s(X2,X0)
| ~ s1most(X2)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p26,plain,
( ~ s(u4r2(exist),X1)
| ~ s(u4r2(exist),X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[p25,c9]) ).
cnf(f15,axiom,
( ~ r(X1,X2)
| ~ e(X1)
| c(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_16) ).
fof(f15_nnf,plain,
! [X2,X1] :
( ~ r(X1,X2)
| ~ e(X1)
| c(X2) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X2,X1] :
( ~ r(X1,X2)
| ~ e(X1)
| c(X2) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( ~ r(X1,X0)
| ~ e(X1)
| c(X0) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p27,plain,
( ~ r(exist,X0)
| c(X0) ),
inference(resolution,[status(thm)],[c15,c0]) ).
cnf(p28,plain,
c(u4r2(exist)),
inference(resolution,[status(thm)],[p27,p21]) ).
cnf(f1,axiom,
( ~ c(X1)
| s2least(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
fof(f1_nnf,plain,
! [X1] :
( ~ c(X1)
| s2least(X1) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X1] :
( ~ c(X1)
| s2least(X1) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ~ c(X0)
| s2least(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p29,plain,
s2least(u4r2(exist)),
inference(resolution,[status(thm)],[p28,c1]) ).
cnf(f5,axiom,
( ~ s2least(X1)
| s(X1,u1r2(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
fof(f5_nnf,plain,
! [X1] :
( ~ s2least(X1)
| s(X1,u1r2(X1)) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X1] :
( ~ s2least(X1)
| s(X1,u1r2(X1)) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ s2least(X0)
| s(X0,u1r2(X0)) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p32,plain,
s(u4r2(exist),u1r2(u4r2(exist))),
inference(resolution,[status(thm)],[p29,c5]) ).
cnf(p35,plain,
( ~ s(u4r2(exist),X0)
| equalish(u1r2(u4r2(exist)),X0) ),
inference(resolution,[status(thm)],[p26,p32]) ).
cnf(f4,axiom,
( ~ s2least(X1)
| s(X1,u1r1(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
fof(f4_nnf,plain,
! [X1] :
( ~ s2least(X1)
| s(X1,u1r1(X1)) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X1] :
( ~ s2least(X1)
| s(X1,u1r1(X1)) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( ~ s2least(X0)
| s(X0,u1r1(X0)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p31,plain,
s(u4r2(exist),u1r1(u4r2(exist))),
inference(resolution,[status(thm)],[p29,c4]) ).
cnf(p41,plain,
equalish(u1r2(u4r2(exist)),u1r1(u4r2(exist))),
inference(resolution,[status(thm)],[p35,p31]) ).
cnf(f3,axiom,
( ~ equalish(u1r2(X1),u1r1(X1))
| ~ s2least(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
fof(f3_nnf,plain,
! [X1] :
( ~ equalish(u1r2(X1),u1r1(X1))
| ~ s2least(X1) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X1] :
( ~ equalish(u1r2(X1),u1r1(X1))
| ~ s2least(X1) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( ~ equalish(u1r2(X0),u1r1(X0))
| ~ s2least(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p30,plain,
~ equalish(u1r2(u4r2(exist)),u1r1(u4r2(exist))),
inference(resolution,[status(thm)],[p29,c3]) ).
cnf(p42,plain,
$false,
inference(resolution,[status(thm)],[p41,p30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS002-1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.35 % Computer : n008.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Wed Sep 23 19:14:39 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.01/1.09 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.01/1.09 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------