%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KRS013-1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 4.83s 1.09s
% Output : Proof 4.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of formulae : 88 ( 9 unt; 0 def)
% Number of atoms : 210 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 208 ( 86 ~; 122 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 93 ( 0 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f25,axiom,
( ~ s(X1,X2)
| ~ s(X1,X3)
| equalish(X3,X2)
| s2least(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_26) ).
fof(f25_nnf,plain,
! [X1,X3,X2] :
( ~ s(X1,X2)
| ~ s(X1,X3)
| equalish(X3,X2)
| s2least(X1) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [X1,X3,X2] :
( ~ s(X1,X2)
| ~ s(X1,X3)
| equalish(X3,X2)
| s2least(X1) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
( ~ s(X0,X2)
| ~ s(X0,X1)
| equalish(X1,X2)
| s2least(X0) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(f32,axiom,
( s(X1,u7r2(X1))
| s1most(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_33) ).
fof(f32_nnf,plain,
! [X1] :
( s(X1,u7r2(X1))
| s1most(X1) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [X1] :
( s(X1,u7r2(X1))
| s1most(X1) ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c32,plain,
( s(X0,u7r2(X0))
| s1most(X0) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p48,plain,
( s1most(X0)
| ~ s(X0,X1)
| equalish(u7r2(X0),X1)
| s2least(X0) ),
inference(resolution,[status(thm)],[c25,c32]) ).
cnf(f31,axiom,
( s(X1,u7r1(X1))
| s1most(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_32) ).
fof(f31_nnf,plain,
! [X1] :
( s(X1,u7r1(X1))
| s1most(X1) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [X1] :
( s(X1,u7r1(X1))
| s1most(X1) ),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c31,plain,
( s(X0,u7r1(X0))
| s1most(X0) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p55,plain,
( s1most(X0)
| s1most(X0)
| equalish(u7r2(X0),u7r1(X0))
| s2least(X0) ),
inference(resolution,[status(thm)],[p48,c31]) ).
cnf(p67,plain,
( s1most(X0)
| equalish(u7r2(X0),u7r1(X0))
| s2least(X0) ),
inference(factoring,[status(thm)],[p55]) ).
cnf(f30,axiom,
( ~ equalish(u7r2(X1),u7r1(X1))
| s1most(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_31) ).
fof(f30_nnf,plain,
! [X1] :
( ~ equalish(u7r2(X1),u7r1(X1))
| s1most(X1) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [X1] :
( ~ equalish(u7r2(X1),u7r1(X1))
| s1most(X1) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
( ~ equalish(u7r2(X0),u7r1(X0))
| s1most(X0) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(p68,plain,
( s1most(X0)
| s1most(X0)
| s2least(X0) ),
inference(resolution,[status(thm)],[p67,c30]) ).
cnf(p69,plain,
( s1most(X0)
| s2least(X0) ),
inference(factoring,[status(thm)],[p68]) ).
cnf(f27,axiom,
( ~ s1most(u6r1(X1))
| f(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_28) ).
fof(f27_nnf,plain,
! [X1] :
( ~ s1most(u6r1(X1))
| f(X1) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [X1] :
( ~ s1most(u6r1(X1))
| f(X1) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
( ~ s1most(u6r1(X0))
| f(X0) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p70,plain,
( f(X0)
| s2least(u6r1(X0)) ),
inference(resolution,[status(thm)],[p69,c27]) ).
cnf(f15,axiom,
( ~ s2least(X2)
| ~ r(X1,X2)
| ~ e(X1)
| c(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_16) ).
fof(f15_nnf,plain,
! [X2,X1] :
( ~ s2least(X2)
| ~ r(X1,X2)
| ~ e(X1)
| c(X2) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X2,X1] :
( ~ s2least(X2)
| ~ r(X1,X2)
| ~ e(X1)
| c(X2) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( ~ s2least(X0)
| ~ r(X1,X0)
| ~ e(X1)
| c(X0) ),
inference(cnf_transformation,[status(esa)],[f15_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(p39,plain,
( ~ s2least(X0)
| ~ r(exist,X0)
| c(X0) ),
inference(resolution,[status(thm)],[c15,c0]) ).
cnf(f28,axiom,
( r(X1,u6r1(X1))
| f(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_29) ).
fof(f28_nnf,plain,
! [X1] :
( r(X1,u6r1(X1))
| f(X1) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [X1] :
( r(X1,u6r1(X1))
| f(X1) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
( r(X0,u6r1(X0))
| f(X0) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p42,plain,
( f(exist)
| ~ s2least(u6r1(exist))
| c(u6r1(exist)) ),
inference(resolution,[status(thm)],[p39,c28]) ).
cnf(p74,plain,
( f(exist)
| c(u6r1(exist))
| f(exist) ),
inference(resolution,[status(thm)],[p70,p42]) ).
cnf(p75,plain,
( c(u6r1(exist))
| f(exist) ),
inference(factoring,[status(thm)],[p74]) ).
cnf(f2,axiom,
( ~ c(X1)
| t2least(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
fof(f2_nnf,plain,
! [X1] :
( ~ c(X1)
| t2least(X1) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X1] :
( ~ c(X1)
| t2least(X1) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ c(X0)
| t2least(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p76,plain,
( t2least(u6r1(exist))
| f(exist) ),
inference(resolution,[status(thm)],[p75,c2]) ).
cnf(f6,axiom,
( ~ t2least(X1)
| t(X1,u1r2(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7) ).
fof(f6_nnf,plain,
! [X1] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X1] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( ~ t2least(X0)
| t(X0,u1r2(X0)) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p79,plain,
( t(u6r1(exist),u1r2(u6r1(exist)))
| f(exist) ),
inference(resolution,[status(thm)],[p76,c6]) ).
cnf(f14,axiom,
( ~ r(X1,X3)
| ~ e(X1)
| d(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_15) ).
fof(f14_nnf,plain,
! [X3,X1] :
( ~ r(X1,X3)
| ~ e(X1)
| d(X3) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X3,X1] :
( ~ r(X1,X3)
| ~ e(X1)
| d(X3) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( ~ r(X1,X0)
| ~ e(X1)
| d(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p37,plain,
( ~ r(exist,X0)
| d(X0) ),
inference(resolution,[status(thm)],[c14,c0]) ).
cnf(p38,plain,
( f(exist)
| d(u6r1(exist)) ),
inference(resolution,[status(thm)],[p37,c28]) ).
cnf(f8,axiom,
( ~ d(X1)
| t1most(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9) ).
fof(f8_nnf,plain,
! [X1] :
( ~ d(X1)
| t1most(X1) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X1] :
( ~ d(X1)
| t1most(X1) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( ~ d(X0)
| t1most(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p40,plain,
( t1most(u6r1(exist))
| f(exist) ),
inference(resolution,[status(thm)],[p38,c8]) ).
cnf(f10,axiom,
( ~ t(X1,X2)
| ~ t(X1,X3)
| ~ t1most(X1)
| equalish(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_11) ).
fof(f10_nnf,plain,
! [X3,X2,X1] :
( ~ t(X1,X2)
| ~ t(X1,X3)
| ~ t1most(X1)
| equalish(X3,X2) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X3,X2,X1] :
( ~ t(X1,X2)
| ~ t(X1,X3)
| ~ t1most(X1)
| equalish(X3,X2) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( ~ t(X2,X1)
| ~ t(X2,X0)
| ~ t1most(X2)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p41,plain,
( ~ t(u6r1(exist),X1)
| ~ t(u6r1(exist),X0)
| equalish(X0,X1)
| f(exist) ),
inference(resolution,[status(thm)],[p40,c10]) ).
cnf(p82,plain,
( ~ t(u6r1(exist),X0)
| equalish(u1r2(u6r1(exist)),X0)
| f(exist)
| f(exist) ),
inference(resolution,[status(thm)],[p79,p41]) ).
cnf(p89,plain,
( ~ t(u6r1(exist),X0)
| equalish(u1r2(u6r1(exist)),X0)
| f(exist) ),
inference(factoring,[status(thm)],[p82]) ).
cnf(f5,axiom,
( ~ t2least(X1)
| t(X1,u1r1(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
fof(f5_nnf,plain,
! [X1] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X1] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ t2least(X0)
| t(X0,u1r1(X0)) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p78,plain,
( t(u6r1(exist),u1r1(u6r1(exist)))
| f(exist) ),
inference(resolution,[status(thm)],[p76,c5]) ).
cnf(p90,plain,
( f(exist)
| equalish(u1r2(u6r1(exist)),u1r1(u6r1(exist)))
| f(exist) ),
inference(resolution,[status(thm)],[p89,p78]) ).
cnf(p91,plain,
( equalish(u1r2(u6r1(exist)),u1r1(u6r1(exist)))
| f(exist) ),
inference(factoring,[status(thm)],[p90]) ).
cnf(f4,axiom,
( ~ equalish(u1r2(X1),u1r1(X1))
| ~ t2least(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
fof(f4_nnf,plain,
! [X1] :
( ~ equalish(u1r2(X1),u1r1(X1))
| ~ t2least(X1) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X1] :
( ~ equalish(u1r2(X1),u1r1(X1))
| ~ t2least(X1) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( ~ equalish(u1r2(X0),u1r1(X0))
| ~ t2least(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p77,plain,
( ~ equalish(u1r2(u6r1(exist)),u1r1(u6r1(exist)))
| f(exist) ),
inference(resolution,[status(thm)],[p76,c4]) ).
cnf(p92,plain,
( f(exist)
| f(exist) ),
inference(resolution,[status(thm)],[p91,p77]) ).
cnf(p93,plain,
f(exist),
inference(factoring,[status(thm)],[p92]) ).
cnf(f1,negated_conjecture,
~ f(exist),
file('/export/starexec/sandbox/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(p94,plain,
$false,
inference(resolution,[status(thm)],[p93,c1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS013-1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.34 % Computer : n014.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Wed Sep 23 19:14:50 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.83/1.09 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.83/1.09 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------