%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KRS012-1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 4.57s 1.11s
% Output : Proof 4.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 9 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 70 ( 32 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 26 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f3,axiom,
( ~ r(X1,X2)
| ~ c(X1)
| d(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
fof(f3_nnf,plain,
! [X2,X1] :
( ~ r(X1,X2)
| ~ c(X1)
| d(X2) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X2,X1] :
( ~ r(X1,X2)
| ~ c(X1)
| d(X2) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( ~ r(X1,X0)
| ~ c(X1)
| d(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(f0,negated_conjecture,
c(exists),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
fof(f0_nnf,plain,
c(exists),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
c(exists),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(p15,plain,
( ~ r(exists,X0)
| d(X0) ),
inference(resolution,[status(thm)],[c3,c0]) ).
cnf(f12,axiom,
( r(X1,u1r1(X1))
| f(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_13) ).
fof(f12_nnf,plain,
! [X1] :
( r(X1,u1r1(X1))
| f(X1) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X1] :
( r(X1,u1r1(X1))
| f(X1) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( r(X0,u1r1(X0))
| f(X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p16,plain,
( f(exists)
| d(u1r1(exists)) ),
inference(resolution,[status(thm)],[p15,c12]) ).
cnf(f2,axiom,
( ~ d(X3)
| ~ r(X1,X3)
| ~ c(X1)
| e(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
fof(f2_nnf,plain,
! [X3,X1] :
( ~ d(X3)
| ~ r(X1,X3)
| ~ c(X1)
| e(X3) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X3,X1] :
( ~ d(X3)
| ~ r(X1,X3)
| ~ c(X1)
| e(X3) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ d(X0)
| ~ r(X1,X0)
| ~ c(X1)
| e(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p13,plain,
( ~ d(X0)
| ~ r(exists,X0)
| e(X0) ),
inference(resolution,[status(thm)],[c2,c0]) ).
cnf(p14,plain,
( f(exists)
| ~ d(u1r1(exists))
| e(u1r1(exists)) ),
inference(resolution,[status(thm)],[p13,c12]) ).
cnf(p17,plain,
( f(exists)
| e(u1r1(exists))
| f(exists) ),
inference(resolution,[status(thm)],[p16,p14]) ).
cnf(p18,plain,
( e(u1r1(exists))
| f(exists) ),
inference(factoring,[status(thm)],[p17]) ).
cnf(f11,axiom,
( ~ e(u1r1(X1))
| f(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_12) ).
fof(f11_nnf,plain,
! [X1] :
( ~ e(u1r1(X1))
| f(X1) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X1] :
( ~ e(u1r1(X1))
| f(X1) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( ~ e(u1r1(X0))
| f(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p19,plain,
( f(exists)
| f(exists) ),
inference(resolution,[status(thm)],[p18,c11]) ).
cnf(p20,plain,
f(exists),
inference(factoring,[status(thm)],[p19]) ).
cnf(f1,negated_conjecture,
~ f(exists),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
fof(f1_nnf,plain,
~ f(exists),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
~ f(exists),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ f(exists),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p21,plain,
$false,
inference(resolution,[status(thm)],[p20,c1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS012-1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.36 % Computer : n026.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.04/0.36 % CPULimit : 300
% 0.04/0.36 % WCLimit : 300
% 0.04/0.36 % DateTime : Wed Sep 23 19:17:39 UTC 2026
% 0.04/0.36 % CPUTime :
% 0.04/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.57/1.11 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.57/1.11 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------