%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL668+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 02:02:33 PM UTC 2026
% Result : Theorem 5.83s 1.32s
% Output : Proof 5.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 2
% Syntax : Number of formulae : 109 ( 11 unt; 0 def)
% Number of atoms : 895 ( 0 equ)
% Maximal formula atoms : 84 ( 8 avg)
% Number of connectives : 1514 ( 728 ~; 680 |; 106 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 47 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 14 con; 0-4 aty)
% Number of variables : 280 ( 0 sgn 129 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
~ ? [X] :
~ ( ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ( p1(X)
& p2(X)
& p3(X)
& p4(X)
& p5(X)
& p6(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( ~ ! [X] :
( ~ ( ~ ! [Y] :
( ~ ( ~ ! [X] :
( ~ ( ~ ! [Y] :
( ~ ~ ! [X] :
( ! [Y] :
( ! [X] :
( ~ ( ( p1(X)
& p2(X) )
| ( ~ p2(X)
& ~ p1(X) ) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ~ ( ( p2(X)
& p3(X) )
| ( ~ p3(X)
& ~ p2(X) ) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ~ r1(Y,X) )
| ! [X] :
( p4(X)
| ~ r1(Y,X) )
| ~ ! [X] :
( ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ~ ( ( p3(X)
& p4(X) )
| ( ~ p4(X)
& ~ p3(X) ) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) ) )
| ~ r1(X,Y) )
| ! [Y] :
( p5(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ~ ( ( p4(X)
& p5(X) )
| ( ~ p5(X)
& ~ p4(X) ) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ~ r1(Y,X) )
| ! [X] :
( p6(X)
| ~ r1(Y,X) )
| ~ ! [X] :
( ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ~ ( ( p5(X)
& p1(X) )
| ( ~ p1(X)
& ~ p5(X) ) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) ) )
| ~ r1(X,Y) )
| ! [Y] :
( p7(Y)
| ~ r1(X,Y) )
| ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ( ~ p2(X)
& ~ p4(X)
& ~ p6(X)
& ~ p8(X)
& ~ p10(X)
& ~ p12(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).
fof(f1_neg,negated_conjecture,
~ ~ ? [X] :
~ ( ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ( p1(X)
& p2(X)
& p3(X)
& p4(X)
& p5(X)
& p6(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( ~ ! [X] :
( ~ ( ~ ! [Y] :
( ~ ( ~ ! [X] :
( ~ ( ~ ! [Y] :
( ~ ~ ! [X] :
( ! [Y] :
( ! [X] :
( ~ ( ( p1(X)
& p2(X) )
| ( ~ p2(X)
& ~ p1(X) ) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ~ ( ( p2(X)
& p3(X) )
| ( ~ p3(X)
& ~ p2(X) ) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ~ r1(Y,X) )
| ! [X] :
( p4(X)
| ~ r1(Y,X) )
| ~ ! [X] :
( ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ~ ( ( p3(X)
& p4(X) )
| ( ~ p4(X)
& ~ p3(X) ) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) ) )
| ~ r1(X,Y) )
| ! [Y] :
( p5(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ~ ( ( p4(X)
& p5(X) )
| ( ~ p5(X)
& ~ p4(X) ) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ~ r1(Y,X) )
| ! [X] :
( p6(X)
| ~ r1(Y,X) )
| ~ ! [X] :
( ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ~ ( ( p5(X)
& p1(X) )
| ( ~ p1(X)
& ~ p5(X) ) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) ) )
| ~ r1(X,Y) )
| ! [Y] :
( p7(Y)
| ~ r1(X,Y) )
| ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ( ~ p2(X)
& ~ p4(X)
& ~ p6(X)
& ~ p8(X)
& ~ p10(X)
& ~ p12(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f1_nnf,plain,
? [X] :
( ? [Y] :
( ? [X] :
( ? [Y] :
( ? [X] :
( ? [Y] :
( ? [X] :
( ( ~ p1(X)
| ~ p2(X)
| ~ p3(X)
| ~ p4(X)
| ~ p5(X)
| ~ p6(X) )
& r1(Y,X) )
& r1(X,Y) )
& r1(Y,X) )
& r1(X,Y) )
& r1(Y,X) )
& r1(X,Y) )
& ! [Y] :
( ( ! [X] :
( ( ! [Y] :
( ( ! [X] :
( ( ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ( ( ~ p1(X)
| ~ p2(X) )
& ( p2(X)
| p1(X) ) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
& ? [Y] :
( ~ p3(Y)
& r1(X,Y) )
& ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ( ( ~ p2(X)
| ~ p3(X) )
& ( p3(X)
| p2(X) ) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ~ r1(Y,X) )
& ? [X] :
( ~ p4(X)
& r1(Y,X) )
& ! [X] :
( ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ( ( ~ p3(X)
| ~ p4(X) )
& ( p4(X)
| p3(X) ) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) ) )
| ~ r1(X,Y) )
& ? [Y] :
( ~ p5(Y)
& r1(X,Y) )
& ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ( ( ~ p4(X)
| ~ p5(X) )
& ( p5(X)
| p4(X) ) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ~ r1(Y,X) )
& ? [X] :
( ~ p6(X)
& r1(Y,X) )
& ! [X] :
( ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ( ( ~ p5(X)
| ~ p1(X) )
& ( p1(X)
| p5(X) ) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) ) )
| ~ r1(X,Y) )
& ? [Y] :
( ~ p7(Y)
& r1(X,Y) )
& ? [Y] :
( ? [X] :
( ? [Y] :
( ? [X] :
( ? [Y] :
( ? [X] :
( ( p2(X)
| p4(X)
| p6(X)
| p8(X)
| p10(X)
| p12(X) )
& r1(Y,X) )
& r1(X,Y) )
& r1(Y,X) )
& r1(X,Y) )
& r1(Y,X) )
& r1(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f1_neg]) ).
fof(f1_sk,plain,
! [Y,X] :
( ( ~ p1(sk17)
| ~ p2(sk17)
| ~ p3(sk17)
| ~ p4(sk17)
| ~ p5(sk17)
| ~ p6(sk17) )
& r1(sk16,sk17)
& r1(sk15,sk16)
& r1(sk14,sk15)
& r1(sk13,sk14)
& r1(sk12,sk13)
& r1(sk0,sk12)
& ( ( ( ( ( ( ( ( ( ( ( ~ p1(X)
| ~ p2(X) )
& ( p2(X)
| p1(X) ) )
| ~ r1(Y,X)
| ~ r1(X,Y)
| ~ r1(Y,X)
| ~ r1(X,Y) )
& ~ p3(sk11(Y,X,Y,X))
& r1(X,sk11(Y,X,Y,X))
& ( ( ( ~ p2(X)
| ~ p3(X) )
& ( p3(X)
| p2(X) ) )
| ~ r1(Y,X)
| ~ r1(X,Y)
| ~ r1(Y,X)
| ~ r1(X,Y) ) )
| ~ r1(Y,X) )
& ~ p4(sk10(Y,X,Y))
& r1(Y,sk10(Y,X,Y))
& ( ( ( ~ p3(X)
| ~ p4(X) )
& ( p4(X)
| p3(X) ) )
| ~ r1(Y,X)
| ~ r1(X,Y)
| ~ r1(Y,X)
| ~ r1(X,Y)
| ~ r1(Y,X) ) )
| ~ r1(X,Y) )
& ~ p5(sk9(Y,X))
& r1(X,sk9(Y,X))
& ( ( ( ~ p4(X)
| ~ p5(X) )
& ( p5(X)
| p4(X) ) )
| ~ r1(Y,X)
| ~ r1(X,Y)
| ~ r1(Y,X)
| ~ r1(X,Y)
| ~ r1(Y,X)
| ~ r1(X,Y) ) )
| ~ r1(Y,X) )
& ~ p6(sk8(Y))
& r1(Y,sk8(Y))
& ( ( ( ~ p5(X)
| ~ p1(X) )
& ( p1(X)
| p5(X) ) )
| ~ r1(Y,X)
| ~ r1(X,Y)
| ~ r1(Y,X)
| ~ r1(X,Y)
| ~ r1(Y,X)
| ~ r1(X,Y)
| ~ r1(Y,X) ) )
| ~ r1(sk0,Y) )
& ~ p7(sk7)
& r1(sk0,sk7)
& ( p2(sk6)
| p4(sk6)
| p6(sk6)
| p8(sk6)
| p10(sk6)
| p12(sk6) )
& r1(sk5,sk6)
& r1(sk4,sk5)
& r1(sk3,sk4)
& r1(sk2,sk3)
& r1(sk1,sk2)
& r1(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3,sk4,sk5,sk6,sk7,sk8,sk9,sk10,sk11,sk12,sk13,sk14,sk15,sk16,sk17])],[f1_nnf]) ).
cnf(c27,plain,
( ~ p1(X0)
| ~ p2(X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(sk0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p175,plain,
( ~ p1(X1)
| ~ p2(X1)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[c27]) ).
cnf(p386,plain,
( ~ p1(X1)
| ~ p2(X1)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p175]) ).
cnf(p635,plain,
( ~ p1(X1)
| ~ p2(X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p386]) ).
cnf(p1052,plain,
( ~ p1(X1)
| ~ p2(X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p635]) ).
cnf(p1330,plain,
( ~ p1(X1)
| ~ p2(X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p1052]) ).
cnf(p1332,plain,
( ~ p1(sk0)
| ~ p2(sk0)
| ~ r1(X0,sk0)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p1330]) ).
cnf(p1342,plain,
( ~ p1(sk0)
| ~ p2(sk0)
| ~ r1(sk0,sk0) ),
inference(factoring,[status(thm)],[p1332]) ).
fof(f0,axiom,
! [X] : r1(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
fof(f0_nnf,plain,
! [X] : r1(X,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : r1(X,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
r1(X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p1350,plain,
( ~ p1(sk0)
| ~ p2(sk0) ),
inference(resolution,[status(thm)],[p1342,c0]) ).
cnf(c26,plain,
( p2(X0)
| p1(X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(sk0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p164,plain,
( p2(X1)
| p1(X1)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[c26]) ).
cnf(p379,plain,
( p2(X1)
| p1(X1)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p164]) ).
cnf(p621,plain,
( p2(X1)
| p1(X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p379]) ).
cnf(p1043,plain,
( p2(X1)
| p1(X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p621]) ).
cnf(p1207,plain,
( p2(X1)
| p1(X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p1043]) ).
cnf(p1209,plain,
( p2(sk0)
| p1(sk0)
| ~ r1(X0,sk0)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p1207]) ).
cnf(p1219,plain,
( p2(sk0)
| p1(sk0)
| ~ r1(sk0,sk0) ),
inference(factoring,[status(thm)],[p1209]) ).
cnf(p1227,plain,
( p2(sk0)
| p1(sk0) ),
inference(resolution,[status(thm)],[p1219,c0]) ).
cnf(c11,plain,
( ~ p5(X0)
| ~ p1(X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(sk0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p47,plain,
( ~ p5(X1)
| ~ p1(X1)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[c11]) ).
cnf(p188,plain,
( ~ p5(X1)
| ~ p1(X1)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p47]) ).
cnf(p408,plain,
( ~ p5(X1)
| ~ p1(X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p188]) ).
cnf(p642,plain,
( ~ p5(X1)
| ~ p1(X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p408]) ).
cnf(p709,plain,
( ~ p5(X1)
| ~ p1(X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p642]) ).
cnf(p711,plain,
( ~ p5(sk0)
| ~ p1(sk0)
| ~ r1(X0,sk0)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p709]) ).
cnf(p721,plain,
( ~ p5(sk0)
| ~ p1(sk0)
| ~ r1(sk0,sk0) ),
inference(factoring,[status(thm)],[p711]) ).
cnf(p729,plain,
( ~ p5(sk0)
| ~ p1(sk0) ),
inference(resolution,[status(thm)],[p721,c0]) ).
cnf(p1228,plain,
( ~ p5(sk0)
| p2(sk0) ),
inference(resolution,[status(thm)],[p1227,p729]) ).
cnf(c14,plain,
( p5(X0)
| p4(X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(sk0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p56,plain,
( p5(X1)
| p4(X1)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[c14]) ).
cnf(p198,plain,
( p5(X1)
| p4(X1)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p56]) ).
cnf(p417,plain,
( p5(X1)
| p4(X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p198]) ).
cnf(p656,plain,
( p5(X1)
| p4(X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p417]) ).
cnf(p783,plain,
( p5(X1)
| p4(X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p656]) ).
cnf(p785,plain,
( p5(sk0)
| p4(sk0)
| ~ r1(X0,sk0)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p783]) ).
cnf(p795,plain,
( p5(sk0)
| p4(sk0)
| ~ r1(sk0,sk0) ),
inference(factoring,[status(thm)],[p785]) ).
cnf(p803,plain,
( p5(sk0)
| p4(sk0) ),
inference(resolution,[status(thm)],[p795,c0]) ).
cnf(p1229,plain,
( p4(sk0)
| p2(sk0) ),
inference(resolution,[status(thm)],[p1228,p803]) ).
cnf(c23,plain,
( ~ p2(X0)
| ~ p3(X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(sk0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p140,plain,
( ~ p2(X1)
| ~ p3(X1)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[c23]) ).
cnf(p335,plain,
( ~ p2(X1)
| ~ p3(X1)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p140]) ).
cnf(p571,plain,
( ~ p2(X1)
| ~ p3(X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p335]) ).
cnf(p966,plain,
( ~ p2(X1)
| ~ p3(X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p571]) ).
cnf(p1128,plain,
( ~ p2(X1)
| ~ p3(X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p966]) ).
cnf(p1130,plain,
( ~ p2(sk0)
| ~ p3(sk0)
| ~ r1(X0,sk0)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p1128]) ).
cnf(p1140,plain,
( ~ p2(sk0)
| ~ p3(sk0)
| ~ r1(sk0,sk0) ),
inference(factoring,[status(thm)],[p1130]) ).
cnf(p1148,plain,
( ~ p2(sk0)
| ~ p3(sk0) ),
inference(resolution,[status(thm)],[p1140,c0]) ).
cnf(c18,plain,
( p4(X0)
| p3(X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(sk0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p85,plain,
( p4(X1)
| p3(X1)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[c18]) ).
cnf(p218,plain,
( p4(X1)
| p3(X1)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p85]) ).
cnf(p432,plain,
( p4(X1)
| p3(X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p218]) ).
cnf(p676,plain,
( p4(X1)
| p3(X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p432]) ).
cnf(p903,plain,
( p4(X1)
| p3(X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p676]) ).
cnf(p905,plain,
( p4(sk0)
| p3(sk0)
| ~ r1(X0,sk0)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p903]) ).
cnf(p915,plain,
( p4(sk0)
| p3(sk0)
| ~ r1(sk0,sk0) ),
inference(factoring,[status(thm)],[p905]) ).
cnf(p923,plain,
( p4(sk0)
| p3(sk0) ),
inference(resolution,[status(thm)],[p915,c0]) ).
cnf(p1149,plain,
( p4(sk0)
| ~ p2(sk0) ),
inference(resolution,[status(thm)],[p1148,p923]) ).
cnf(p1230,plain,
( p4(sk0)
| p4(sk0) ),
inference(resolution,[status(thm)],[p1229,p1149]) ).
cnf(p1231,plain,
p4(sk0),
inference(factoring,[status(thm)],[p1230]) ).
cnf(c19,plain,
( ~ p3(X0)
| ~ p4(X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(sk0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p93,plain,
( ~ p3(X1)
| ~ p4(X1)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[c19]) ).
cnf(p223,plain,
( ~ p3(X1)
| ~ p4(X1)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p93]) ).
cnf(p465,plain,
( ~ p3(X1)
| ~ p4(X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p223]) ).
cnf(p746,plain,
( ~ p3(X1)
| ~ p4(X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p465]) ).
cnf(p981,plain,
( ~ p3(X1)
| ~ p4(X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p746]) ).
cnf(p983,plain,
( ~ p3(sk0)
| ~ p4(sk0)
| ~ r1(X0,sk0)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p981]) ).
cnf(p993,plain,
( ~ p3(sk0)
| ~ p4(sk0)
| ~ r1(sk0,sk0) ),
inference(factoring,[status(thm)],[p983]) ).
cnf(p1001,plain,
( ~ p3(sk0)
| ~ p4(sk0) ),
inference(resolution,[status(thm)],[p993,c0]) ).
cnf(p1232,plain,
~ p3(sk0),
inference(resolution,[status(thm)],[p1231,p1001]) ).
cnf(c22,plain,
( p3(X0)
| p2(X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(sk0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p134,plain,
( p3(X1)
| p2(X1)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[c22]) ).
cnf(p327,plain,
( p3(X1)
| p2(X1)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p134]) ).
cnf(p566,plain,
( p3(X1)
| p2(X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p327]) ).
cnf(p957,plain,
( p3(X1)
| p2(X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p566]) ).
cnf(p1056,plain,
( p3(X1)
| p2(X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p957]) ).
cnf(p1058,plain,
( p3(sk0)
| p2(sk0)
| ~ r1(X0,sk0)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p1056]) ).
cnf(p1068,plain,
( p3(sk0)
| p2(sk0)
| ~ r1(sk0,sk0) ),
inference(factoring,[status(thm)],[p1058]) ).
cnf(p1076,plain,
( p3(sk0)
| p2(sk0) ),
inference(resolution,[status(thm)],[p1068,c0]) ).
cnf(p1233,plain,
p2(sk0),
inference(resolution,[status(thm)],[p1232,p1076]) ).
cnf(p1351,plain,
~ p1(sk0),
inference(resolution,[status(thm)],[p1350,p1233]) ).
cnf(c10,plain,
( p1(X0)
| p5(X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(sk0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p38,plain,
( p1(X1)
| p5(X1)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[c10]) ).
cnf(p180,plain,
( p1(X1)
| p5(X1)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p38]) ).
cnf(p398,plain,
( p1(X1)
| p5(X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p180]) ).
cnf(p593,plain,
( p1(X1)
| p5(X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p398]) ).
cnf(p598,plain,
( p1(X1)
| p5(X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p593]) ).
cnf(p600,plain,
( p1(sk0)
| p5(sk0)
| ~ r1(X0,sk0)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p598]) ).
cnf(p610,plain,
( p1(sk0)
| p5(sk0)
| ~ r1(sk0,sk0) ),
inference(factoring,[status(thm)],[p600]) ).
cnf(p623,plain,
( p1(sk0)
| p5(sk0) ),
inference(resolution,[status(thm)],[p610,c0]) ).
cnf(p1352,plain,
p5(sk0),
inference(resolution,[status(thm)],[p1351,p623]) ).
cnf(c15,plain,
( ~ p4(X0)
| ~ p5(X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(sk0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p63,plain,
( ~ p4(X1)
| ~ p5(X1)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[c15]) ).
cnf(p206,plain,
( ~ p4(X1)
| ~ p5(X1)
| ~ r1(X0,X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p63]) ).
cnf(p427,plain,
( ~ p4(X1)
| ~ p5(X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p206]) ).
cnf(p665,plain,
( ~ p4(X1)
| ~ p5(X1)
| ~ r1(X1,X0)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p427]) ).
cnf(p855,plain,
( ~ p4(X1)
| ~ p5(X1)
| ~ r1(X1,X0)
| ~ r1(X0,X1)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p665]) ).
cnf(p857,plain,
( ~ p4(sk0)
| ~ p5(sk0)
| ~ r1(X0,sk0)
| ~ r1(sk0,X0) ),
inference(factoring,[status(thm)],[p855]) ).
cnf(p867,plain,
( ~ p4(sk0)
| ~ p5(sk0)
| ~ r1(sk0,sk0) ),
inference(factoring,[status(thm)],[p857]) ).
cnf(p875,plain,
( ~ p4(sk0)
| ~ p5(sk0) ),
inference(resolution,[status(thm)],[p867,c0]) ).
cnf(p1353,plain,
~ p4(sk0),
inference(resolution,[status(thm)],[p1352,p875]) ).
cnf(p1354,plain,
$false,
inference(resolution,[status(thm)],[p1353,p1231]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL668+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 00:07:23 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.83/1.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.83/1.32 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------