%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL650+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 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 02:07:06 PM UTC 2026
% Result : Theorem 1.62s 1.17s
% Output : CNFRefutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 2
% Syntax : Number of formulae : 47 ( 9 unt; 1 def)
% Number of atoms : 562 ( 0 equ)
% Maximal formula atoms : 43 ( 11 avg)
% Number of connectives : 981 ( 466 ~; 367 |; 148 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 12 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-1 aty)
% Number of variables : 308 ( 0 sgn 264 !; 44 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
~ ? [X0] :
~ ( ! [X1] :
( ! [X0] :
( ! [X1] :
( ! [X0] :
( ( p1(X0)
& p2(X0)
& p3(X0)
& p4(X0) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ( ~ ! [X0] :
( ~ ( ~ ! [X1] :
( ~ ~ ! [X0] :
( ~ ( ( p1(X0)
& p2(X0) )
| ( ~ p2(X0)
& ~ p1(X0) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( p3(X1)
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ! [X0] :
( ~ ( ( p2(X0)
& p3(X0) )
| ( ~ p3(X0)
& ~ p2(X0) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| ! [X0] :
( p4(X0)
| ~ r1(X1,X0) )
| ~ ! [X0] :
( ! [X1] :
( ! [X0] :
( ~ ( ( p3(X0)
& p1(X0) )
| ( ~ p1(X0)
& ~ p3(X0) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) )
| ! [X1] :
( p5(X1)
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( ! [X1] :
( ! [X0] :
( ( ~ p2(X0)
& ~ p4(X0)
& ~ p6(X0)
& ~ p8(X0) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).
fof(f2,negated_conjecture,
~ ~ ? [X0] :
~ ( ! [X1] :
( ! [X0] :
( ! [X1] :
( ! [X0] :
( ( p1(X0)
& p2(X0)
& p3(X0)
& p4(X0) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ( ~ ! [X0] :
( ~ ( ~ ! [X1] :
( ~ ~ ! [X0] :
( ~ ( ( p1(X0)
& p2(X0) )
| ( ~ p2(X0)
& ~ p1(X0) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( p3(X1)
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ! [X0] :
( ~ ( ( p2(X0)
& p3(X0) )
| ( ~ p3(X0)
& ~ p2(X0) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| ! [X0] :
( p4(X0)
| ~ r1(X1,X0) )
| ~ ! [X0] :
( ! [X1] :
( ! [X0] :
( ~ ( ( p3(X0)
& p1(X0) )
| ( ~ p1(X0)
& ~ p3(X0) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) )
| ! [X1] :
( p5(X1)
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( ! [X1] :
( ! [X0] :
( ( ~ p2(X0)
& ~ p4(X0)
& ~ p6(X0)
& ~ p8(X0) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ~ ? [X0] :
~ ( ! [X17] :
( ! [X18] :
( ! [X19] :
( ! [X20] :
( ( p1(X20)
& p2(X20)
& p3(X20)
& p4(X20) )
| ~ r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ r1(X17,X18) )
| ~ r1(X0,X17) )
| ~ ! [X6] :
( ~ ( ~ ! [X11] :
( ~ ( ~ ! [X15] :
( ~ ~ ! [X16] :
( ~ ( ( p1(X16)
& p2(X16) )
| ( ~ p2(X16)
& ~ p1(X16) ) )
| ~ r1(X15,X16) )
| ~ r1(X11,X15) )
| ! [X14] :
( p3(X14)
| ~ r1(X11,X14) )
| ~ ! [X12] :
( ! [X13] :
( ~ ( ( p2(X13)
& p3(X13) )
| ( ~ p3(X13)
& ~ p2(X13) ) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) ) )
| ~ r1(X6,X11) )
| ! [X10] :
( p4(X10)
| ~ r1(X6,X10) )
| ~ ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ ( ( p3(X9)
& p1(X9) )
| ( ~ p1(X9)
& ~ p3(X9) ) )
| ~ r1(X8,X9) )
| ~ r1(X7,X8) )
| ~ r1(X6,X7) ) )
| ~ r1(X0,X6) )
| ! [X5] :
( p5(X5)
| ~ r1(X0,X5) )
| ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( ~ p2(X4)
& ~ p4(X4)
& ~ p6(X4)
& ~ p8(X4) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
? [X0] :
~ ( ! [X17] :
( ! [X18] :
( ! [X19] :
( ! [X20] :
( ( p1(X20)
& p2(X20)
& p3(X20)
& p4(X20) )
| ~ r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ r1(X17,X18) )
| ~ r1(X0,X17) )
| ~ ! [X6] :
( ~ ( ~ ! [X11] :
( ~ ( ~ ! [X15] :
( ! [X16] :
( ~ ( ( p1(X16)
& p2(X16) )
| ( ~ p2(X16)
& ~ p1(X16) ) )
| ~ r1(X15,X16) )
| ~ r1(X11,X15) )
| ! [X14] :
( p3(X14)
| ~ r1(X11,X14) )
| ~ ! [X12] :
( ! [X13] :
( ~ ( ( p2(X13)
& p3(X13) )
| ( ~ p3(X13)
& ~ p2(X13) ) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) ) )
| ~ r1(X6,X11) )
| ! [X10] :
( p4(X10)
| ~ r1(X6,X10) )
| ~ ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ ( ( p3(X9)
& p1(X9) )
| ( ~ p1(X9)
& ~ p3(X9) ) )
| ~ r1(X8,X9) )
| ~ r1(X7,X8) )
| ~ r1(X6,X7) ) )
| ~ r1(X0,X6) )
| ! [X5] :
( p5(X5)
| ~ r1(X0,X5) )
| ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( ~ p2(X4)
& ~ p4(X4)
& ~ p6(X4)
& ~ p8(X4) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
? [X0] :
~ ( ! [X17] :
( ! [X18] :
( ! [X19] :
( ! [X20] :
( ( p1(X20)
& p2(X20)
& p3(X20)
& p4(X20) )
| ~ r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ r1(X17,X18) )
| ~ r1(X0,X17) )
| ~ ! [X6] :
( ~ ( ~ ! [X11] :
( ~ ( ~ ! [X15] :
( ! [X16] :
( ~ ( ( p1(X16)
& p2(X16) )
| ( ~ p2(X16)
& ~ p1(X16) ) )
| ~ r1(X15,X16) )
| ~ r1(X11,X15) )
| ! [X14] :
( p3(X14)
| ~ r1(X11,X14) )
| ~ ! [X12] :
( ! [X13] :
( ~ ( ( p2(X13)
& p3(X13) )
| ( ~ p3(X13)
& ~ p2(X13) ) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) ) )
| ~ r1(X6,X11) )
| ! [X10] :
( p4(X10)
| ~ r1(X6,X10) )
| ~ ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ ( ( p3(X9)
& p1(X9) )
| ( ~ p1(X9)
& ~ p3(X9) ) )
| ~ r1(X8,X9) )
| ~ r1(X7,X8) )
| ~ r1(X6,X7) ) )
| ~ r1(X0,X6) )
| ! [X5] : ~ r1(X0,X5)
| ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( ~ p2(X4)
& ~ p4(X4)
& ~ p6(X4)
& ~ p8(X4) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) ) ),
inference(pure_predicate_removal,[],[f4]) ).
fof(f6,plain,
? [X0] :
~ ( ! [X17] :
( ! [X18] :
( ! [X19] :
( ! [X20] :
( ( p1(X20)
& p2(X20)
& p3(X20)
& p4(X20) )
| ~ r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ r1(X17,X18) )
| ~ r1(X0,X17) )
| ~ ! [X6] :
( ~ ( ~ ! [X11] :
( ~ ( ~ ! [X15] :
( ! [X16] :
( ~ ( ( p1(X16)
& p2(X16) )
| ( ~ p2(X16)
& ~ p1(X16) ) )
| ~ r1(X15,X16) )
| ~ r1(X11,X15) )
| ! [X14] :
( p3(X14)
| ~ r1(X11,X14) )
| ~ ! [X12] :
( ! [X13] :
( ~ ( ( p2(X13)
& p3(X13) )
| ( ~ p3(X13)
& ~ p2(X13) ) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) ) )
| ~ r1(X6,X11) )
| ! [X10] :
( p4(X10)
| ~ r1(X6,X10) )
| ~ ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ ( ( p3(X9)
& p1(X9) )
| ( ~ p1(X9)
& ~ p3(X9) ) )
| ~ r1(X8,X9) )
| ~ r1(X7,X8) )
| ~ r1(X6,X7) ) )
| ~ r1(X0,X6) )
| ! [X5] : ~ r1(X0,X5)
| ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] : ~ r1(X3,X4)
| ~ r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) ) ),
inference(pure_predicate_removal,[],[f5]) ).
fof(f7,plain,
? [X0] :
~ ( ! [X17] :
( ! [X18] :
( ! [X19] :
( ! [X20] : ~ r1(X19,X20)
| ~ r1(X18,X19) )
| ~ r1(X17,X18) )
| ~ r1(X0,X17) )
| ~ ! [X6] :
( ~ ( ~ ! [X11] :
( ~ ( ~ ! [X15] :
( ! [X16] :
( ~ ( ( p1(X16)
& p2(X16) )
| ( ~ p2(X16)
& ~ p1(X16) ) )
| ~ r1(X15,X16) )
| ~ r1(X11,X15) )
| ! [X14] :
( p3(X14)
| ~ r1(X11,X14) )
| ~ ! [X12] :
( ! [X13] :
( ~ ( ( p2(X13)
& p3(X13) )
| ( ~ p3(X13)
& ~ p2(X13) ) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) ) )
| ~ r1(X6,X11) )
| ! [X10] : ~ r1(X6,X10)
| ~ ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ ( ( p3(X9)
& p1(X9) )
| ( ~ p1(X9)
& ~ p3(X9) ) )
| ~ r1(X8,X9) )
| ~ r1(X7,X8) )
| ~ r1(X6,X7) ) )
| ~ r1(X0,X6) )
| ! [X5] : ~ r1(X0,X5)
| ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] : ~ r1(X3,X4)
| ~ r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) ) ),
inference(pure_predicate_removal,[],[f6]) ).
fof(f8,plain,
? [X0] :
( ? [X17] :
( ? [X18] :
( ? [X19] :
( ? [X20] : r1(X19,X20)
& r1(X18,X19) )
& r1(X17,X18) )
& r1(X0,X17) )
& ! [X6] :
( ( ! [X11] :
( ( ! [X15] :
( ! [X16] :
( ( ( ~ p1(X16)
| ~ p2(X16) )
& ( p2(X16)
| p1(X16) ) )
| ~ r1(X15,X16) )
| ~ r1(X11,X15) )
& ? [X14] :
( ~ p3(X14)
& r1(X11,X14) )
& ! [X12] :
( ! [X13] :
( ( ( ~ p2(X13)
| ~ p3(X13) )
& ( p3(X13)
| p2(X13) ) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) ) )
| ~ r1(X6,X11) )
& ? [X10] : r1(X6,X10)
& ! [X7] :
( ! [X8] :
( ! [X9] :
( ( ( ~ p3(X9)
| ~ p1(X9) )
& ( p1(X9)
| p3(X9) ) )
| ~ r1(X8,X9) )
| ~ r1(X7,X8) )
| ~ r1(X6,X7) ) )
| ~ r1(X0,X6) )
& ? [X5] : r1(X0,X5)
& ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] : r1(X3,X4)
& r1(X2,X3) )
& r1(X1,X2) )
& r1(X0,X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f14,plain,
? [X0] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( ? [X14] : r1(X13,X14)
& r1(X12,X13) )
& r1(X11,X12) )
& r1(X0,X11) )
& ! [X6] :
( ( sP0(X6)
& ? [X10] : r1(X6,X10)
& ! [X7] :
( ! [X8] :
( ! [X9] :
( ( ( ~ p3(X9)
| ~ p1(X9) )
& ( p1(X9)
| p3(X9) ) )
| ~ r1(X8,X9) )
| ~ r1(X7,X8) )
| ~ r1(X6,X7) ) )
| ~ r1(X0,X6) )
& ? [X5] : r1(X0,X5)
& ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] : r1(X3,X4)
& r1(X2,X3) )
& r1(X1,X2) )
& r1(X0,X1) ) ),
inference(rectify,[],[f10]) ).
fof(f15,plain,
( r1(sK11,sK12)
& r1(sK10,sK11)
& r1(sK9,sK10)
& r1(sK2,sK9)
& ! [X6] :
( ( sP0(X6)
& r1(X6,sK8(X6))
& ! [X7] :
( ! [X8] :
( ! [X9] :
( ( ( ~ p3(X9)
| ~ p1(X9) )
& ( p1(X9)
| p3(X9) ) )
| ~ r1(X8,X9) )
| ~ r1(X7,X8) )
| ~ r1(X6,X7) ) )
| ~ r1(sK2,X6) )
& r1(sK2,sK7)
& r1(sK5,sK6)
& r1(sK4,sK5)
& r1(sK3,sK4)
& r1(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5),skolemize(X4,sK6),skolemize(X5,sK7),skolemize(X10,sK8(X6)),skolemize(X11,sK9),skolemize(X12,sK10),skolemize(X13,sK11),skolemize(X14,sK12)],[f14]) ).
fof(f26,plain,
! [X6] :
( sP0(X6)
| ~ r1(sK2,X6) ),
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
! [X8,X6,X9,X7] :
( ~ p3(X9)
| ~ p1(X9)
| ~ r1(X8,X9)
| ~ r1(X7,X8)
| ~ r1(X6,X7)
| ~ r1(sK2,X6) ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X8,X6,X9,X7] :
( p1(X9)
| p3(X9)
| ~ r1(X8,X9)
| ~ r1(X7,X8)
| ~ r1(X6,X7)
| ~ r1(sK2,X6) ),
inference(cnf_transformation,[],[f15]) ).
fof(f31,plain,
r1(sK5,sK6),
inference(cnf_transformation,[],[f15]) ).
fof(f32,plain,
r1(sK4,sK5),
inference(cnf_transformation,[],[f15]) ).
fof(f33,plain,
r1(sK3,sK4),
inference(cnf_transformation,[],[f15]) ).
fof(f34,plain,
r1(sK2,sK3),
inference(cnf_transformation,[],[f15]) ).
tcf(c_55,negated_conjecture,
r1(sK2,sK3),
inference(cnf_transformation,[],[f34]) ).
tcf(c_56,negated_conjecture,
r1(sK3,sK4),
inference(cnf_transformation,[],[f33]) ).
tcf(c_57,negated_conjecture,
r1(sK4,sK5),
inference(cnf_transformation,[],[f32]) ).
tcf(c_58,negated_conjecture,
r1(sK5,sK6),
inference(cnf_transformation,[],[f31]) ).
tcf(c_60,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p1(X3)
| p3(X3)
| ~ r1(sK2,X0)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_61,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ p1(X3)
| ~ p3(X3)
| ~ r1(sK2,X0)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_63,negated_conjecture,
! [X0: $i] :
( sP0(X0)
| ~ r1(sK2,X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f9,definition,
! [X6] :
( ~ sP0(X6)
| ! [X11] :
( ( ! [X15] :
( ! [X16] :
( ( ( ~ p1(X16)
| ~ p2(X16) )
& ( p2(X16)
| p1(X16) ) )
| ~ r1(X15,X16) )
| ~ r1(X11,X15) )
& ? [X14] :
( ~ p3(X14)
& r1(X11,X14) )
& ! [X12] :
( ! [X13] :
( ( ( ~ p2(X13)
| ~ p3(X13) )
& ( p3(X13)
| p2(X13) ) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) ) )
| ~ r1(X6,X11) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f10,plain,
? [X0] :
( ? [X17] :
( ? [X18] :
( ? [X19] :
( ? [X20] : r1(X19,X20)
& r1(X18,X19) )
& r1(X17,X18) )
& r1(X0,X17) )
& ! [X6] :
( ( sP0(X6)
& ? [X10] : r1(X6,X10)
& ! [X7] :
( ! [X8] :
( ! [X9] :
( ( ( ~ p3(X9)
| ~ p1(X9) )
& ( p1(X9)
| p3(X9) ) )
| ~ r1(X8,X9) )
| ~ r1(X7,X8) )
| ~ r1(X6,X7) ) )
| ~ r1(X0,X6) )
& ? [X5] : r1(X0,X5)
& ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] : r1(X3,X4)
& r1(X2,X3) )
& r1(X1,X2) )
& r1(X0,X1) ) ),
inference(definition_folding,[],[f8,f9]) ).
fof(f11,plain,
! [X6] :
( ~ sP0(X6)
| ! [X11] :
( ( ! [X15] :
( ! [X16] :
( ( ( ~ p1(X16)
| ~ p2(X16) )
& ( p2(X16)
| p1(X16) ) )
| ~ r1(X15,X16) )
| ~ r1(X11,X15) )
& ? [X14] :
( ~ p3(X14)
& r1(X11,X14) )
& ! [X12] :
( ! [X13] :
( ( ( ~ p2(X13)
| ~ p3(X13) )
& ( p3(X13)
| p2(X13) ) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) ) )
| ~ r1(X6,X11) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f12,plain,
! [X0] :
( ~ sP0(X0)
| ! [X1] :
( ( ! [X5] :
( ! [X6] :
( ( ( ~ p1(X6)
| ~ p2(X6) )
& ( p2(X6)
| p1(X6) ) )
| ~ r1(X5,X6) )
| ~ r1(X1,X5) )
& ? [X4] :
( ~ p3(X4)
& r1(X1,X4) )
& ! [X2] :
( ! [X3] :
( ( ( ~ p2(X3)
| ~ p3(X3) )
& ( p3(X3)
| p2(X3) ) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) ) )
| ~ r1(X0,X1) ) ),
inference(rectify,[],[f11]) ).
fof(f13,plain,
! [X0] :
( ~ sP0(X0)
| ! [X1] :
( ( ! [X5] :
( ! [X6] :
( ( ( ~ p1(X6)
| ~ p2(X6) )
& ( p2(X6)
| p1(X6) ) )
| ~ r1(X5,X6) )
| ~ r1(X1,X5) )
& ~ p3(sK1(X1))
& r1(X1,sK1(X1))
& ! [X2] :
( ! [X3] :
( ( ( ~ p2(X3)
| ~ p3(X3) )
& ( p3(X3)
| p2(X3) ) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) ) )
| ~ r1(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X4,sK1(X1))],[f12]) ).
fof(f16,plain,
! [X0,X1,X6,X5] :
( ~ sP0(X0)
| ~ p1(X6)
| ~ p2(X6)
| ~ r1(X5,X6)
| ~ r1(X1,X5)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f17,plain,
! [X0,X1,X6,X5] :
( ~ sP0(X0)
| p2(X6)
| p1(X6)
| ~ r1(X5,X6)
| ~ r1(X1,X5)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0)
| ~ p2(X3)
| ~ p3(X3)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0)
| p3(X3)
| p2(X3)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p3(X3)
| p2(X3)
| ~ sP0(X0)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ sP0(X0)
| ~ p3(X3)
| ~ p2(X3)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p1(X3)
| p2(X3)
| ~ sP0(X0)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ p1(X3)
| ~ sP0(X0)
| ~ p2(X3)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p1(X3)
| ~ r1(X0,X1)
| ~ r1(X1,X2)
| ~ r1(X2,X3)
| ~ r1(sK2,X0) ),
inference(global_subsumption_just,[status(thm)],[c_60,c_63,c_53,c_49,c_60,c_54,c_50,c_61]) ).
tcf(c_79,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p1(X3)
| ~ r1(sK2,X0)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(renaming,[status(thm)],[c_78]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ r1(X0,X1)
| ~ r1(X1,X2)
| ~ r1(X2,X3)
| ~ r1(sK2,X0) ),
inference(global_subsumption_just,[status(thm)],[c_79,c_63,c_49,c_54,c_61,c_79]) ).
tcf(c_82,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ r1(sK2,X0)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(renaming,[status(thm)],[c_81]) ).
tcf(c_84,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ r1(sK2,X0)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_61,c_82]) ).
tcf(c_230,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ r1(sK2,X0)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_244,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ r1(sK2,sK3)
| ~ r1(sK3,X0)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(instantiation,[status(thm)],[c_230]) ).
tcf(c_258,plain,
! [X0: $i,X1: $i] :
( ~ r1(sK3,sK4)
| ~ r1(sK2,sK3)
| ~ r1(sK4,X0)
| ~ r1(X0,X1) ),
inference(instantiation,[status(thm)],[c_244]) ).
tcf(c_266,plain,
( ~ r1(sK5,sK6)
| ~ r1(sK4,sK5)
| ~ r1(sK3,sK4)
| ~ r1(sK2,sK3) ),
inference(instantiation,[status(thm)],[c_258]) ).
tcf(c_267,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_266,c_55,c_56,c_57,c_58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL650+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 23:59:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.62/1.17 % SZS status Started for theBenchmark.p
% 1.62/1.17 % SZS status Theorem for theBenchmark.p
% 1.62/1.17
% 1.62/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.62/1.17
% 1.62/1.17 % ------ iProver source info
% 1.62/1.17
% 1.62/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 1.62/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.62/1.17 % git: non_committed_changes: false
% 1.62/1.17
% 1.62/1.17 % ------ Parsing...
% 1.62/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.62/1.17
% 1.62/1.17 % ------ Preprocessing... sf_s rm: 5 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.62/1.17
% 1.62/1.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.62/1.17 % ------ Proving...
% 1.62/1.17 % ------ Problem Properties
% 1.62/1.17
% 1.62/1.17 %
% 1.62/1.17 % clauses 12
% 1.62/1.17 % conjectures 11
% 1.62/1.17 % EPR 10
% 1.62/1.17 % Horn 12
% 1.62/1.17 % unary 9
% 1.62/1.17 % binary 1
% 1.62/1.17 % lits 18
% 1.62/1.17 % lits eq 0
% 1.62/1.17 % fd_pure 0
% 1.62/1.18 % fd_pseudo 0
% 1.62/1.18 % fd_cond 0
% 1.62/1.18 % fd_pseudo_cond 0
% 1.62/1.18 % AC symbols 0
% 1.62/1.18
% 1.62/1.18 % ------ Schedule dynamic 5 is on
% 1.62/1.18
% 1.62/1.18 % ------ no equalities: superposition off
% 1.62/1.18
% 1.62/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.62/1.18
% 1.62/1.18
% 1.62/1.18 % ------
% 1.62/1.18 % Current options:
% 1.62/1.18 % ------
% 1.62/1.18
% 1.62/1.18
% 1.62/1.18 %
% 1.62/1.18
% 1.62/1.18 % ------ Proving...
% 1.62/1.18 %
% 1.62/1.18
% 1.62/1.18 % SZS status Theorem for theBenchmark.p
% 1.62/1.18
% 1.62/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.62/1.18
% 1.62/1.18
%------------------------------------------------------------------------------