%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL672+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 02:08:02 PM UTC 2026
% Result : Theorem 3.41s 1.53s
% Output : CNFRefutation 3.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 2
% Syntax : Number of formulae : 68 ( 21 unt; 0 def)
% Number of atoms : 634 ( 0 equ)
% Maximal formula atoms : 49 ( 9 avg)
% Number of connectives : 1103 ( 537 ~; 463 |; 103 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 8 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 : 7 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-1 aty)
% Number of variables : 340 ( 0 sgn 313 !; 27 ?; 85 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : r1(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
fof(f3,conjecture,
~ ? [X0] :
~ ( ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ! [X0] :
( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ~ ! [X0] :
( $false
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
& ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) )
| ( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ~ ( ~ ! [X0] :
( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
& ~ ! [X0] :
( ~ ! [X1] :
( ~ ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) )
& ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) )
| ( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ! [X0] :
( ~ ( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ~ ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
& ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) )
| ( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ~ ( p1(X1)
& ~ ! [X0] :
( ~ ! [X1] :
( ~ p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) )
& ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
fof(f4,negated_conjecture,
~ ~ ? [X0] :
~ ( ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ! [X0] :
( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ~ ! [X0] :
( $false
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
& ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) )
| ( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ~ ( ~ ! [X0] :
( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
& ~ ! [X0] :
( ~ ! [X1] :
( ~ ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) )
& ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) )
| ( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ! [X0] :
( ~ ( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ~ ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
& ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) )
| ( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ~ ( p1(X1)
& ~ ! [X0] :
( ~ ! [X1] :
( ~ p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) )
& ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
~ ~ ? [X0] :
~ ( ! [X30] :
( p1(X30)
| ~ r1(X0,X30) )
| ! [X26] :
( ! [X29] :
( p1(X29)
| ~ r1(X26,X29) )
| ! [X27] :
( ~ ! [X28] :
( p1(X28)
| ~ r1(X27,X28) )
| ~ r1(X26,X27) )
| ~ r1(X0,X26) )
| ! [X25] :
( p2(X25)
| ~ r1(X0,X25) )
| ( ~ ! [X24] :
( p1(X24)
| ~ r1(X0,X24) )
& ~ ! [X22] :
( ~ ! [X23] :
( $false
| ~ r1(X22,X23) )
| ~ r1(X0,X22) )
& ~ ! [X21] :
( p2(X21)
| ~ r1(X0,X21) ) )
| ( ~ ! [X20] :
( p1(X20)
| ~ r1(X0,X20) )
& ~ ! [X14] :
( ~ ( ~ ! [X18] :
( ~ ! [X19] :
( p1(X19)
| ~ r1(X18,X19) )
| ~ r1(X14,X18) )
& ~ ! [X15] :
( ~ ! [X16] :
( ~ ! [X17] :
( p1(X17)
| ~ r1(X16,X17) )
| ~ r1(X15,X16) )
| ~ r1(X14,X15) ) )
| ~ r1(X0,X14) )
& ~ ! [X13] :
( p2(X13)
| ~ r1(X0,X13) ) )
| ( ~ ! [X12] :
( p1(X12)
| ~ r1(X0,X12) )
& ~ ! [X7] :
( ! [X8] :
( ~ ( ~ ! [X11] :
( p1(X11)
| ~ r1(X8,X11) )
& ~ ! [X9] :
( ~ ! [X10] :
( p1(X10)
| ~ r1(X9,X10) )
| ~ r1(X8,X9) ) )
| ~ r1(X7,X8) )
| ~ r1(X0,X7) )
& ~ ! [X6] :
( p2(X6)
| ~ r1(X0,X6) ) )
| ( ~ ! [X5] :
( p1(X5)
| ~ r1(X0,X5) )
& ~ ! [X2] :
( ~ ( p1(X2)
& ~ ! [X3] :
( ~ ! [X4] :
( ~ p1(X4)
| ~ r1(X3,X4) )
| ~ r1(X2,X3) ) )
| ~ r1(X0,X2) )
& ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) ) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
~ ~ ? [X0] :
~ ( ! [X30] :
( p1(X30)
| ~ r1(X0,X30) )
| ! [X26] :
( ! [X29] :
( p1(X29)
| ~ r1(X26,X29) )
| ! [X27] :
( ~ ! [X28] :
( p1(X28)
| ~ r1(X27,X28) )
| ~ r1(X26,X27) )
| ~ r1(X0,X26) )
| ! [X25] :
( p2(X25)
| ~ r1(X0,X25) )
| ( ~ ! [X24] :
( p1(X24)
| ~ r1(X0,X24) )
& ~ ! [X22] :
( ~ ! [X23] : ~ r1(X22,X23)
| ~ r1(X0,X22) )
& ~ ! [X21] :
( p2(X21)
| ~ r1(X0,X21) ) )
| ( ~ ! [X20] :
( p1(X20)
| ~ r1(X0,X20) )
& ~ ! [X14] :
( ~ ( ~ ! [X18] :
( ~ ! [X19] :
( p1(X19)
| ~ r1(X18,X19) )
| ~ r1(X14,X18) )
& ~ ! [X15] :
( ~ ! [X16] :
( ~ ! [X17] :
( p1(X17)
| ~ r1(X16,X17) )
| ~ r1(X15,X16) )
| ~ r1(X14,X15) ) )
| ~ r1(X0,X14) )
& ~ ! [X13] :
( p2(X13)
| ~ r1(X0,X13) ) )
| ( ~ ! [X12] :
( p1(X12)
| ~ r1(X0,X12) )
& ~ ! [X7] :
( ! [X8] :
( ~ ( ~ ! [X11] :
( p1(X11)
| ~ r1(X8,X11) )
& ~ ! [X9] :
( ~ ! [X10] :
( p1(X10)
| ~ r1(X9,X10) )
| ~ r1(X8,X9) ) )
| ~ r1(X7,X8) )
| ~ r1(X0,X7) )
& ~ ! [X6] :
( p2(X6)
| ~ r1(X0,X6) ) )
| ( ~ ! [X5] :
( p1(X5)
| ~ r1(X0,X5) )
& ~ ! [X2] :
( ~ ( p1(X2)
& ~ ! [X3] :
( ~ ! [X4] :
( ~ p1(X4)
| ~ r1(X3,X4) )
| ~ r1(X2,X3) ) )
| ~ r1(X0,X2) )
& ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) ) ),
inference(true_and_false_elimination,[],[f5]) ).
fof(f7,plain,
? [X0] :
~ ( ! [X30] :
( p1(X30)
| ~ r1(X0,X30) )
| ! [X26] :
( ! [X29] :
( p1(X29)
| ~ r1(X26,X29) )
| ! [X27] :
( ~ ! [X28] :
( p1(X28)
| ~ r1(X27,X28) )
| ~ r1(X26,X27) )
| ~ r1(X0,X26) )
| ! [X25] :
( p2(X25)
| ~ r1(X0,X25) )
| ( ~ ! [X24] :
( p1(X24)
| ~ r1(X0,X24) )
& ~ ! [X22] :
( ~ ! [X23] : ~ r1(X22,X23)
| ~ r1(X0,X22) )
& ~ ! [X21] :
( p2(X21)
| ~ r1(X0,X21) ) )
| ( ~ ! [X20] :
( p1(X20)
| ~ r1(X0,X20) )
& ~ ! [X14] :
( ~ ( ~ ! [X18] :
( ~ ! [X19] :
( p1(X19)
| ~ r1(X18,X19) )
| ~ r1(X14,X18) )
& ~ ! [X15] :
( ~ ! [X16] :
( ~ ! [X17] :
( p1(X17)
| ~ r1(X16,X17) )
| ~ r1(X15,X16) )
| ~ r1(X14,X15) ) )
| ~ r1(X0,X14) )
& ~ ! [X13] :
( p2(X13)
| ~ r1(X0,X13) ) )
| ( ~ ! [X12] :
( p1(X12)
| ~ r1(X0,X12) )
& ~ ! [X7] :
( ! [X8] :
( ~ ( ~ ! [X11] :
( p1(X11)
| ~ r1(X8,X11) )
& ~ ! [X9] :
( ~ ! [X10] :
( p1(X10)
| ~ r1(X9,X10) )
| ~ r1(X8,X9) ) )
| ~ r1(X7,X8) )
| ~ r1(X0,X7) )
& ~ ! [X6] :
( p2(X6)
| ~ r1(X0,X6) ) )
| ( ~ ! [X5] :
( p1(X5)
| ~ r1(X0,X5) )
& ~ ! [X2] :
( ~ ( p1(X2)
& ~ ! [X3] :
( ~ ! [X4] :
( ~ p1(X4)
| ~ r1(X3,X4) )
| ~ r1(X2,X3) ) )
| ~ r1(X0,X2) )
& ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) ) ),
inference(flattening,[],[f6]) ).
fof(f10,plain,
? [X0] :
( ? [X30] :
( ~ p1(X30)
& r1(X0,X30) )
& ? [X26] :
( ? [X29] :
( ~ p1(X29)
& r1(X26,X29) )
& ? [X27] :
( ! [X28] :
( p1(X28)
| ~ r1(X27,X28) )
& r1(X26,X27) )
& r1(X0,X26) )
& ? [X25] :
( ~ p2(X25)
& r1(X0,X25) )
& ( ! [X24] :
( p1(X24)
| ~ r1(X0,X24) )
| ! [X22] :
( ? [X23] : r1(X22,X23)
| ~ r1(X0,X22) )
| ! [X21] :
( p2(X21)
| ~ r1(X0,X21) ) )
& ( ! [X20] :
( p1(X20)
| ~ r1(X0,X20) )
| ! [X14] :
( ! [X18] :
( ? [X19] :
( ~ p1(X19)
& r1(X18,X19) )
| ~ r1(X14,X18) )
| ! [X15] :
( ? [X16] :
( ! [X17] :
( p1(X17)
| ~ r1(X16,X17) )
& r1(X15,X16) )
| ~ r1(X14,X15) )
| ~ r1(X0,X14) )
| ! [X13] :
( p2(X13)
| ~ r1(X0,X13) ) )
& ( ! [X12] :
( p1(X12)
| ~ r1(X0,X12) )
| ! [X7] :
( ! [X8] :
( ! [X11] :
( p1(X11)
| ~ r1(X8,X11) )
| ! [X9] :
( ? [X10] :
( ~ p1(X10)
& r1(X9,X10) )
| ~ r1(X8,X9) )
| ~ r1(X7,X8) )
| ~ r1(X0,X7) )
| ! [X6] :
( p2(X6)
| ~ r1(X0,X6) ) )
& ( ! [X5] :
( p1(X5)
| ~ r1(X0,X5) )
| ! [X2] :
( ~ p1(X2)
| ! [X3] :
( ? [X4] :
( p1(X4)
& r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X0,X2) )
| ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f11,plain,
? [X0] :
( ? [X30] :
( ~ p1(X30)
& r1(X0,X30) )
& ? [X26] :
( ? [X29] :
( ~ p1(X29)
& r1(X26,X29) )
& ? [X27] :
( ! [X28] :
( p1(X28)
| ~ r1(X27,X28) )
& r1(X26,X27) )
& r1(X0,X26) )
& ? [X25] :
( ~ p2(X25)
& r1(X0,X25) )
& ( ! [X24] :
( p1(X24)
| ~ r1(X0,X24) )
| ! [X22] :
( ? [X23] : r1(X22,X23)
| ~ r1(X0,X22) )
| ! [X21] :
( p2(X21)
| ~ r1(X0,X21) ) )
& ( ! [X20] :
( p1(X20)
| ~ r1(X0,X20) )
| ! [X14] :
( ! [X18] :
( ? [X19] :
( ~ p1(X19)
& r1(X18,X19) )
| ~ r1(X14,X18) )
| ! [X15] :
( ? [X16] :
( ! [X17] :
( p1(X17)
| ~ r1(X16,X17) )
& r1(X15,X16) )
| ~ r1(X14,X15) )
| ~ r1(X0,X14) )
| ! [X13] :
( p2(X13)
| ~ r1(X0,X13) ) )
& ( ! [X12] :
( p1(X12)
| ~ r1(X0,X12) )
| ! [X7] :
( ! [X8] :
( ! [X11] :
( p1(X11)
| ~ r1(X8,X11) )
| ! [X9] :
( ? [X10] :
( ~ p1(X10)
& r1(X9,X10) )
| ~ r1(X8,X9) )
| ~ r1(X7,X8) )
| ~ r1(X0,X7) )
| ! [X6] :
( p2(X6)
| ~ r1(X0,X6) ) )
& ( ! [X5] :
( p1(X5)
| ~ r1(X0,X5) )
| ! [X2] :
( ~ p1(X2)
| ! [X3] :
( ? [X4] :
( p1(X4)
& r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X0,X2) )
| ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) ) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
( ~ p1(sK10)
& r1(sK0,sK10)
& ~ p1(sK9)
& r1(sK7,sK9)
& ! [X28] :
( p1(X28)
| ~ r1(sK8,X28) )
& r1(sK7,sK8)
& r1(sK0,sK7)
& ~ p2(sK6)
& r1(sK0,sK6)
& ( ! [X24] :
( p1(X24)
| ~ r1(sK0,X24) )
| ! [X22] :
( r1(X22,sK5(X22))
| ~ r1(sK0,X22) )
| ! [X21] :
( p2(X21)
| ~ r1(sK0,X21) ) )
& ( ! [X20] :
( p1(X20)
| ~ r1(sK0,X20) )
| ! [X14] :
( ! [X18] :
( ( ~ p1(sK4(X18))
& r1(X18,sK4(X18)) )
| ~ r1(X14,X18) )
| ! [X15] :
( ( ! [X17] :
( p1(X17)
| ~ r1(sK3(X15),X17) )
& r1(X15,sK3(X15)) )
| ~ r1(X14,X15) )
| ~ r1(sK0,X14) )
| ! [X13] :
( p2(X13)
| ~ r1(sK0,X13) ) )
& ( ! [X12] :
( p1(X12)
| ~ r1(sK0,X12) )
| ! [X7] :
( ! [X8] :
( ! [X11] :
( p1(X11)
| ~ r1(X8,X11) )
| ! [X9] :
( ( ~ p1(sK2(X9))
& r1(X9,sK2(X9)) )
| ~ r1(X8,X9) )
| ~ r1(X7,X8) )
| ~ r1(sK0,X7) )
| ! [X6] :
( p2(X6)
| ~ r1(sK0,X6) ) )
& ( ! [X5] :
( p1(X5)
| ~ r1(sK0,X5) )
| ! [X2] :
( ~ p1(X2)
| ! [X3] :
( ( p1(sK1(X3))
& r1(X3,sK1(X3)) )
| ~ r1(X2,X3) )
| ~ r1(sK0,X2) )
| ! [X1] :
( p2(X1)
| ~ r1(sK0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10]),skolemize(X0,sK0),skolemize(X4,sK1(X3)),skolemize(X10,sK2(X9)),skolemize(X16,sK3(X15)),skolemize(X19,sK4(X18)),skolemize(X23,sK5(X22)),skolemize(X25,sK6),skolemize(X26,sK7),skolemize(X27,sK8),skolemize(X29,sK9),skolemize(X30,sK10)],[f11]) ).
fof(f13,plain,
! [X0] : r1(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f15,plain,
~ p1(sK10),
inference(cnf_transformation,[],[f12]) ).
fof(f16,plain,
r1(sK0,sK10),
inference(cnf_transformation,[],[f12]) ).
fof(f17,plain,
~ p1(sK9),
inference(cnf_transformation,[],[f12]) ).
fof(f18,plain,
r1(sK7,sK9),
inference(cnf_transformation,[],[f12]) ).
fof(f19,plain,
! [X28] :
( p1(X28)
| ~ r1(sK8,X28) ),
inference(cnf_transformation,[],[f12]) ).
fof(f20,plain,
r1(sK7,sK8),
inference(cnf_transformation,[],[f12]) ).
fof(f21,plain,
r1(sK0,sK7),
inference(cnf_transformation,[],[f12]) ).
fof(f22,plain,
~ p2(sK6),
inference(cnf_transformation,[],[f12]) ).
fof(f23,plain,
r1(sK0,sK6),
inference(cnf_transformation,[],[f12]) ).
fof(f24,plain,
! [X21,X24,X22] :
( p1(X24)
| ~ r1(sK0,X24)
| r1(X22,sK5(X22))
| ~ r1(sK0,X22)
| p2(X21)
| ~ r1(sK0,X21) ),
inference(cnf_transformation,[],[f12]) ).
fof(f29,plain,
! [X11,X8,X6,X9,X7,X12] :
( p1(X12)
| ~ r1(sK0,X12)
| p1(X11)
| ~ r1(X8,X11)
| ~ p1(sK2(X9))
| ~ r1(X8,X9)
| ~ r1(X7,X8)
| ~ r1(sK0,X7)
| p2(X6)
| ~ r1(sK0,X6) ),
inference(cnf_transformation,[],[f12]) ).
fof(f30,plain,
! [X11,X8,X6,X9,X7,X12] :
( p1(X12)
| ~ r1(sK0,X12)
| p1(X11)
| ~ r1(X8,X11)
| r1(X9,sK2(X9))
| ~ r1(X8,X9)
| ~ r1(X7,X8)
| ~ r1(sK0,X7)
| p2(X6)
| ~ r1(sK0,X6) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_49,plain,
! [X0: $i] : r1(X0,X0),
inference(cnf_transformation,[],[f13]) ).
tcf(c_53,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( p1(X5)
| p1(X3)
| p2(X4)
| r1(X2,sK2(X2))
| ~ r1(sK0,X5)
| ~ r1(sK0,X4)
| ~ r1(sK0,X0)
| ~ r1(X1,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_54,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( p1(X5)
| p1(X3)
| p2(X4)
| ~ p1(sK2(X2))
| ~ r1(sK0,X5)
| ~ r1(sK0,X4)
| ~ r1(sK0,X0)
| ~ r1(X1,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_59,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( p1(X2)
| p2(X0)
| r1(X1,sK5(X1))
| ~ r1(sK0,X2)
| ~ r1(sK0,X1)
| ~ r1(sK0,X0) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_60,negated_conjecture,
r1(sK0,sK6),
inference(cnf_transformation,[],[f23]) ).
tcf(c_61,negated_conjecture,
~ p2(sK6),
inference(cnf_transformation,[],[f22]) ).
tcf(c_62,negated_conjecture,
r1(sK0,sK7),
inference(cnf_transformation,[],[f21]) ).
tcf(c_63,negated_conjecture,
r1(sK7,sK8),
inference(cnf_transformation,[],[f20]) ).
tcf(c_64,negated_conjecture,
! [X0: $i] :
( p1(X0)
| ~ r1(sK8,X0) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_65,negated_conjecture,
r1(sK7,sK9),
inference(cnf_transformation,[],[f18]) ).
tcf(c_66,negated_conjecture,
~ p1(sK9),
inference(cnf_transformation,[],[f17]) ).
tcf(c_67,negated_conjecture,
r1(sK0,sK10),
inference(cnf_transformation,[],[f16]) ).
tcf(c_68,negated_conjecture,
~ p1(sK10),
inference(cnf_transformation,[],[f15]) ).
tcf(c_69,plain,
r1(sK0,sK0),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_366,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( p1(X4)
| p1(X3)
| ~ r1(sK0,sK6)
| ~ p1(sK2(X2))
| ~ r1(sK0,X4)
| ~ r1(sK0,X0)
| ~ r1(X1,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(resolution,[status(thm)],[c_54,c_61]) ).
tcf(c_368,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( p1(X4)
| p1(X3)
| ~ r1(X0,X1)
| ~ r1(X1,X2)
| ~ r1(X1,X3)
| ~ r1(sK0,X0)
| ~ r1(sK0,X4)
| ~ p1(sK2(X2)) ),
inference(global_subsumption_just,[status(thm)],[c_366,c_60,c_366]) ).
tcf(c_369,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( p1(X4)
| p1(X3)
| ~ p1(sK2(X2))
| ~ r1(sK0,X4)
| ~ r1(sK0,X0)
| ~ r1(X1,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(renaming,[status(thm)],[c_368]) ).
tcf(c_395,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( p1(X4)
| p1(X3)
| r1(X2,sK2(X2))
| ~ r1(sK0,sK6)
| ~ r1(sK0,X4)
| ~ r1(sK0,X0)
| ~ r1(X1,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(resolution,[status(thm)],[c_53,c_61]) ).
tcf(c_397,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( p1(X4)
| p1(X3)
| r1(X2,sK2(X2))
| ~ r1(X0,X1)
| ~ r1(X1,X2)
| ~ r1(X1,X3)
| ~ r1(sK0,X0)
| ~ r1(sK0,X4) ),
inference(global_subsumption_just,[status(thm)],[c_395,c_60,c_395]) ).
tcf(c_398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( p1(X4)
| p1(X3)
| r1(X2,sK2(X2))
| ~ r1(sK0,X4)
| ~ r1(sK0,X0)
| ~ r1(X1,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(renaming,[status(thm)],[c_397]) ).
tcf(c_476,plain,
! [X0: $i,X1: $i] :
( p1(X1)
| r1(X0,sK5(X0))
| ~ r1(sK0,sK6)
| ~ r1(sK0,X1)
| ~ r1(sK0,X0) ),
inference(resolution,[status(thm)],[c_59,c_61]) ).
tcf(c_478,plain,
! [X0: $i,X1: $i] :
( p1(X1)
| r1(X0,sK5(X0))
| ~ r1(sK0,X0)
| ~ r1(sK0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_476,c_60,c_476]) ).
tcf(c_479,plain,
! [X0: $i,X1: $i] :
( p1(X1)
| r1(X0,sK5(X0))
| ~ r1(sK0,X1)
| ~ r1(sK0,X0) ),
inference(renaming,[status(thm)],[c_478]) ).
tcf(c_705,plain,
! [X0: $i] :
( ~ iPr_def_10
| p1(X0)
| ~ r1(sK0,X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_479]) ).
tcf(c_712,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ iPr_def_14
| p1(X3)
| ~ r1(sK0,X0)
| r1(X2,sK2(X2))
| ~ r1(X1,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_14])],[c_398]) ).
tcf(c_713,plain,
( iPr_def_14
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_398]) ).
tcf(c_714,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ iPr_def_15
| ~ p1(sK2(X2))
| p1(X3)
| ~ r1(sK0,X0)
| ~ r1(X1,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_15])],[c_369]) ).
tcf(c_715,plain,
( iPr_def_15
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_369]) ).
tcf(c_733,plain,
( iPr_def_14
| iPr_def_10 ),
inference(demodulation,[status(thm)],[c_713]) ).
tcf(c_734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p1(X3)
| r1(X2,sK2(X2))
| ~ iPr_def_14
| ~ r1(sK0,X0)
| ~ r1(X1,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(demodulation,[status(thm)],[c_712]) ).
tcf(c_736,plain,
( iPr_def_15
| iPr_def_10 ),
inference(demodulation,[status(thm)],[c_715]) ).
tcf(c_737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p1(X3)
| ~ iPr_def_15
| ~ p1(sK2(X2))
| ~ r1(sK0,X0)
| ~ r1(X1,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(demodulation,[status(thm)],[c_714]) ).
tcf(c_750,plain,
! [X0: $i] :
( p1(X0)
| ~ iPr_def_10
| ~ r1(sK0,X0) ),
inference(demodulation,[status(thm)],[c_705]) ).
tcf(c_755,negated_conjecture,
! [X0: $i] :
( p1(X0)
| ~ r1(sK8,X0) ),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_768,plain,
( p1(sK10)
| ~ iPr_def_10
| ~ r1(sK0,sK10) ),
inference(instantiation,[status(thm)],[c_750]) ).
tcf(c_773,plain,
! [X0: $i,X1: $i,X2: $i] :
( p1(sK9)
| r1(X2,sK2(X2))
| ~ iPr_def_14
| ~ r1(sK0,X0)
| ~ r1(X1,sK9)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(instantiation,[status(thm)],[c_734]) ).
tcf(c_777,plain,
! [X0: $i,X1: $i,X2: $i] :
( p1(sK9)
| ~ iPr_def_15
| ~ p1(sK2(X2))
| ~ r1(sK0,X0)
| ~ r1(X1,sK9)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(instantiation,[status(thm)],[c_737]) ).
tcf(c_792,plain,
! [X0: $i,X1: $i] :
( p1(sK9)
| ~ iPr_def_15
| ~ r1(sK7,sK9)
| ~ p1(sK2(X1))
| ~ r1(sK7,X1)
| ~ r1(sK0,X0)
| ~ r1(X0,sK7) ),
inference(instantiation,[status(thm)],[c_777]) ).
tcf(c_814,plain,
! [X0: $i] :
( p1(sK2(X0))
| ~ r1(sK8,sK2(X0)) ),
inference(instantiation,[status(thm)],[c_755]) ).
tcf(c_836,plain,
! [X0: $i,X1: $i] :
( p1(sK9)
| r1(sK8,sK2(sK8))
| ~ iPr_def_14
| ~ r1(sK0,X0)
| ~ r1(X1,sK9)
| ~ r1(X1,sK8)
| ~ r1(X0,X1) ),
inference(instantiation,[status(thm)],[c_773]) ).
tcf(c_846,plain,
( p1(sK2(sK8))
| ~ r1(sK8,sK2(sK8)) ),
inference(instantiation,[status(thm)],[c_814]) ).
tcf(c_865,plain,
! [X0: $i] :
( p1(sK9)
| ~ iPr_def_15
| ~ p1(sK2(sK8))
| ~ r1(sK7,sK9)
| ~ r1(sK7,sK8)
| ~ r1(sK0,X0)
| ~ r1(X0,sK7) ),
inference(instantiation,[status(thm)],[c_792]) ).
tcf(c_866,plain,
( p1(sK9)
| ~ iPr_def_15
| ~ p1(sK2(sK8))
| ~ r1(sK7,sK9)
| ~ r1(sK7,sK8)
| ~ r1(sK0,sK7)
| ~ r1(sK0,sK0) ),
inference(instantiation,[status(thm)],[c_865]) ).
tcf(c_920,plain,
! [X0: $i] :
( p1(sK9)
| r1(sK8,sK2(sK8))
| ~ iPr_def_14
| ~ r1(sK7,sK9)
| ~ r1(sK7,sK8)
| ~ r1(sK0,X0)
| ~ r1(X0,sK7) ),
inference(instantiation,[status(thm)],[c_836]) ).
tcf(c_921,plain,
( p1(sK9)
| r1(sK8,sK2(sK8))
| ~ iPr_def_14
| ~ r1(sK7,sK9)
| ~ r1(sK7,sK8)
| ~ r1(sK0,sK7)
| ~ r1(sK0,sK0) ),
inference(instantiation,[status(thm)],[c_920]) ).
tcf(c_922,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_921,c_866,c_846,c_768,c_736,c_733,c_69,c_62,c_63,c_65,c_66,c_67,c_68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL672+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/0.45 % Computer : n008.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Thu Sep 24 00:12:09 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.23/0.51 Running first-order theorem proving
% 0.23/0.51 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.53
% 0.23/0.53 % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.53
% 0.23/0.53 % Detected problem language: tptp
% 0.23/0.55 % Proving...
% 3.41/1.53 % SZS status Started for theBenchmark.p
% 3.41/1.53 % SZS status Theorem for theBenchmark.p
% 3.41/1.53
% 3.41/1.53 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.41/1.53
% 3.41/1.53 % ------ iProver source info
% 3.41/1.53
% 3.41/1.53 % git: date: 2026-07-19 20:42:38 +0200
% 3.41/1.53 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.41/1.53 % git: non_committed_changes: false
% 3.41/1.53
% 3.41/1.53 % ------ Parsing...
% 3.41/1.53 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.41/1.53
% 3.41/1.53 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.41/1.53
% 3.41/1.53 % ------ Preprocessing... gs_s sp: 18 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.41/1.53 % ------ Proving...
% 3.41/1.53 % ------ Problem Properties
% 3.41/1.53
% 3.41/1.53 %
% 3.41/1.53 % clauses 29
% 3.41/1.53 % conjectures 8
% 3.41/1.53 % EPR 20
% 3.41/1.53 % Horn 17
% 3.41/1.53 % unary 8
% 3.41/1.53 % binary 10
% 3.41/1.53 % lits 87
% 3.41/1.53 % lits eq 0
% 3.41/1.53 % fd_pure 0
% 3.41/1.53 % fd_pseudo 0
% 3.41/1.53 % fd_cond 0
% 3.41/1.53 % fd_pseudo_cond 0
% 3.41/1.53 % AC symbols 0
% 3.41/1.53
% 3.41/1.53 % ------ Schedule dynamic 5 is on
% 3.41/1.53
% 3.41/1.53 % ------ no equalities: superposition off
% 3.41/1.53
% 3.41/1.53 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.41/1.53
% 3.41/1.53
% 3.41/1.53 % ------
% 3.41/1.53 % Current options:
% 3.41/1.53 % ------
% 3.41/1.53
% 3.41/1.53
% 3.41/1.53 %
% 3.41/1.53
% 3.41/1.53 % ------ Proving...
% 3.41/1.53 %
% 3.41/1.53
% 3.41/1.53 % SZS status Theorem for theBenchmark.p
% 3.41/1.53
% 3.41/1.53 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.41/1.53
% 3.41/1.53
%------------------------------------------------------------------------------