%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL654+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 : 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 02:07:09 PM UTC 2026
% Result : Theorem 3.54s 1.29s
% Output : CNFRefutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 2
% Syntax : Number of formulae : 93 ( 20 unt; 0 def)
% Number of atoms : 562 ( 0 equ)
% Maximal formula atoms : 29 ( 6 avg)
% Number of connectives : 958 ( 489 ~; 418 |; 51 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-1 aty)
% Number of variables : 288 ( 0 sgn 265 !; 23 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : r1(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
fof(f2,conjecture,
~ ? [X0] :
~ ( ! [X1] :
( ~ ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ! [X0] :
( ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ! [X0] :
( $false
| ~ r1(X1,X0) )
| ~ 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] :
( ! [X0] :
( ~ ( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ~ ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ( p1(X1)
& ~ ! [X0] :
( ~ ! [X1] :
( ~ p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
fof(f3,negated_conjecture,
~ ~ ? [X0] :
~ ( ! [X1] :
( ~ ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ! [X0] :
( ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ! [X0] :
( $false
| ~ r1(X1,X0) )
| ~ 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] :
( ! [X0] :
( ~ ( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ~ ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ( p1(X1)
& ~ ! [X0] :
( ~ ! [X1] :
( ~ p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f4,plain,
~ ~ ? [X0] :
~ ( ! [X17] :
( ~ ! [X20] :
( p1(X20)
| ~ r1(X17,X20) )
| ! [X18] :
( ! [X19] :
( p1(X19)
| ~ r1(X18,X19) )
| ~ r1(X17,X18) )
| ~ r1(X0,X17) )
| ~ ! [X15] :
( ~ ! [X16] :
( $false
| ~ r1(X15,X16) )
| ~ r1(X0,X15) )
| ~ ! [X9] :
( ~ ( ~ ! [X13] :
( ~ ! [X14] :
( p1(X14)
| ~ r1(X13,X14) )
| ~ r1(X9,X13) )
& ~ ! [X10] :
( ~ ! [X11] :
( ~ ! [X12] :
( p1(X12)
| ~ r1(X11,X12) )
| ~ r1(X10,X11) )
| ~ r1(X9,X10) ) )
| ~ r1(X0,X9) )
| ~ ! [X4] :
( ! [X5] :
( ~ ( ~ ! [X8] :
( p1(X8)
| ~ r1(X5,X8) )
& ~ ! [X6] :
( ~ ! [X7] :
( p1(X7)
| ~ r1(X6,X7) )
| ~ r1(X5,X6) ) )
| ~ r1(X4,X5) )
| ~ r1(X0,X4) )
| ~ ! [X1] :
( ~ ( p1(X1)
& ~ ! [X2] :
( ~ ! [X3] :
( ~ p1(X3)
| ~ r1(X2,X3) )
| ~ r1(X1,X2) ) )
| ~ r1(X0,X1) ) ),
inference(rectify,[],[f3]) ).
fof(f5,plain,
~ ~ ? [X0] :
~ ( ! [X17] :
( ~ ! [X20] :
( p1(X20)
| ~ r1(X17,X20) )
| ! [X18] :
( ! [X19] :
( p1(X19)
| ~ r1(X18,X19) )
| ~ r1(X17,X18) )
| ~ r1(X0,X17) )
| ~ ! [X15] :
( ~ ! [X16] : ~ r1(X15,X16)
| ~ r1(X0,X15) )
| ~ ! [X9] :
( ~ ( ~ ! [X13] :
( ~ ! [X14] :
( p1(X14)
| ~ r1(X13,X14) )
| ~ r1(X9,X13) )
& ~ ! [X10] :
( ~ ! [X11] :
( ~ ! [X12] :
( p1(X12)
| ~ r1(X11,X12) )
| ~ r1(X10,X11) )
| ~ r1(X9,X10) ) )
| ~ r1(X0,X9) )
| ~ ! [X4] :
( ! [X5] :
( ~ ( ~ ! [X8] :
( p1(X8)
| ~ r1(X5,X8) )
& ~ ! [X6] :
( ~ ! [X7] :
( p1(X7)
| ~ r1(X6,X7) )
| ~ r1(X5,X6) ) )
| ~ r1(X4,X5) )
| ~ r1(X0,X4) )
| ~ ! [X1] :
( ~ ( p1(X1)
& ~ ! [X2] :
( ~ ! [X3] :
( ~ p1(X3)
| ~ r1(X2,X3) )
| ~ r1(X1,X2) ) )
| ~ r1(X0,X1) ) ),
inference(true_and_false_elimination,[],[f4]) ).
fof(f6,plain,
? [X0] :
~ ( ! [X17] :
( ~ ! [X20] :
( p1(X20)
| ~ r1(X17,X20) )
| ! [X18] :
( ! [X19] :
( p1(X19)
| ~ r1(X18,X19) )
| ~ r1(X17,X18) )
| ~ r1(X0,X17) )
| ~ ! [X15] :
( ~ ! [X16] : ~ r1(X15,X16)
| ~ r1(X0,X15) )
| ~ ! [X9] :
( ~ ( ~ ! [X13] :
( ~ ! [X14] :
( p1(X14)
| ~ r1(X13,X14) )
| ~ r1(X9,X13) )
& ~ ! [X10] :
( ~ ! [X11] :
( ~ ! [X12] :
( p1(X12)
| ~ r1(X11,X12) )
| ~ r1(X10,X11) )
| ~ r1(X9,X10) ) )
| ~ r1(X0,X9) )
| ~ ! [X4] :
( ! [X5] :
( ~ ( ~ ! [X8] :
( p1(X8)
| ~ r1(X5,X8) )
& ~ ! [X6] :
( ~ ! [X7] :
( p1(X7)
| ~ r1(X6,X7) )
| ~ r1(X5,X6) ) )
| ~ r1(X4,X5) )
| ~ r1(X0,X4) )
| ~ ! [X1] :
( ~ ( p1(X1)
& ~ ! [X2] :
( ~ ! [X3] :
( ~ p1(X3)
| ~ r1(X2,X3) )
| ~ r1(X1,X2) ) )
| ~ r1(X0,X1) ) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
? [X0] :
( ? [X17] :
( ! [X20] :
( p1(X20)
| ~ r1(X17,X20) )
& ? [X18] :
( ? [X19] :
( ~ p1(X19)
& r1(X18,X19) )
& r1(X17,X18) )
& r1(X0,X17) )
& ! [X15] :
( ? [X16] : r1(X15,X16)
| ~ r1(X0,X15) )
& ! [X9] :
( ! [X13] :
( ? [X14] :
( ~ p1(X14)
& r1(X13,X14) )
| ~ r1(X9,X13) )
| ! [X10] :
( ? [X11] :
( ! [X12] :
( p1(X12)
| ~ r1(X11,X12) )
& r1(X10,X11) )
| ~ r1(X9,X10) )
| ~ r1(X0,X9) )
& ! [X4] :
( ! [X5] :
( ! [X8] :
( p1(X8)
| ~ r1(X5,X8) )
| ! [X6] :
( ? [X7] :
( ~ p1(X7)
& r1(X6,X7) )
| ~ r1(X5,X6) )
| ~ r1(X4,X5) )
| ~ r1(X0,X4) )
& ! [X1] :
( ~ p1(X1)
| ! [X2] :
( ? [X3] :
( p1(X3)
& r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f8,plain,
? [X0] :
( ? [X17] :
( ! [X20] :
( p1(X20)
| ~ r1(X17,X20) )
& ? [X18] :
( ? [X19] :
( ~ p1(X19)
& r1(X18,X19) )
& r1(X17,X18) )
& r1(X0,X17) )
& ! [X15] :
( ? [X16] : r1(X15,X16)
| ~ r1(X0,X15) )
& ! [X9] :
( ! [X13] :
( ? [X14] :
( ~ p1(X14)
& r1(X13,X14) )
| ~ r1(X9,X13) )
| ! [X10] :
( ? [X11] :
( ! [X12] :
( p1(X12)
| ~ r1(X11,X12) )
& r1(X10,X11) )
| ~ r1(X9,X10) )
| ~ r1(X0,X9) )
& ! [X4] :
( ! [X5] :
( ! [X8] :
( p1(X8)
| ~ r1(X5,X8) )
| ! [X6] :
( ? [X7] :
( ~ p1(X7)
& r1(X6,X7) )
| ~ r1(X5,X6) )
| ~ r1(X4,X5) )
| ~ r1(X0,X4) )
& ! [X1] :
( ~ p1(X1)
| ! [X2] :
( ? [X3] :
( p1(X3)
& r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) ) ),
inference(flattening,[],[f7]) ).
fof(f9,plain,
( ! [X20] :
( p1(X20)
| ~ r1(sK6,X20) )
& ~ p1(sK8)
& r1(sK7,sK8)
& r1(sK6,sK7)
& r1(sK0,sK6)
& ! [X15] :
( r1(X15,sK5(X15))
| ~ r1(sK0,X15) )
& ! [X9] :
( ! [X13] :
( ( ~ p1(sK4(X13))
& r1(X13,sK4(X13)) )
| ~ r1(X9,X13) )
| ! [X10] :
( ( ! [X12] :
( p1(X12)
| ~ r1(sK3(X10),X12) )
& r1(X10,sK3(X10)) )
| ~ r1(X9,X10) )
| ~ r1(sK0,X9) )
& ! [X4] :
( ! [X5] :
( ! [X8] :
( p1(X8)
| ~ r1(X5,X8) )
| ! [X6] :
( ( ~ p1(sK2(X6))
& r1(X6,sK2(X6)) )
| ~ r1(X5,X6) )
| ~ r1(X4,X5) )
| ~ r1(sK0,X4) )
& ! [X1] :
( ~ p1(X1)
| ! [X2] :
( ( p1(sK1(X2))
& r1(X2,sK1(X2)) )
| ~ r1(X1,X2) )
| ~ r1(sK0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8]),skolemize(X0,sK0),skolemize(X3,sK1(X2)),skolemize(X7,sK2(X6)),skolemize(X11,sK3(X10)),skolemize(X14,sK4(X13)),skolemize(X16,sK5(X15)),skolemize(X17,sK6),skolemize(X18,sK7),skolemize(X19,sK8)],[f8]) ).
fof(f10,plain,
! [X0] : r1(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f11,plain,
! [X20] :
( p1(X20)
| ~ r1(sK6,X20) ),
inference(cnf_transformation,[],[f9]) ).
fof(f12,plain,
~ p1(sK8),
inference(cnf_transformation,[],[f9]) ).
fof(f13,plain,
r1(sK7,sK8),
inference(cnf_transformation,[],[f9]) ).
fof(f14,plain,
r1(sK6,sK7),
inference(cnf_transformation,[],[f9]) ).
fof(f15,plain,
r1(sK0,sK6),
inference(cnf_transformation,[],[f9]) ).
fof(f17,plain,
! [X10,X9,X12,X13] :
( ~ p1(sK4(X13))
| ~ r1(X9,X13)
| p1(X12)
| ~ r1(sK3(X10),X12)
| ~ r1(X9,X10)
| ~ r1(sK0,X9) ),
inference(cnf_transformation,[],[f9]) ).
fof(f18,plain,
! [X10,X9,X12,X13] :
( r1(X13,sK4(X13))
| ~ r1(X9,X13)
| p1(X12)
| ~ r1(sK3(X10),X12)
| ~ r1(X9,X10)
| ~ r1(sK0,X9) ),
inference(cnf_transformation,[],[f9]) ).
fof(f19,plain,
! [X10,X9,X13] :
( ~ p1(sK4(X13))
| ~ r1(X9,X13)
| r1(X10,sK3(X10))
| ~ r1(X9,X10)
| ~ r1(sK0,X9) ),
inference(cnf_transformation,[],[f9]) ).
fof(f20,plain,
! [X10,X9,X13] :
( r1(X13,sK4(X13))
| ~ r1(X9,X13)
| r1(X10,sK3(X10))
| ~ r1(X9,X10)
| ~ r1(sK0,X9) ),
inference(cnf_transformation,[],[f9]) ).
fof(f21,plain,
! [X8,X6,X4,X5] :
( p1(X8)
| ~ r1(X5,X8)
| ~ p1(sK2(X6))
| ~ r1(X5,X6)
| ~ r1(X4,X5)
| ~ r1(sK0,X4) ),
inference(cnf_transformation,[],[f9]) ).
fof(f22,plain,
! [X8,X6,X4,X5] :
( p1(X8)
| ~ r1(X5,X8)
| r1(X6,sK2(X6))
| ~ r1(X5,X6)
| ~ r1(X4,X5)
| ~ r1(sK0,X4) ),
inference(cnf_transformation,[],[f9]) ).
fof(f24,plain,
! [X2,X1] :
( ~ p1(X1)
| r1(X2,sK1(X2))
| ~ r1(X1,X2)
| ~ r1(sK0,X1) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_49,plain,
! [X0: $i] : r1(X0,X0),
inference(cnf_transformation,[],[f10]) ).
tcf(c_50,negated_conjecture,
! [X0: $i,X1: $i] :
( r1(X1,sK1(X1))
| ~ p1(X0)
| ~ r1(sK0,X0)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_52,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p1(X3)
| r1(X2,sK2(X2))
| ~ r1(sK0,X0)
| ~ r1(X1,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_53,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p1(X3)
| ~ p1(sK2(X2))
| ~ r1(sK0,X0)
| ~ r1(X1,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_54,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( r1(X2,sK4(X2))
| r1(X1,sK3(X1))
| ~ r1(sK0,X0)
| ~ r1(X0,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_55,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( r1(X1,sK3(X1))
| ~ p1(sK4(X2))
| ~ r1(sK0,X0)
| ~ r1(X0,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_56,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p1(X1)
| r1(X3,sK4(X3))
| ~ r1(sK0,X2)
| ~ r1(X2,X3)
| ~ r1(X2,X0)
| ~ r1(sK3(X0),X1) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_57,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p1(X1)
| ~ p1(sK4(X3))
| ~ r1(sK0,X2)
| ~ r1(X2,X3)
| ~ r1(X2,X0)
| ~ r1(sK3(X0),X1) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_59,negated_conjecture,
r1(sK0,sK6),
inference(cnf_transformation,[],[f15]) ).
tcf(c_60,negated_conjecture,
r1(sK6,sK7),
inference(cnf_transformation,[],[f14]) ).
tcf(c_61,negated_conjecture,
r1(sK7,sK8),
inference(cnf_transformation,[],[f13]) ).
tcf(c_62,negated_conjecture,
~ p1(sK8),
inference(cnf_transformation,[],[f12]) ).
tcf(c_63,negated_conjecture,
! [X0: $i] :
( p1(X0)
| ~ r1(sK6,X0) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_64,plain,
r1(sK0,sK0),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_177,negated_conjecture,
! [X0: $i] :
( p1(X0)
| ~ r1(sK6,X0) ),
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_180,negated_conjecture,
r1(sK6,sK7),
inference(demodulation,[status(thm)],[c_60]) ).
tcf(c_181,negated_conjecture,
r1(sK0,sK6),
inference(demodulation,[status(thm)],[c_59]) ).
tcf(c_183,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p1(X1)
| ~ p1(sK4(X3))
| ~ r1(sK0,X2)
| ~ r1(X2,X3)
| ~ r1(X2,X0)
| ~ r1(sK3(X0),X1) ),
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_184,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p1(X1)
| r1(X3,sK4(X3))
| ~ r1(sK0,X2)
| ~ r1(X2,X3)
| ~ r1(X2,X0)
| ~ r1(sK3(X0),X1) ),
inference(demodulation,[status(thm)],[c_56]) ).
tcf(c_185,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( r1(X1,sK3(X1))
| ~ p1(sK4(X2))
| ~ r1(sK0,X0)
| ~ r1(X0,X2)
| ~ r1(X0,X1) ),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_186,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( r1(X2,sK4(X2))
| r1(X1,sK3(X1))
| ~ r1(sK0,X0)
| ~ r1(X0,X2)
| ~ r1(X0,X1) ),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_187,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p1(X3)
| ~ p1(sK2(X2))
| ~ r1(sK0,X0)
| ~ r1(X1,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_188,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p1(X3)
| r1(X2,sK2(X2))
| ~ r1(sK0,X0)
| ~ r1(X1,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(demodulation,[status(thm)],[c_52]) ).
tcf(c_190,negated_conjecture,
! [X0: $i,X1: $i] :
( r1(X1,sK1(X1))
| ~ p1(X0)
| ~ r1(sK0,X0)
| ~ r1(X0,X1) ),
inference(demodulation,[status(thm)],[c_50]) ).
tcf(c_194,plain,
! [X0: $i,X1: $i,X2: $i] :
( p1(sK8)
| ~ p1(sK2(X2))
| ~ r1(sK0,X0)
| ~ r1(X1,sK8)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(instantiation,[status(thm)],[c_187]) ).
tcf(c_198,plain,
! [X0: $i,X1: $i,X2: $i] :
( p1(sK8)
| r1(X2,sK2(X2))
| ~ r1(sK0,X0)
| ~ r1(X1,sK8)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(instantiation,[status(thm)],[c_188]) ).
tcf(c_203,plain,
! [X0: $i] :
( p1(sK4(X0))
| ~ r1(sK6,sK4(X0)) ),
inference(instantiation,[status(thm)],[c_177]) ).
tcf(c_211,plain,
! [X0: $i,X1: $i] :
( p1(sK8)
| ~ r1(sK7,sK8)
| ~ p1(sK2(X1))
| ~ r1(sK7,X1)
| ~ r1(sK0,X0)
| ~ r1(X0,sK7) ),
inference(instantiation,[status(thm)],[c_194]) ).
tcf(c_215,plain,
! [X0: $i,X1: $i] :
( p1(sK8)
| r1(X1,sK2(X1))
| ~ r1(sK7,sK8)
| ~ r1(sK7,X1)
| ~ r1(sK0,X0)
| ~ r1(X0,sK7) ),
inference(instantiation,[status(thm)],[c_198]) ).
tcf(c_218,plain,
r1(sK7,sK7),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_220,plain,
! [X0: $i] :
( p1(sK8)
| ~ r1(sK7,sK8)
| ~ r1(sK6,sK7)
| ~ r1(sK0,sK6)
| ~ p1(sK2(X0))
| ~ r1(sK7,X0) ),
inference(instantiation,[status(thm)],[c_211]) ).
tcf(c_224,plain,
! [X0: $i] :
( p1(sK8)
| r1(X0,sK2(X0))
| ~ r1(sK7,sK8)
| ~ r1(sK6,sK7)
| ~ r1(sK0,sK6)
| ~ r1(sK7,X0) ),
inference(instantiation,[status(thm)],[c_215]) ).
tcf(c_232,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p1(sK2(X1))
| ~ p1(sK4(X3))
| ~ r1(sK0,X2)
| ~ r1(X2,X3)
| ~ r1(X2,X0)
| ~ r1(sK3(X0),sK2(X1)) ),
inference(instantiation,[status(thm)],[c_183]) ).
tcf(c_235,plain,
! [X0: $i] :
( p1(sK2(X0))
| ~ r1(sK6,sK2(X0)) ),
inference(instantiation,[status(thm)],[c_177]) ).
tcf(c_237,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p1(sK2(X1))
| r1(X3,sK2(X3))
| ~ r1(sK0,X2)
| ~ r1(X2,X0)
| ~ r1(X0,X3)
| ~ r1(X0,sK2(X1)) ),
inference(instantiation,[status(thm)],[c_188]) ).
tcf(c_255,plain,
( p1(sK8)
| ~ r1(sK7,sK8)
| ~ r1(sK6,sK7)
| ~ r1(sK0,sK6)
| ~ p1(sK2(sK3(sK7)))
| ~ r1(sK7,sK3(sK7)) ),
inference(instantiation,[status(thm)],[c_220]) ).
tcf(c_256,plain,
! [X0: $i,X1: $i] :
( r1(sK7,sK3(sK7))
| r1(X1,sK4(X1))
| ~ r1(sK0,X0)
| ~ r1(X0,sK7)
| ~ r1(X0,X1) ),
inference(instantiation,[status(thm)],[c_186]) ).
tcf(c_257,plain,
! [X0: $i,X1: $i] :
( r1(sK7,sK3(sK7))
| ~ p1(sK4(X1))
| ~ r1(sK0,X0)
| ~ r1(X0,sK7)
| ~ r1(X0,X1) ),
inference(instantiation,[status(thm)],[c_185]) ).
tcf(c_289,plain,
( p1(sK8)
| r1(sK7,sK2(sK7))
| ~ r1(sK7,sK8)
| ~ r1(sK7,sK7)
| ~ r1(sK6,sK7)
| ~ r1(sK0,sK6) ),
inference(instantiation,[status(thm)],[c_224]) ).
tcf(c_290,plain,
( p1(sK8)
| ~ p1(sK2(sK7))
| ~ r1(sK7,sK8)
| ~ r1(sK7,sK7)
| ~ r1(sK6,sK7)
| ~ r1(sK0,sK6) ),
inference(instantiation,[status(thm)],[c_220]) ).
tcf(c_333,plain,
! [X0: $i] :
( r1(sK7,sK3(sK7))
| ~ r1(sK6,sK7)
| ~ r1(sK0,sK6)
| ~ p1(sK4(X0))
| ~ r1(sK6,X0) ),
inference(instantiation,[status(thm)],[c_257]) ).
tcf(c_339,plain,
! [X0: $i] :
( r1(sK7,sK3(sK7))
| r1(X0,sK4(X0))
| ~ r1(sK6,sK7)
| ~ r1(sK0,sK6)
| ~ r1(sK6,X0) ),
inference(instantiation,[status(thm)],[c_256]) ).
tcf(c_375,plain,
! [X0: $i,X1: $i] :
( p1(sK2(sK7))
| r1(X1,sK2(X1))
| ~ r1(sK7,X1)
| ~ r1(sK0,X0)
| ~ r1(X0,sK7)
| ~ r1(sK7,sK2(sK7)) ),
inference(instantiation,[status(thm)],[c_237]) ).
tcf(c_466,plain,
r1(sK6,sK6),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_484,plain,
! [X0: $i,X1: $i,X2: $i] :
( p1(X1)
| r1(sK6,sK4(sK6))
| ~ r1(sK0,X2)
| ~ r1(X2,sK6)
| ~ r1(X2,X0)
| ~ r1(sK3(X0),X1) ),
inference(instantiation,[status(thm)],[c_184]) ).
tcf(c_485,plain,
( p1(sK4(sK6))
| ~ r1(sK6,sK4(sK6)) ),
inference(instantiation,[status(thm)],[c_203]) ).
tcf(c_508,plain,
( r1(sK6,sK1(sK6))
| ~ p1(sK0)
| ~ r1(sK0,sK0) ),
inference(superposition,[status(thm)],[c_181,c_190]) ).
tcf(c_558,plain,
( p1(sK2(sK6))
| ~ r1(sK6,sK2(sK6)) ),
inference(instantiation,[status(thm)],[c_235]) ).
tcf(c_583,plain,
( r1(sK7,sK3(sK7))
| r1(sK6,sK4(sK6))
| ~ r1(sK6,sK7)
| ~ r1(sK6,sK6)
| ~ r1(sK0,sK6) ),
inference(instantiation,[status(thm)],[c_339]) ).
tcf(c_754,plain,
( r1(sK7,sK3(sK7))
| ~ p1(sK4(sK6))
| ~ r1(sK6,sK7)
| ~ r1(sK6,sK6)
| ~ r1(sK0,sK6) ),
inference(instantiation,[status(thm)],[c_333]) ).
tcf(c_813,plain,
! [X0: $i] :
( r1(sK7,sK3(sK7))
| ~ r1(sK0,sK6)
| ~ p1(sK4(X0))
| ~ r1(sK6,X0) ),
inference(superposition,[status(thm)],[c_180,c_185]) ).
tcf(c_819,plain,
! [X0: $i] :
( r1(sK7,sK3(sK7))
| ~ p1(sK4(X0))
| ~ r1(sK6,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_813,c_181]) ).
tcf(c_888,plain,
! [X0: $i,X1: $i,X2: $i] :
( p1(sK2(X1))
| r1(sK6,sK4(sK6))
| ~ r1(sK0,X2)
| ~ r1(X2,sK6)
| ~ r1(X2,X0)
| ~ r1(sK3(X0),sK2(X1)) ),
inference(instantiation,[status(thm)],[c_484]) ).
tcf(c_1154,plain,
! [X0: $i,X1: $i] :
( p1(X1)
| ~ p1(sK2(sK6))
| ~ r1(sK0,X1)
| ~ r1(sK0,X0)
| ~ r1(X0,sK0) ),
inference(superposition,[status(thm)],[c_181,c_187]) ).
tcf(c_1184,plain,
( p1(sK0)
| ~ p1(sK2(sK6))
| ~ r1(sK0,sK0) ),
inference(instantiation,[status(thm)],[c_1154]) ).
tcf(c_1266,plain,
! [X0: $i] :
( p1(sK2(sK7))
| r1(X0,sK2(X0))
| ~ r1(sK6,sK7)
| ~ r1(sK0,sK6)
| ~ r1(sK7,X0)
| ~ r1(sK7,sK2(sK7)) ),
inference(instantiation,[status(thm)],[c_375]) ).
tcf(c_1289,plain,
( p1(sK2(sK7))
| r1(sK3(sK7),sK2(sK3(sK7)))
| ~ r1(sK6,sK7)
| ~ r1(sK0,sK6)
| ~ r1(sK7,sK3(sK7))
| ~ r1(sK7,sK2(sK7)) ),
inference(instantiation,[status(thm)],[c_1266]) ).
tcf(c_1350,plain,
! [X0: $i,X1: $i] :
( p1(X1)
| r1(sK6,sK2(sK6))
| ~ r1(sK0,X1)
| ~ r1(sK0,X0)
| ~ r1(X0,sK0) ),
inference(superposition,[status(thm)],[c_181,c_188]) ).
tcf(c_1380,plain,
( p1(sK0)
| r1(sK6,sK2(sK6))
| ~ r1(sK0,sK0) ),
inference(instantiation,[status(thm)],[c_1350]) ).
tcf(c_1652,plain,
! [X0: $i] :
( p1(sK2(sK3(sK7)))
| r1(sK6,sK4(sK6))
| ~ r1(sK0,X0)
| ~ r1(X0,sK7)
| ~ r1(X0,sK6)
| ~ r1(sK3(sK7),sK2(sK3(sK7))) ),
inference(instantiation,[status(thm)],[c_888]) ).
tcf(c_1653,plain,
! [X0: $i,X1: $i] :
( p1(sK2(sK3(sK7)))
| ~ p1(sK4(X1))
| ~ r1(sK0,X0)
| ~ r1(X0,sK7)
| ~ r1(X0,X1)
| ~ r1(sK3(sK7),sK2(sK3(sK7))) ),
inference(instantiation,[status(thm)],[c_232]) ).
tcf(c_1929,plain,
r1(sK6,sK1(sK6)),
inference(global_subsumption_just,[status(thm)],[c_508,c_64,c_508,c_558,c_1184,c_1380]) ).
tcf(c_1934,plain,
! [X0: $i] :
( r1(sK1(sK6),sK3(sK1(sK6)))
| ~ r1(sK0,sK6)
| ~ p1(sK4(X0))
| ~ r1(sK6,X0) ),
inference(superposition,[status(thm)],[c_1929,c_185]) ).
tcf(c_1940,plain,
! [X0: $i] :
( r1(sK1(sK6),sK3(sK1(sK6)))
| ~ p1(sK4(X0))
| ~ r1(sK6,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1934,c_181]) ).
tcf(c_2878,plain,
( p1(sK2(sK3(sK7)))
| r1(sK6,sK4(sK6))
| ~ r1(sK6,sK7)
| ~ r1(sK6,sK6)
| ~ r1(sK0,sK6)
| ~ r1(sK3(sK7),sK2(sK3(sK7))) ),
inference(instantiation,[status(thm)],[c_1652]) ).
tcf(c_3202,plain,
! [X0: $i] :
( p1(sK2(sK3(sK7)))
| ~ r1(sK6,sK7)
| ~ r1(sK0,sK6)
| ~ p1(sK4(X0))
| ~ r1(sK6,X0)
| ~ r1(sK3(sK7),sK2(sK3(sK7))) ),
inference(instantiation,[status(thm)],[c_1653]) ).
tcf(c_3218,plain,
r1(sK7,sK3(sK7)),
inference(global_subsumption_just,[status(thm)],[c_819,c_60,c_59,c_466,c_485,c_583,c_754]) ).
tcf(c_3595,plain,
! [X0: $i] :
( ~ r1(sK6,X0)
| ~ p1(sK4(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_1940,c_62,c_61,c_60,c_59,c_218,c_255,c_290,c_289,c_1289,c_3202,c_3218]) ).
tcf(c_3596,plain,
! [X0: $i] :
( ~ p1(sK4(X0))
| ~ r1(sK6,X0) ),
inference(renaming,[status(thm)],[c_3595]) ).
tcf(c_3602,plain,
~ p1(sK4(sK6)),
inference(superposition,[status(thm)],[c_49,c_3596]) ).
tcf(c_3608,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3602,c_3218,c_2878,c_1289,c_485,c_466,c_289,c_290,c_255,c_218,c_59,c_60,c_61,c_62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL654+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 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 : Wed Sep 23 23:58:52 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 3.54/1.29 % SZS status Started for theBenchmark.p
% 3.54/1.29 % SZS status Theorem for theBenchmark.p
% 3.54/1.29
% 3.54/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.54/1.29
% 3.54/1.29 % ------ iProver source info
% 3.54/1.29
% 3.54/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 3.54/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.54/1.29 % git: non_committed_changes: false
% 3.54/1.29
% 3.54/1.29 % ------ Parsing...
% 3.54/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.54/1.29
% 3.54/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.54/1.29
% 3.54/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.54/1.29 % ------ Proving...
% 3.54/1.29 % ------ Problem Properties
% 3.54/1.29
% 3.54/1.29 %
% 3.54/1.29 % clauses 15
% 3.54/1.29 % conjectures 14
% 3.54/1.29 % EPR 6
% 3.54/1.29 % Horn 12
% 3.54/1.29 % unary 5
% 3.54/1.29 % binary 2
% 3.54/1.29 % lits 51
% 3.54/1.29 % lits eq 0
% 3.54/1.29 % fd_pure 0
% 3.54/1.29 % fd_pseudo 0
% 3.54/1.29 % fd_cond 0
% 3.54/1.29 % fd_pseudo_cond 0
% 3.54/1.29 % AC symbols 0
% 3.54/1.29
% 3.54/1.29 % ------ Schedule dynamic 5 is on
% 3.54/1.29
% 3.54/1.29 % ------ no equalities: superposition off
% 3.54/1.29
% 3.54/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.54/1.29
% 3.54/1.29
% 3.54/1.29 % ------
% 3.54/1.29 % Current options:
% 3.54/1.29 % ------
% 3.54/1.29
% 3.54/1.29
% 3.54/1.29 %
% 3.54/1.29
% 3.54/1.29 % ------ Proving...
% 3.54/1.29 %
% 3.54/1.29
% 3.54/1.29 % SZS status Theorem for theBenchmark.p
% 3.54/1.29
% 3.54/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.54/1.29
% 3.54/1.29
%------------------------------------------------------------------------------