%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL688+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 : n005.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 02:08:12 PM UTC 2026
% Result : Theorem 4.42s 6.32s
% Output : CNFRefutation 4.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 65 ( 7 unt; 0 def)
% Number of atoms : 629 ( 0 equ)
% Maximal formula atoms : 44 ( 9 avg)
% Number of connectives : 1147 ( 583 ~; 456 |; 107 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 9 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-1 aty)
% Number of variables : 356 ( 0 sgn 311 !; 45 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : r1(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( r1(X1,X2)
& r1(X0,X1) )
=> r1(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
fof(f3,conjecture,
~ ? [X0] :
~ ( ~ ! [X1] :
( ~ ! [X0] :
( ~ p1(X0)
| ~ r1(X1,X0) )
| ! [X0] :
( ! [X1] :
( ~ p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( ~ ! [X0] :
( ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ! [X0] :
( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ( ! [X1] :
( ~ ! [X0] :
( ~ ( p1(X0)
& ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ~ ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
& ~ p1(X0) )
| ~ ! [X1] :
( ~ ( ~ ! [X0] :
( ~ ( ~ ! [X1] :
( ~ ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
& p2(X0)
& ~ ! [X1] :
( ~ ( ~ p2(X1)
| ! [X0] :
( p3(X0)
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| ~ ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ! [X0] :
( p3(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ p4(X1)
| ~ r1(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).
fof(f4,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] :
( ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ! [X0] :
( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ( ! [X1] :
( ~ ! [X0] :
( ~ ( p1(X0)
& ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ~ ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
& ~ p1(X0) )
| ~ ! [X1] :
( ~ ( ~ ! [X0] :
( ~ ( ~ ! [X1] :
( ~ ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
& p2(X0)
& ~ ! [X1] :
( ~ ( ~ p2(X1)
| ! [X0] :
( p3(X0)
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| ~ ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ! [X0] :
( p3(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ p4(X1)
| ~ r1(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
~ ~ ? [X0] :
~ ( ~ ! [X24] :
( ~ ! [X27] :
( ~ p1(X27)
| ~ r1(X24,X27) )
| ! [X25] :
( ! [X26] :
( ~ p1(X26)
| ~ r1(X25,X26) )
| ~ r1(X24,X25) )
| ~ r1(X0,X24) )
| ! [X21] :
( ~ ! [X22] :
( ~ ! [X23] :
( p2(X23)
| ~ r1(X22,X23) )
| ~ r1(X21,X22) )
| ~ r1(X0,X21) )
| ! [X17] :
( ! [X20] :
( p1(X20)
| ~ r1(X17,X20) )
| ! [X18] :
( ~ ! [X19] :
( p1(X19)
| ~ r1(X18,X19) )
| ~ r1(X17,X18) )
| ~ r1(X0,X17) )
| ( ! [X14] :
( ~ ! [X15] :
( ~ ( p1(X15)
& ~ ! [X16] :
( p1(X16)
| ~ r1(X15,X16) ) )
| ~ r1(X14,X15) )
| p1(X14)
| ~ r1(X0,X14) )
& ~ ! [X12] :
( ~ ! [X13] :
( p1(X13)
| ~ r1(X12,X13) )
| ~ r1(X0,X12) )
& ~ p1(X0) )
| ~ ! [X2] :
( ~ ( ~ ! [X6] :
( ~ ( ~ ! [X9] :
( ~ ! [X10] :
( ~ ! [X11] :
( ~ p2(X11)
| ~ r1(X10,X11) )
| ~ r1(X9,X10) )
| ~ r1(X6,X9) )
& p2(X6)
& ~ ! [X7] :
( ~ ( ~ p2(X7)
| ! [X8] :
( p3(X8)
| ~ r1(X7,X8) ) )
| ~ r1(X6,X7) ) )
| ~ r1(X2,X6) )
| ~ ! [X3] :
( ~ ! [X4] :
( ~ p2(X4)
| ! [X5] :
( p3(X5)
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) ) )
| ~ r1(X0,X2) )
| ~ ! [X1] :
( ~ p4(X1)
| ~ r1(X0,X1) ) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
? [X0] :
~ ( ~ ! [X24] :
( ~ ! [X27] :
( ~ p1(X27)
| ~ r1(X24,X27) )
| ! [X25] :
( ! [X26] :
( ~ p1(X26)
| ~ r1(X25,X26) )
| ~ r1(X24,X25) )
| ~ r1(X0,X24) )
| ! [X21] :
( ~ ! [X22] :
( ~ ! [X23] :
( p2(X23)
| ~ r1(X22,X23) )
| ~ r1(X21,X22) )
| ~ r1(X0,X21) )
| ! [X17] :
( ! [X20] :
( p1(X20)
| ~ r1(X17,X20) )
| ! [X18] :
( ~ ! [X19] :
( p1(X19)
| ~ r1(X18,X19) )
| ~ r1(X17,X18) )
| ~ r1(X0,X17) )
| ( ! [X14] :
( ~ ! [X15] :
( ~ ( p1(X15)
& ~ ! [X16] :
( p1(X16)
| ~ r1(X15,X16) ) )
| ~ r1(X14,X15) )
| p1(X14)
| ~ r1(X0,X14) )
& ~ ! [X12] :
( ~ ! [X13] :
( p1(X13)
| ~ r1(X12,X13) )
| ~ r1(X0,X12) )
& ~ p1(X0) )
| ~ ! [X2] :
( ~ ( ~ ! [X6] :
( ~ ( ~ ! [X9] :
( ~ ! [X10] :
( ~ ! [X11] :
( ~ p2(X11)
| ~ r1(X10,X11) )
| ~ r1(X9,X10) )
| ~ r1(X6,X9) )
& p2(X6)
& ~ ! [X7] :
( ~ ( ~ p2(X7)
| ! [X8] :
( p3(X8)
| ~ r1(X7,X8) ) )
| ~ r1(X6,X7) ) )
| ~ r1(X2,X6) )
| ~ ! [X3] :
( ~ ! [X4] :
( ~ p2(X4)
| ! [X5] :
( p3(X5)
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) ) )
| ~ r1(X0,X2) )
| ~ ! [X1] :
( ~ p4(X1)
| ~ r1(X0,X1) ) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
? [X0] :
~ ( ~ ! [X24] :
( ~ ! [X27] :
( ~ p1(X27)
| ~ r1(X24,X27) )
| ! [X25] :
( ! [X26] :
( ~ p1(X26)
| ~ r1(X25,X26) )
| ~ r1(X24,X25) )
| ~ r1(X0,X24) )
| ! [X21] :
( ~ ! [X22] :
( ~ ! [X23] :
( p2(X23)
| ~ r1(X22,X23) )
| ~ r1(X21,X22) )
| ~ r1(X0,X21) )
| ! [X17] :
( ! [X20] :
( p1(X20)
| ~ r1(X17,X20) )
| ! [X18] :
( ~ ! [X19] :
( p1(X19)
| ~ r1(X18,X19) )
| ~ r1(X17,X18) )
| ~ r1(X0,X17) )
| ( ! [X14] :
( ~ ! [X15] :
( ~ ( p1(X15)
& ~ ! [X16] :
( p1(X16)
| ~ r1(X15,X16) ) )
| ~ r1(X14,X15) )
| p1(X14)
| ~ r1(X0,X14) )
& ~ ! [X12] :
( ~ ! [X13] :
( p1(X13)
| ~ r1(X12,X13) )
| ~ r1(X0,X12) )
& ~ p1(X0) )
| ~ ! [X2] :
( ~ ( ~ ! [X6] :
( ~ ( ~ ! [X9] :
( ~ ! [X10] :
( ~ ! [X11] :
( ~ p2(X11)
| ~ r1(X10,X11) )
| ~ r1(X9,X10) )
| ~ r1(X6,X9) )
& p2(X6)
& ~ ! [X7] :
( ~ ( ~ p2(X7)
| ! [X8] : ~ r1(X7,X8) )
| ~ r1(X6,X7) ) )
| ~ r1(X2,X6) )
| ~ ! [X3] :
( ~ ! [X4] :
( ~ p2(X4)
| ! [X5] : ~ r1(X4,X5)
| ~ r1(X3,X4) )
| ~ r1(X2,X3) ) )
| ~ r1(X0,X2) )
| ~ ! [X1] :
( ~ p4(X1)
| ~ r1(X0,X1) ) ),
inference(pure_predicate_removal,[],[f6]) ).
fof(f8,plain,
? [X0] :
~ ( ~ ! [X24] :
( ~ ! [X27] :
( ~ p1(X27)
| ~ r1(X24,X27) )
| ! [X25] :
( ! [X26] :
( ~ p1(X26)
| ~ r1(X25,X26) )
| ~ r1(X24,X25) )
| ~ r1(X0,X24) )
| ! [X21] :
( ~ ! [X22] :
( ~ ! [X23] :
( p2(X23)
| ~ r1(X22,X23) )
| ~ r1(X21,X22) )
| ~ r1(X0,X21) )
| ! [X17] :
( ! [X20] :
( p1(X20)
| ~ r1(X17,X20) )
| ! [X18] :
( ~ ! [X19] :
( p1(X19)
| ~ r1(X18,X19) )
| ~ r1(X17,X18) )
| ~ r1(X0,X17) )
| ( ! [X14] :
( ~ ! [X15] :
( ~ ( p1(X15)
& ~ ! [X16] :
( p1(X16)
| ~ r1(X15,X16) ) )
| ~ r1(X14,X15) )
| p1(X14)
| ~ r1(X0,X14) )
& ~ ! [X12] :
( ~ ! [X13] :
( p1(X13)
| ~ r1(X12,X13) )
| ~ r1(X0,X12) )
& ~ p1(X0) )
| ~ ! [X2] :
( ~ ( ~ ! [X6] :
( ~ ( ~ ! [X9] :
( ~ ! [X10] :
( ~ ! [X11] :
( ~ p2(X11)
| ~ r1(X10,X11) )
| ~ r1(X9,X10) )
| ~ r1(X6,X9) )
& p2(X6)
& ~ ! [X7] :
( ~ ( ~ p2(X7)
| ! [X8] : ~ r1(X7,X8) )
| ~ r1(X6,X7) ) )
| ~ r1(X2,X6) )
| ~ ! [X3] :
( ~ ! [X4] :
( ~ p2(X4)
| ! [X5] : ~ r1(X4,X5)
| ~ r1(X3,X4) )
| ~ r1(X2,X3) ) )
| ~ r1(X0,X2) ) ),
inference(pure_predicate_removal,[],[f7]) ).
fof(f9,plain,
! [X0,X1,X2] :
( ~ r1(X1,X2)
| ~ r1(X0,X1)
| r1(X0,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f10,plain,
! [X0,X1,X2] :
( ~ r1(X1,X2)
| ~ r1(X0,X1)
| r1(X0,X2) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
? [X0] :
( ! [X24] :
( ? [X27] :
( p1(X27)
& r1(X24,X27) )
| ! [X25] :
( ! [X26] :
( ~ p1(X26)
| ~ r1(X25,X26) )
| ~ r1(X24,X25) )
| ~ r1(X0,X24) )
& ? [X21] :
( ! [X22] :
( ? [X23] :
( ~ p2(X23)
& r1(X22,X23) )
| ~ r1(X21,X22) )
& r1(X0,X21) )
& ? [X17] :
( ? [X20] :
( ~ p1(X20)
& r1(X17,X20) )
& ? [X18] :
( ! [X19] :
( p1(X19)
| ~ r1(X18,X19) )
& r1(X17,X18) )
& r1(X0,X17) )
& ( ? [X14] :
( ! [X15] :
( ~ p1(X15)
| ! [X16] :
( p1(X16)
| ~ r1(X15,X16) )
| ~ r1(X14,X15) )
& ~ p1(X14)
& r1(X0,X14) )
| ! [X12] :
( ? [X13] :
( ~ p1(X13)
& r1(X12,X13) )
| ~ r1(X0,X12) )
| p1(X0) )
& ! [X2] :
( ( ! [X6] :
( ! [X9] :
( ? [X10] :
( ! [X11] :
( ~ p2(X11)
| ~ r1(X10,X11) )
& r1(X9,X10) )
| ~ r1(X6,X9) )
| ~ p2(X6)
| ! [X7] :
( ( p2(X7)
& ? [X8] : r1(X7,X8) )
| ~ r1(X6,X7) )
| ~ r1(X2,X6) )
& ! [X3] :
( ? [X4] :
( p2(X4)
& ? [X5] : r1(X4,X5)
& r1(X3,X4) )
| ~ r1(X2,X3) ) )
| ~ r1(X0,X2) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f12,plain,
? [X0] :
( ! [X24] :
( ? [X27] :
( p1(X27)
& r1(X24,X27) )
| ! [X25] :
( ! [X26] :
( ~ p1(X26)
| ~ r1(X25,X26) )
| ~ r1(X24,X25) )
| ~ r1(X0,X24) )
& ? [X21] :
( ! [X22] :
( ? [X23] :
( ~ p2(X23)
& r1(X22,X23) )
| ~ r1(X21,X22) )
& r1(X0,X21) )
& ? [X17] :
( ? [X20] :
( ~ p1(X20)
& r1(X17,X20) )
& ? [X18] :
( ! [X19] :
( p1(X19)
| ~ r1(X18,X19) )
& r1(X17,X18) )
& r1(X0,X17) )
& ( ? [X14] :
( ! [X15] :
( ~ p1(X15)
| ! [X16] :
( p1(X16)
| ~ r1(X15,X16) )
| ~ r1(X14,X15) )
& ~ p1(X14)
& r1(X0,X14) )
| ! [X12] :
( ? [X13] :
( ~ p1(X13)
& r1(X12,X13) )
| ~ r1(X0,X12) )
| p1(X0) )
& ! [X2] :
( ( ! [X6] :
( ! [X9] :
( ? [X10] :
( ! [X11] :
( ~ p2(X11)
| ~ r1(X10,X11) )
& r1(X9,X10) )
| ~ r1(X6,X9) )
| ~ p2(X6)
| ! [X7] :
( ( p2(X7)
& ? [X8] : r1(X7,X8) )
| ~ r1(X6,X7) )
| ~ r1(X2,X6) )
& ! [X3] :
( ? [X4] :
( p2(X4)
& ? [X5] : r1(X4,X5)
& r1(X3,X4) )
| ~ r1(X2,X3) ) )
| ~ r1(X0,X2) ) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
? [X0] :
( ! [X23] :
( ? [X26] :
( p1(X26)
& r1(X23,X26) )
| ! [X24] :
( ! [X25] :
( ~ p1(X25)
| ~ r1(X24,X25) )
| ~ r1(X23,X24) )
| ~ r1(X0,X23) )
& ? [X20] :
( ! [X21] :
( ? [X22] :
( ~ p2(X22)
& r1(X21,X22) )
| ~ r1(X20,X21) )
& r1(X0,X20) )
& ? [X16] :
( ? [X19] :
( ~ p1(X19)
& r1(X16,X19) )
& ? [X17] :
( ! [X18] :
( p1(X18)
| ~ r1(X17,X18) )
& r1(X16,X17) )
& r1(X0,X16) )
& ( ? [X13] :
( ! [X14] :
( ~ p1(X14)
| ! [X15] :
( p1(X15)
| ~ r1(X14,X15) )
| ~ r1(X13,X14) )
& ~ p1(X13)
& r1(X0,X13) )
| ! [X11] :
( ? [X12] :
( ~ p1(X12)
& r1(X11,X12) )
| ~ r1(X0,X11) )
| p1(X0) )
& ! [X1] :
( ( ! [X5] :
( ! [X8] :
( ? [X9] :
( ! [X10] :
( ~ p2(X10)
| ~ r1(X9,X10) )
& r1(X8,X9) )
| ~ r1(X5,X8) )
| ~ p2(X5)
| ! [X6] :
( ( p2(X6)
& ? [X7] : r1(X6,X7) )
| ~ r1(X5,X6) )
| ~ r1(X1,X5) )
& ! [X2] :
( ? [X3] :
( p2(X3)
& ? [X4] : r1(X3,X4)
& r1(X2,X3) )
| ~ r1(X1,X2) ) )
| ~ r1(X0,X1) ) ),
inference(rectify,[],[f12]) ).
fof(f14,plain,
( ! [X23] :
( ( p1(sK12(X23))
& r1(X23,sK12(X23)) )
| ! [X24] :
( ! [X25] :
( ~ p1(X25)
| ~ r1(X24,X25) )
| ~ r1(X23,X24) )
| ~ r1(sK0,X23) )
& ! [X21] :
( ( ~ p2(sK11(X21))
& r1(X21,sK11(X21)) )
| ~ r1(sK10,X21) )
& r1(sK0,sK10)
& ~ p1(sK9)
& r1(sK7,sK9)
& ! [X18] :
( p1(X18)
| ~ r1(sK8,X18) )
& r1(sK7,sK8)
& r1(sK0,sK7)
& ( ( ! [X14] :
( ~ p1(X14)
| ! [X15] :
( p1(X15)
| ~ r1(X14,X15) )
| ~ r1(sK6,X14) )
& ~ p1(sK6)
& r1(sK0,sK6) )
| ! [X11] :
( ( ~ p1(sK5(X11))
& r1(X11,sK5(X11)) )
| ~ r1(sK0,X11) )
| p1(sK0) )
& ! [X1] :
( ( ! [X5] :
( ! [X8] :
( ( ! [X10] :
( ~ p2(X10)
| ~ r1(sK4(X8),X10) )
& r1(X8,sK4(X8)) )
| ~ r1(X5,X8) )
| ~ p2(X5)
| ! [X6] :
( ( p2(X6)
& r1(X6,sK3(X6)) )
| ~ r1(X5,X6) )
| ~ r1(X1,X5) )
& ! [X2] :
( ( p2(sK1(X2))
& r1(sK1(X2),sK2(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,sK9,sK10,sK11,sK12]),skolemize(X0,sK0),skolemize(X3,sK1(X2)),skolemize(X4,sK2(X2)),skolemize(X7,sK3(X6)),skolemize(X9,sK4(X8)),skolemize(X12,sK5(X11)),skolemize(X13,sK6),skolemize(X16,sK7),skolemize(X17,sK8),skolemize(X19,sK9),skolemize(X20,sK10),skolemize(X22,sK11(X21)),skolemize(X26,sK12(X23))],[f13]) ).
fof(f15,plain,
! [X0] : r1(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f16,plain,
! [X2,X0,X1] :
( ~ r1(X1,X2)
| ~ r1(X0,X1)
| r1(X0,X2) ),
inference(cnf_transformation,[],[f10]) ).
fof(f19,plain,
! [X21] :
( ~ p2(sK11(X21))
| ~ r1(sK10,X21) ),
inference(cnf_transformation,[],[f14]) ).
fof(f20,plain,
! [X21] :
( r1(X21,sK11(X21))
| ~ r1(sK10,X21) ),
inference(cnf_transformation,[],[f14]) ).
fof(f21,plain,
r1(sK0,sK10),
inference(cnf_transformation,[],[f14]) ).
fof(f33,plain,
! [X10,X1,X8,X6,X5] :
( ~ p2(X10)
| ~ r1(sK4(X8),X10)
| ~ r1(X5,X8)
| ~ p2(X5)
| p2(X6)
| ~ r1(X5,X6)
| ~ r1(X1,X5)
| ~ r1(sK0,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f34,plain,
! [X1,X8,X6,X5] :
( r1(X8,sK4(X8))
| ~ r1(X5,X8)
| ~ p2(X5)
| p2(X6)
| ~ r1(X5,X6)
| ~ r1(X1,X5)
| ~ r1(sK0,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f37,plain,
! [X2,X1] :
( p2(sK1(X2))
| ~ r1(X1,X2)
| ~ r1(sK0,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f39,plain,
! [X2,X1] :
( r1(X2,sK1(X2))
| ~ r1(X1,X2)
| ~ r1(sK0,X1) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_49,plain,
! [X0: $i] : r1(X0,X0),
inference(cnf_transformation,[],[f15]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( r1(X0,X2)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_51,negated_conjecture,
! [X0: $i,X1: $i] :
( r1(X1,sK1(X1))
| ~ r1(sK0,X0)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_53,negated_conjecture,
! [X0: $i,X1: $i] :
( p2(sK1(X1))
| ~ r1(sK0,X0)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_56,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p2(X2)
| r1(X3,sK4(X3))
| ~ p2(X1)
| ~ r1(sK0,X0)
| ~ r1(X1,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_57,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( p2(X4)
| ~ p2(X3)
| ~ p2(X1)
| ~ r1(sK0,X2)
| ~ r1(X3,X4)
| ~ r1(X3,X0)
| ~ r1(X2,X3)
| ~ r1(sK4(X0),X1) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_69,negated_conjecture,
r1(sK0,sK10),
inference(cnf_transformation,[],[f21]) ).
tcf(c_70,negated_conjecture,
! [X0: $i] :
( r1(X0,sK11(X0))
| ~ r1(sK10,X0) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_71,negated_conjecture,
! [X0: $i] :
( ~ p2(sK11(X0))
| ~ r1(sK10,X0) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_74,plain,
r1(sK0,sK0),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_288,negated_conjecture,
! [X0: $i] :
( ~ p2(sK11(X0))
| ~ r1(sK10,X0) ),
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_289,negated_conjecture,
! [X0: $i] :
( r1(X0,sK11(X0))
| ~ r1(sK10,X0) ),
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_310,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( p2(X4)
| ~ p2(X3)
| ~ p2(X1)
| ~ r1(sK0,X2)
| ~ r1(X3,X4)
| ~ r1(X3,X0)
| ~ r1(X2,X3)
| ~ r1(sK4(X0),X1) ),
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_311,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p2(X2)
| r1(X3,sK4(X3))
| ~ p2(X1)
| ~ r1(sK0,X0)
| ~ r1(X1,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(demodulation,[status(thm)],[c_56]) ).
tcf(c_314,negated_conjecture,
! [X0: $i,X1: $i] :
( p2(sK1(X1))
| ~ r1(sK0,X0)
| ~ r1(X0,X1) ),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_316,negated_conjecture,
! [X0: $i,X1: $i] :
( r1(X1,sK1(X1))
| ~ r1(sK0,X0)
| ~ r1(X0,X1) ),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_320,plain,
! [X0: $i] :
( r1(sK10,sK1(sK10))
| ~ r1(sK0,X0)
| ~ r1(X0,sK10) ),
inference(instantiation,[status(thm)],[c_316]) ).
tcf(c_321,plain,
( r1(sK1(sK10),sK11(sK1(sK10)))
| ~ r1(sK10,sK1(sK10)) ),
inference(instantiation,[status(thm)],[c_289]) ).
tcf(c_322,plain,
( ~ p2(sK11(sK1(sK10)))
| ~ r1(sK10,sK1(sK10)) ),
inference(instantiation,[status(thm)],[c_288]) ).
tcf(c_323,plain,
( r1(sK10,sK1(sK10))
| ~ r1(sK0,sK10)
| ~ r1(sK0,sK0) ),
inference(instantiation,[status(thm)],[c_320]) ).
tcf(c_328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p2(X1)
| r1(X2,sK4(X2))
| ~ p2(sK1(X0))
| ~ r1(sK0,X3)
| ~ r1(X3,sK1(X0))
| ~ r1(sK1(X0),X2)
| ~ r1(sK1(X0),X1) ),
inference(instantiation,[status(thm)],[c_311]) ).
tcf(c_330,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( p2(X4)
| ~ p2(X3)
| ~ p2(sK1(X1))
| ~ r1(sK0,X2)
| ~ r1(X3,X4)
| ~ r1(X3,X0)
| ~ r1(X2,X3)
| ~ r1(sK4(X0),sK1(X1)) ),
inference(instantiation,[status(thm)],[c_310]) ).
tcf(c_386,plain,
! [X0: $i,X1: $i] :
( p2(sK11(sK1(sK10)))
| r1(X0,sK4(X0))
| ~ p2(sK1(sK10))
| ~ r1(sK0,X1)
| ~ r1(X1,sK1(sK10))
| ~ r1(sK1(sK10),X0)
| ~ r1(sK1(sK10),sK11(sK1(sK10))) ),
inference(instantiation,[status(thm)],[c_328]) ).
tcf(c_388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( p2(X3)
| ~ p2(sK1(X2))
| ~ p2(sK1(X1))
| ~ r1(sK0,X4)
| ~ r1(X4,sK1(X2))
| ~ r1(sK1(X2),X3)
| ~ r1(sK1(X2),X0)
| ~ r1(sK4(X0),sK1(X1)) ),
inference(instantiation,[status(thm)],[c_330]) ).
tcf(c_468,plain,
! [X0: $i,X1: $i,X2: $i] :
( p2(X1)
| ~ p2(sK1(sK10))
| ~ p2(sK1(X0))
| ~ r1(sK0,X2)
| ~ r1(X2,sK1(sK10))
| ~ r1(sK1(sK10),X1)
| ~ r1(sK1(sK10),sK11(sK1(sK10)))
| ~ r1(sK4(sK11(sK1(sK10))),sK1(X0)) ),
inference(instantiation,[status(thm)],[c_388]) ).
tcf(c_556,plain,
! [X0: $i] :
( p2(sK1(sK10))
| ~ r1(sK0,X0)
| ~ r1(X0,sK10) ),
inference(instantiation,[status(thm)],[c_314]) ).
tcf(c_557,plain,
( p2(sK1(sK10))
| ~ r1(sK0,sK10)
| ~ r1(sK0,sK0) ),
inference(instantiation,[status(thm)],[c_556]) ).
tcf(c_755,plain,
! [X0: $i] :
( p2(sK11(sK1(sK10)))
| r1(sK11(sK1(sK10)),sK4(sK11(sK1(sK10))))
| ~ p2(sK1(sK10))
| ~ r1(sK0,X0)
| ~ r1(X0,sK1(sK10))
| ~ r1(sK1(sK10),sK11(sK1(sK10))) ),
inference(instantiation,[status(thm)],[c_386]) ).
tcf(c_756,plain,
( p2(sK11(sK1(sK10)))
| r1(sK11(sK1(sK10)),sK4(sK11(sK1(sK10))))
| ~ p2(sK1(sK10))
| ~ r1(sK0,sK0)
| ~ r1(sK0,sK1(sK10))
| ~ r1(sK1(sK10),sK11(sK1(sK10))) ),
inference(instantiation,[status(thm)],[c_755]) ).
tcf(c_862,plain,
! [X0: $i] :
( r1(sK0,sK1(sK10))
| ~ r1(sK0,X0)
| ~ r1(X0,sK1(sK10)) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_960,plain,
! [X0: $i,X1: $i] :
( p2(sK11(sK1(sK10)))
| ~ p2(sK1(sK10))
| ~ p2(sK1(X0))
| ~ r1(sK0,X1)
| ~ r1(X1,sK1(sK10))
| ~ r1(sK1(sK10),sK11(sK1(sK10)))
| ~ r1(sK4(sK11(sK1(sK10))),sK1(X0)) ),
inference(instantiation,[status(thm)],[c_468]) ).
tcf(c_1566,plain,
! [X0: $i,X1: $i] :
( r1(X1,sK11(sK1(sK10)))
| ~ r1(X1,X0)
| ~ r1(X0,sK11(sK1(sK10))) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_2537,plain,
! [X0: $i] :
( p2(sK11(sK1(sK10)))
| ~ p2(sK1(sK10))
| ~ r1(sK0,sK10)
| ~ p2(sK1(X0))
| ~ r1(sK10,sK1(sK10))
| ~ r1(sK1(sK10),sK11(sK1(sK10)))
| ~ r1(sK4(sK11(sK1(sK10))),sK1(X0)) ),
inference(instantiation,[status(thm)],[c_960]) ).
tcf(c_3347,plain,
( r1(sK0,sK1(sK10))
| ~ r1(sK0,sK10)
| ~ r1(sK10,sK1(sK10)) ),
inference(instantiation,[status(thm)],[c_862]) ).
tcf(c_3391,plain,
! [X0: $i] :
( r1(sK4(sK11(sK1(sK10))),sK1(sK4(sK11(sK1(sK10)))))
| ~ r1(sK0,X0)
| ~ r1(X0,sK4(sK11(sK1(sK10)))) ),
inference(instantiation,[status(thm)],[c_316]) ).
tcf(c_3680,plain,
! [X0: $i] :
( p2(sK1(sK4(sK11(sK1(sK10)))))
| ~ r1(sK0,X0)
| ~ r1(X0,sK4(sK11(sK1(sK10)))) ),
inference(instantiation,[status(thm)],[c_314]) ).
tcf(c_3685,plain,
( r1(sK4(sK11(sK1(sK10))),sK1(sK4(sK11(sK1(sK10)))))
| ~ r1(sK0,sK11(sK1(sK10)))
| ~ r1(sK11(sK1(sK10)),sK4(sK11(sK1(sK10)))) ),
inference(instantiation,[status(thm)],[c_3391]) ).
tcf(c_5992,plain,
! [X0: $i] :
( r1(X0,sK11(sK1(sK10)))
| ~ r1(X0,sK1(sK10))
| ~ r1(sK1(sK10),sK11(sK1(sK10))) ),
inference(instantiation,[status(thm)],[c_1566]) ).
tcf(c_5993,plain,
( r1(sK0,sK11(sK1(sK10)))
| ~ r1(sK0,sK1(sK10))
| ~ r1(sK1(sK10),sK11(sK1(sK10))) ),
inference(instantiation,[status(thm)],[c_5992]) ).
tcf(c_10260,plain,
( p2(sK1(sK4(sK11(sK1(sK10)))))
| ~ r1(sK0,sK11(sK1(sK10)))
| ~ r1(sK11(sK1(sK10)),sK4(sK11(sK1(sK10)))) ),
inference(instantiation,[status(thm)],[c_3680]) ).
tcf(c_13275,plain,
( p2(sK11(sK1(sK10)))
| ~ p2(sK1(sK10))
| ~ r1(sK0,sK10)
| ~ r1(sK10,sK1(sK10))
| ~ p2(sK1(sK4(sK11(sK1(sK10)))))
| ~ r1(sK1(sK10),sK11(sK1(sK10)))
| ~ r1(sK4(sK11(sK1(sK10))),sK1(sK4(sK11(sK1(sK10))))) ),
inference(instantiation,[status(thm)],[c_2537]) ).
tcf(c_13277,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_13275,c_10260,c_5993,c_3685,c_3347,c_756,c_557,c_321,c_322,c_323,c_74,c_69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL688+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
% 0.12/5.38 % Computer : n005.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Thu Sep 24 00:21:08 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.43 Running first-order theorem proving
% 0.16/5.43 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
% 0.16/5.44
% 0.16/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.44
% 0.16/5.44 % Detected problem language: tptp
% 0.16/5.45 % Proving...
% 4.42/6.32 % SZS status Started for theBenchmark.p
% 4.42/6.32 % SZS status Theorem for theBenchmark.p
% 4.42/6.32
% 4.42/6.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.42/6.32
% 4.42/6.32 % ------ iProver source info
% 4.42/6.32
% 4.42/6.32 % git: date: 2026-07-19 20:42:38 +0200
% 4.42/6.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.42/6.32 % git: non_committed_changes: false
% 4.42/6.32
% 4.42/6.32 % ------ Parsing...
% 4.42/6.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.42/6.32
% 4.42/6.32 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.42/6.32
% 4.42/6.32 % ------ Preprocessing... gs_s sp: 8 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.42/6.32 % ------ Proving...
% 4.42/6.32 % ------ Problem Properties
% 4.42/6.32
% 4.42/6.32 %
% 4.42/6.32 % clauses 28
% 4.42/6.32 % conjectures 26
% 4.42/6.32 % EPR 15
% 4.42/6.32 % Horn 20
% 4.42/6.32 % unary 6
% 4.42/6.32 % binary 3
% 4.42/6.32 % lits 93
% 4.42/6.32 % lits eq 0
% 4.42/6.32 % fd_pure 0
% 4.42/6.32 % fd_pseudo 0
% 4.42/6.32 % fd_cond 0
% 4.42/6.32 % fd_pseudo_cond 0
% 4.42/6.32 % AC symbols 0
% 4.42/6.32
% 4.42/6.32 % ------ Schedule dynamic 5 is on
% 4.42/6.32
% 4.42/6.32 % ------ no equalities: superposition off
% 4.42/6.32
% 4.42/6.32 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.42/6.32
% 4.42/6.32
% 4.42/6.32 % ------
% 4.42/6.32 % Current options:
% 4.42/6.32 % ------
% 4.42/6.32
% 4.42/6.32
% 4.42/6.32 %
% 4.42/6.32
% 4.42/6.32 % ------ Proving...
% 4.42/6.32 %
% 4.42/6.32
% 4.42/6.32 % SZS status Theorem for theBenchmark.p
% 4.42/6.32
% 4.42/6.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.42/6.32
% 4.42/6.32
%------------------------------------------------------------------------------