%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT034+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 : Tue Sep 29 09:36:47 AM UTC 2026
% Result : Theorem 7.28s 1.59s
% Output : Refutation 8.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 41
% Syntax : Number of formulae : 232 ( 61 unt; 28 def)
% Number of atoms : 990 ( 167 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 1251 ( 493 ~; 485 |; 198 &)
% ( 24 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 5 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 8 prp; 0-5 aty)
% Number of functors : 49 ( 49 usr; 17 con; 0-7 aty)
% Number of variables : 354 ( 0 sgn 300 !; 54 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( v2_cat_1(X0)
& l1_cat_1(X0) )
=> ! [X1] :
( m1_subset_1(X1,u2_cat_1(X0))
=> m1_subset_1(k4_tarski(k4_tarski(k2_yoneda_1(X0,k3_cat_1(X0,X1)),k2_yoneda_1(X0,k2_cat_1(X0,X1))),k3_yoneda_1(X0,X1)),u2_cat_1(k12_nattra_1(X0,k1_yoneda_1(X0)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_yoneda_1) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( v2_cat_1(X0)
& l1_cat_1(X0) )
=> ! [X1] :
( m1_subset_1(X1,u2_cat_1(X0))
=> m1_subset_1(k4_tarski(k4_tarski(k2_yoneda_1(X0,k3_cat_1(X0,X1)),k2_yoneda_1(X0,k2_cat_1(X0,X1))),k3_yoneda_1(X0,X1)),u2_cat_1(k12_nattra_1(X0,k1_yoneda_1(X0)))) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f9,axiom,
! [X0] :
( ( v2_cat_1(X0)
& l1_cat_1(X0) )
=> ! [X1] :
( ( v2_cat_1(X1)
& l1_cat_1(X1) )
=> ! [X2] :
( m4_nattra_1(X2,X0,X1)
=> ( X2 = k11_nattra_1(X0,X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ? [X4] :
( m2_cat_1(X4,X0,X1)
& ? [X5] :
( m2_cat_1(X5,X0,X1)
& ? [X6] :
( m2_nattra_1(X6,X0,X1,X4,X5)
& X3 = k4_tarski(k4_tarski(X4,X5),X6)
& r2_nattra_1(X0,X1,X4,X5) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_nattra_1) ).
fof(f10,axiom,
! [X0] :
( ( v2_cat_1(X0)
& l1_cat_1(X0) )
=> ! [X1] :
( ( v2_cat_1(X1)
& l1_cat_1(X1) )
=> ! [X2] :
( ( v1_cat_1(X2)
& v2_cat_1(X2)
& l1_cat_1(X2) )
=> ( X2 = k12_nattra_1(X0,X1)
<=> ( u1_cat_1(X2) = k7_cat_2(X0,X1)
& u2_cat_1(X2) = k11_nattra_1(X0,X1)
& ! [X3] :
( m1_subset_1(X3,u2_cat_1(X2))
=> ( k2_cat_1(X2,X3) = k1_mcart_1(k1_mcart_1(X3))
& k3_cat_1(X2,X3) = k2_mcart_1(k1_mcart_1(X3)) ) )
& ! [X3] :
( m1_subset_1(X3,u2_cat_1(X2))
=> ! [X4] :
( m1_subset_1(X4,u2_cat_1(X2))
=> ( k2_cat_1(X2,X4) = k3_cat_1(X2,X3)
=> r2_hidden(k13_cat_2(X2,X2,X4,X3),k1_relat_1(u5_cat_1(X2))) ) ) )
& ! [X3] :
( m1_subset_1(X3,u2_cat_1(X2))
=> ! [X4] :
( m1_subset_1(X4,u2_cat_1(X2))
=> ~ ( r2_hidden(k13_cat_2(X2,X2,X4,X3),k1_relat_1(u5_cat_1(X2)))
& ! [X5] :
( m2_cat_1(X5,X0,X1)
=> ! [X6] :
( m2_cat_1(X6,X0,X1)
=> ! [X7] :
( m2_cat_1(X7,X0,X1)
=> ! [X8] :
( m2_nattra_1(X8,X0,X1,X5,X6)
=> ! [X9] :
( m2_nattra_1(X9,X0,X1,X6,X7)
=> ~ ( X3 = k4_tarski(k4_tarski(X5,X6),X8)
& X4 = k4_tarski(k4_tarski(X6,X7),X9)
& k1_funct_1(u5_cat_1(X2),k13_cat_2(X2,X2,X4,X3)) = k4_tarski(k4_tarski(X5,X7),k8_nattra_1(X0,X1,X5,X6,X7,X8,X9)) ) ) ) ) ) ) ) ) )
& ! [X3] :
( m1_subset_1(X3,u1_cat_1(X2))
=> ! [X4] :
( m2_cat_1(X4,X0,X1)
=> ( X4 = X3
=> k10_cat_1(X2,X3) = k4_tarski(k4_tarski(X4,X4),k7_nattra_1(X0,X1,X4)) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d18_nattra_1) ).
fof(f13,axiom,
! [X0,X1] : k4_tarski(X0,X1) = k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f17,axiom,
! [X0,X1] :
( ( v2_cat_1(X0)
& l1_cat_1(X0)
& v2_cat_1(X1)
& l1_cat_1(X1) )
=> m4_nattra_1(k11_nattra_1(X0,X1),X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_nattra_1) ).
fof(f19,axiom,
! [X0,X1] :
( ( v2_cat_1(X0)
& l1_cat_1(X0)
& v2_cat_1(X1)
& l1_cat_1(X1) )
=> ( v1_cat_1(k12_nattra_1(X0,X1))
& v2_cat_1(k12_nattra_1(X0,X1))
& l1_cat_1(k12_nattra_1(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_nattra_1) ).
fof(f27,axiom,
! [X0] :
( ( v2_cat_1(X0)
& l1_cat_1(X0) )
=> ( v2_cat_1(k1_yoneda_1(X0))
& l1_cat_1(k1_yoneda_1(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_yoneda_1) ).
fof(f30,axiom,
! [X0,X1] :
( ( l1_cat_1(X0)
& m1_subset_1(X1,u2_cat_1(X0)) )
=> m1_subset_1(k2_cat_1(X0,X1),u1_cat_1(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_cat_1) ).
fof(f34,axiom,
! [X0,X1] :
( ( v2_cat_1(X0)
& l1_cat_1(X0)
& m1_subset_1(X1,u1_cat_1(X0)) )
=> m2_cat_1(k2_yoneda_1(X0,X1),X0,k1_yoneda_1(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_yoneda_1) ).
fof(f36,axiom,
! [X0,X1] :
( ( l1_cat_1(X0)
& m1_subset_1(X1,u2_cat_1(X0)) )
=> m1_subset_1(k3_cat_1(X0,X1),u1_cat_1(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_cat_1) ).
fof(f37,axiom,
! [X0,X1] :
( ( v2_cat_1(X0)
& l1_cat_1(X0)
& m1_subset_1(X1,u2_cat_1(X0)) )
=> m2_nattra_1(k3_yoneda_1(X0,X1),X0,k1_yoneda_1(X0),k2_yoneda_1(X0,k3_cat_1(X0,X1)),k2_yoneda_1(X0,k2_cat_1(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_yoneda_1) ).
fof(f89,axiom,
! [X0,X1] :
( r2_hidden(X0,X1)
=> m1_subset_1(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f92,axiom,
! [X0] :
( ( v2_cat_1(X0)
& l1_cat_1(X0) )
=> ! [X1] :
( m1_subset_1(X1,u2_cat_1(X0))
=> r2_nattra_1(X0,k1_yoneda_1(X0),k2_yoneda_1(X0,k3_cat_1(X0,X1)),k2_yoneda_1(X0,k2_cat_1(X0,X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_yoneda_1) ).
fof(f98,plain,
! [X0] :
( ( v2_cat_1(X0)
& l1_cat_1(X0) )
=> ! [X1] :
( ( v2_cat_1(X1)
& l1_cat_1(X1) )
=> ! [X2] :
( ( v1_cat_1(X2)
& v2_cat_1(X2)
& l1_cat_1(X2) )
=> ( X2 = k12_nattra_1(X0,X1)
<=> ( u1_cat_1(X2) = k7_cat_2(X0,X1)
& u2_cat_1(X2) = k11_nattra_1(X0,X1)
& ! [X3] :
( m1_subset_1(X3,u2_cat_1(X2))
=> ( k2_cat_1(X2,X3) = k1_mcart_1(k1_mcart_1(X3))
& k3_cat_1(X2,X3) = k2_mcart_1(k1_mcart_1(X3)) ) )
& ! [X4] :
( m1_subset_1(X4,u2_cat_1(X2))
=> ! [X5] :
( m1_subset_1(X5,u2_cat_1(X2))
=> ( k3_cat_1(X2,X4) = k2_cat_1(X2,X5)
=> r2_hidden(k13_cat_2(X2,X2,X5,X4),k1_relat_1(u5_cat_1(X2))) ) ) )
& ! [X6] :
( m1_subset_1(X6,u2_cat_1(X2))
=> ! [X7] :
( m1_subset_1(X7,u2_cat_1(X2))
=> ~ ( r2_hidden(k13_cat_2(X2,X2,X7,X6),k1_relat_1(u5_cat_1(X2)))
& ! [X8] :
( m2_cat_1(X8,X0,X1)
=> ! [X9] :
( m2_cat_1(X9,X0,X1)
=> ! [X10] :
( m2_cat_1(X10,X0,X1)
=> ! [X11] :
( m2_nattra_1(X11,X0,X1,X8,X9)
=> ! [X12] :
( m2_nattra_1(X12,X0,X1,X9,X10)
=> ~ ( k4_tarski(k4_tarski(X8,X9),X11) = X6
& k4_tarski(k4_tarski(X9,X10),X12) = X7
& k1_funct_1(u5_cat_1(X2),k13_cat_2(X2,X2,X7,X6)) = k4_tarski(k4_tarski(X8,X10),k8_nattra_1(X0,X1,X8,X9,X10,X11,X12)) ) ) ) ) ) ) ) ) )
& ! [X13] :
( m1_subset_1(X13,u1_cat_1(X2))
=> ! [X14] :
( m2_cat_1(X14,X0,X1)
=> ( X13 = X14
=> k10_cat_1(X2,X13) = k4_tarski(k4_tarski(X14,X14),k7_nattra_1(X0,X1,X14)) ) ) ) ) ) ) ) ),
inference(rectify,[],[f10]) ).
fof(f103,plain,
? [X0] :
( ? [X1] :
( ~ m1_subset_1(k4_tarski(k4_tarski(k2_yoneda_1(X0,k3_cat_1(X0,X1)),k2_yoneda_1(X0,k2_cat_1(X0,X1))),k3_yoneda_1(X0,X1)),u2_cat_1(k12_nattra_1(X0,k1_yoneda_1(X0))))
& m1_subset_1(X1,u2_cat_1(X0)) )
& v2_cat_1(X0)
& l1_cat_1(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f104,plain,
? [X0] :
( ? [X1] :
( ~ m1_subset_1(k4_tarski(k4_tarski(k2_yoneda_1(X0,k3_cat_1(X0,X1)),k2_yoneda_1(X0,k2_cat_1(X0,X1))),k3_yoneda_1(X0,X1)),u2_cat_1(k12_nattra_1(X0,k1_yoneda_1(X0))))
& m1_subset_1(X1,u2_cat_1(X0)) )
& v2_cat_1(X0)
& l1_cat_1(X0) ),
inference(flattening,[],[f103]) ).
fof(f112,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = k11_nattra_1(X0,X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ? [X4] :
( m2_cat_1(X4,X0,X1)
& ? [X5] :
( m2_cat_1(X5,X0,X1)
& ? [X6] :
( m2_nattra_1(X6,X0,X1,X4,X5)
& X3 = k4_tarski(k4_tarski(X4,X5),X6)
& r2_nattra_1(X0,X1,X4,X5) ) ) ) ) )
| ~ m4_nattra_1(X2,X0,X1) )
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) )
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f113,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = k11_nattra_1(X0,X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ? [X4] :
( m2_cat_1(X4,X0,X1)
& ? [X5] :
( m2_cat_1(X5,X0,X1)
& ? [X6] :
( m2_nattra_1(X6,X0,X1,X4,X5)
& X3 = k4_tarski(k4_tarski(X4,X5),X6)
& r2_nattra_1(X0,X1,X4,X5) ) ) ) ) )
| ~ m4_nattra_1(X2,X0,X1) )
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) )
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(flattening,[],[f112]) ).
fof(f114,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = k12_nattra_1(X0,X1)
<=> ( u1_cat_1(X2) = k7_cat_2(X0,X1)
& u2_cat_1(X2) = k11_nattra_1(X0,X1)
& ! [X3] :
( ( k2_cat_1(X2,X3) = k1_mcart_1(k1_mcart_1(X3))
& k3_cat_1(X2,X3) = k2_mcart_1(k1_mcart_1(X3)) )
| ~ m1_subset_1(X3,u2_cat_1(X2)) )
& ! [X4] :
( ! [X5] :
( r2_hidden(k13_cat_2(X2,X2,X5,X4),k1_relat_1(u5_cat_1(X2)))
| k3_cat_1(X2,X4) != k2_cat_1(X2,X5)
| ~ m1_subset_1(X5,u2_cat_1(X2)) )
| ~ m1_subset_1(X4,u2_cat_1(X2)) )
& ! [X6] :
( ! [X7] :
( ~ r2_hidden(k13_cat_2(X2,X2,X7,X6),k1_relat_1(u5_cat_1(X2)))
| ? [X8] :
( ? [X9] :
( ? [X10] :
( ? [X11] :
( ? [X12] :
( k4_tarski(k4_tarski(X8,X9),X11) = X6
& k4_tarski(k4_tarski(X9,X10),X12) = X7
& k1_funct_1(u5_cat_1(X2),k13_cat_2(X2,X2,X7,X6)) = k4_tarski(k4_tarski(X8,X10),k8_nattra_1(X0,X1,X8,X9,X10,X11,X12))
& m2_nattra_1(X12,X0,X1,X9,X10) )
& m2_nattra_1(X11,X0,X1,X8,X9) )
& m2_cat_1(X10,X0,X1) )
& m2_cat_1(X9,X0,X1) )
& m2_cat_1(X8,X0,X1) )
| ~ m1_subset_1(X7,u2_cat_1(X2)) )
| ~ m1_subset_1(X6,u2_cat_1(X2)) )
& ! [X13] :
( ! [X14] :
( k10_cat_1(X2,X13) = k4_tarski(k4_tarski(X14,X14),k7_nattra_1(X0,X1,X14))
| X13 != X14
| ~ m2_cat_1(X14,X0,X1) )
| ~ m1_subset_1(X13,u1_cat_1(X2)) ) ) )
| ~ v1_cat_1(X2)
| ~ v2_cat_1(X2)
| ~ l1_cat_1(X2) )
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) )
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f115,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = k12_nattra_1(X0,X1)
<=> ( u1_cat_1(X2) = k7_cat_2(X0,X1)
& u2_cat_1(X2) = k11_nattra_1(X0,X1)
& ! [X3] :
( ( k2_cat_1(X2,X3) = k1_mcart_1(k1_mcart_1(X3))
& k3_cat_1(X2,X3) = k2_mcart_1(k1_mcart_1(X3)) )
| ~ m1_subset_1(X3,u2_cat_1(X2)) )
& ! [X4] :
( ! [X5] :
( r2_hidden(k13_cat_2(X2,X2,X5,X4),k1_relat_1(u5_cat_1(X2)))
| k3_cat_1(X2,X4) != k2_cat_1(X2,X5)
| ~ m1_subset_1(X5,u2_cat_1(X2)) )
| ~ m1_subset_1(X4,u2_cat_1(X2)) )
& ! [X6] :
( ! [X7] :
( ~ r2_hidden(k13_cat_2(X2,X2,X7,X6),k1_relat_1(u5_cat_1(X2)))
| ? [X8] :
( ? [X9] :
( ? [X10] :
( ? [X11] :
( ? [X12] :
( k4_tarski(k4_tarski(X8,X9),X11) = X6
& k4_tarski(k4_tarski(X9,X10),X12) = X7
& k1_funct_1(u5_cat_1(X2),k13_cat_2(X2,X2,X7,X6)) = k4_tarski(k4_tarski(X8,X10),k8_nattra_1(X0,X1,X8,X9,X10,X11,X12))
& m2_nattra_1(X12,X0,X1,X9,X10) )
& m2_nattra_1(X11,X0,X1,X8,X9) )
& m2_cat_1(X10,X0,X1) )
& m2_cat_1(X9,X0,X1) )
& m2_cat_1(X8,X0,X1) )
| ~ m1_subset_1(X7,u2_cat_1(X2)) )
| ~ m1_subset_1(X6,u2_cat_1(X2)) )
& ! [X13] :
( ! [X14] :
( k10_cat_1(X2,X13) = k4_tarski(k4_tarski(X14,X14),k7_nattra_1(X0,X1,X14))
| X13 != X14
| ~ m2_cat_1(X14,X0,X1) )
| ~ m1_subset_1(X13,u1_cat_1(X2)) ) ) )
| ~ v1_cat_1(X2)
| ~ v2_cat_1(X2)
| ~ l1_cat_1(X2) )
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) )
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(flattening,[],[f114]) ).
fof(f126,plain,
! [X0,X1] :
( m4_nattra_1(k11_nattra_1(X0,X1),X0,X1)
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f127,plain,
! [X0,X1] :
( m4_nattra_1(k11_nattra_1(X0,X1),X0,X1)
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) ),
inference(flattening,[],[f126]) ).
fof(f129,plain,
! [X0,X1] :
( ( v1_cat_1(k12_nattra_1(X0,X1))
& v2_cat_1(k12_nattra_1(X0,X1))
& l1_cat_1(k12_nattra_1(X0,X1)) )
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f130,plain,
! [X0,X1] :
( ( v1_cat_1(k12_nattra_1(X0,X1))
& v2_cat_1(k12_nattra_1(X0,X1))
& l1_cat_1(k12_nattra_1(X0,X1)) )
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) ),
inference(flattening,[],[f129]) ).
fof(f133,plain,
! [X0] :
( ( v2_cat_1(k1_yoneda_1(X0))
& l1_cat_1(k1_yoneda_1(X0)) )
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f134,plain,
! [X0] :
( ( v2_cat_1(k1_yoneda_1(X0))
& l1_cat_1(k1_yoneda_1(X0)) )
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(flattening,[],[f133]) ).
fof(f137,plain,
! [X0,X1] :
( m1_subset_1(k2_cat_1(X0,X1),u1_cat_1(X0))
| ~ l1_cat_1(X0)
| ~ m1_subset_1(X1,u2_cat_1(X0)) ),
inference(ennf_transformation,[],[f30]) ).
fof(f138,plain,
! [X0,X1] :
( m1_subset_1(k2_cat_1(X0,X1),u1_cat_1(X0))
| ~ l1_cat_1(X0)
| ~ m1_subset_1(X1,u2_cat_1(X0)) ),
inference(flattening,[],[f137]) ).
fof(f139,plain,
! [X0,X1] :
( m2_cat_1(k2_yoneda_1(X0,X1),X0,k1_yoneda_1(X0))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| ~ m1_subset_1(X1,u1_cat_1(X0)) ),
inference(ennf_transformation,[],[f34]) ).
fof(f140,plain,
! [X0,X1] :
( m2_cat_1(k2_yoneda_1(X0,X1),X0,k1_yoneda_1(X0))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| ~ m1_subset_1(X1,u1_cat_1(X0)) ),
inference(flattening,[],[f139]) ).
fof(f141,plain,
! [X0,X1] :
( m1_subset_1(k3_cat_1(X0,X1),u1_cat_1(X0))
| ~ l1_cat_1(X0)
| ~ m1_subset_1(X1,u2_cat_1(X0)) ),
inference(ennf_transformation,[],[f36]) ).
fof(f142,plain,
! [X0,X1] :
( m1_subset_1(k3_cat_1(X0,X1),u1_cat_1(X0))
| ~ l1_cat_1(X0)
| ~ m1_subset_1(X1,u2_cat_1(X0)) ),
inference(flattening,[],[f141]) ).
fof(f143,plain,
! [X0,X1] :
( m2_nattra_1(k3_yoneda_1(X0,X1),X0,k1_yoneda_1(X0),k2_yoneda_1(X0,k3_cat_1(X0,X1)),k2_yoneda_1(X0,k2_cat_1(X0,X1)))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| ~ m1_subset_1(X1,u2_cat_1(X0)) ),
inference(ennf_transformation,[],[f37]) ).
fof(f144,plain,
! [X0,X1] :
( m2_nattra_1(k3_yoneda_1(X0,X1),X0,k1_yoneda_1(X0),k2_yoneda_1(X0,k3_cat_1(X0,X1)),k2_yoneda_1(X0,k2_cat_1(X0,X1)))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| ~ m1_subset_1(X1,u2_cat_1(X0)) ),
inference(flattening,[],[f143]) ).
fof(f204,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f89]) ).
fof(f208,plain,
! [X0] :
( ! [X1] :
( r2_nattra_1(X0,k1_yoneda_1(X0),k2_yoneda_1(X0,k3_cat_1(X0,X1)),k2_yoneda_1(X0,k2_cat_1(X0,X1)))
| ~ m1_subset_1(X1,u2_cat_1(X0)) )
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(ennf_transformation,[],[f92]) ).
fof(f209,plain,
! [X0] :
( ! [X1] :
( r2_nattra_1(X0,k1_yoneda_1(X0),k2_yoneda_1(X0,k3_cat_1(X0,X1)),k2_yoneda_1(X0,k2_cat_1(X0,X1)))
| ~ m1_subset_1(X1,u2_cat_1(X0)) )
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(flattening,[],[f208]) ).
fof(f216,definition,
! [X1,X0,X2] :
( sP0(X1,X0,X2)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ? [X4] :
( m2_cat_1(X4,X0,X1)
& ? [X5] :
( m2_cat_1(X5,X0,X1)
& ? [X6] :
( m2_nattra_1(X6,X0,X1,X4,X5)
& X3 = k4_tarski(k4_tarski(X4,X5),X6)
& r2_nattra_1(X0,X1,X4,X5) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f217,definition,
! [X2,X0,X1] :
( ( X2 = k11_nattra_1(X0,X1)
<=> sP0(X1,X0,X2) )
| ~ sP1(X2,X0,X1) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f218,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( sP1(X2,X0,X1)
| ~ m4_nattra_1(X2,X0,X1) )
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) )
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(definition_folding,[],[f113,f217,f216]) ).
fof(f219,definition,
! [X1,X0,X2] :
( sP2(X1,X0,X2)
<=> ! [X13] :
( ! [X14] :
( k10_cat_1(X2,X13) = k4_tarski(k4_tarski(X14,X14),k7_nattra_1(X0,X1,X14))
| X13 != X14
| ~ m2_cat_1(X14,X0,X1) )
| ~ m1_subset_1(X13,u1_cat_1(X2)) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f220,definition,
! [X2,X1,X0] :
( sP3(X2,X1,X0)
<=> ! [X6] :
( ! [X7] :
( ~ r2_hidden(k13_cat_2(X2,X2,X7,X6),k1_relat_1(u5_cat_1(X2)))
| ? [X8] :
( ? [X9] :
( ? [X10] :
( ? [X11] :
( ? [X12] :
( k4_tarski(k4_tarski(X8,X9),X11) = X6
& k4_tarski(k4_tarski(X9,X10),X12) = X7
& k1_funct_1(u5_cat_1(X2),k13_cat_2(X2,X2,X7,X6)) = k4_tarski(k4_tarski(X8,X10),k8_nattra_1(X0,X1,X8,X9,X10,X11,X12))
& m2_nattra_1(X12,X0,X1,X9,X10) )
& m2_nattra_1(X11,X0,X1,X8,X9) )
& m2_cat_1(X10,X0,X1) )
& m2_cat_1(X9,X0,X1) )
& m2_cat_1(X8,X0,X1) )
| ~ m1_subset_1(X7,u2_cat_1(X2)) )
| ~ m1_subset_1(X6,u2_cat_1(X2)) ) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f221,definition,
! [X1,X0,X2] :
( sP4(X1,X0,X2)
<=> ( u1_cat_1(X2) = k7_cat_2(X0,X1)
& u2_cat_1(X2) = k11_nattra_1(X0,X1)
& ! [X3] :
( ( k2_cat_1(X2,X3) = k1_mcart_1(k1_mcart_1(X3))
& k3_cat_1(X2,X3) = k2_mcart_1(k1_mcart_1(X3)) )
| ~ m1_subset_1(X3,u2_cat_1(X2)) )
& ! [X4] :
( ! [X5] :
( r2_hidden(k13_cat_2(X2,X2,X5,X4),k1_relat_1(u5_cat_1(X2)))
| k3_cat_1(X2,X4) != k2_cat_1(X2,X5)
| ~ m1_subset_1(X5,u2_cat_1(X2)) )
| ~ m1_subset_1(X4,u2_cat_1(X2)) )
& sP3(X2,X1,X0)
& sP2(X1,X0,X2) ) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f222,definition,
! [X2,X0,X1] :
( ( X2 = k12_nattra_1(X0,X1)
<=> sP4(X1,X0,X2) )
| ~ sP5(X2,X0,X1) ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f223,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( sP5(X2,X0,X1)
| ~ v1_cat_1(X2)
| ~ v2_cat_1(X2)
| ~ l1_cat_1(X2) )
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) )
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(definition_folding,[],[f115,f222,f221,f220,f219]) ).
fof(f224,plain,
( ~ m1_subset_1(k4_tarski(k4_tarski(k2_yoneda_1(sK6,k3_cat_1(sK6,sK7)),k2_yoneda_1(sK6,k2_cat_1(sK6,sK7))),k3_yoneda_1(sK6,sK7)),u2_cat_1(k12_nattra_1(sK6,k1_yoneda_1(sK6))))
& m1_subset_1(sK7,u2_cat_1(sK6))
& v2_cat_1(sK6)
& l1_cat_1(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f104]) ).
fof(f225,plain,
! [X2,X0,X1] :
( ( ( X2 = k11_nattra_1(X0,X1)
| ~ sP0(X1,X0,X2) )
& ( sP0(X1,X0,X2)
| k11_nattra_1(X0,X1) != X2 ) )
| ~ sP1(X2,X0,X1) ),
inference(nnf_transformation,[],[f217]) ).
fof(f226,plain,
! [X0,X1,X2] :
( ( ( k11_nattra_1(X1,X2) = X0
| ~ sP0(X2,X1,X0) )
& ( sP0(X2,X1,X0)
| k11_nattra_1(X1,X2) != X0 ) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f225]) ).
fof(f227,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( ! [X4] :
( ~ m2_cat_1(X4,X0,X1)
| ! [X5] :
( ~ m2_cat_1(X5,X0,X1)
| ! [X6] :
( ~ m2_nattra_1(X6,X0,X1,X4,X5)
| k4_tarski(k4_tarski(X4,X5),X6) != X3
| ~ r2_nattra_1(X0,X1,X4,X5) ) ) )
| ~ r2_hidden(X3,X2) )
& ( ? [X4] :
( m2_cat_1(X4,X0,X1)
& ? [X5] :
( m2_cat_1(X5,X0,X1)
& ? [X6] :
( m2_nattra_1(X6,X0,X1,X4,X5)
& X3 = k4_tarski(k4_tarski(X4,X5),X6)
& r2_nattra_1(X0,X1,X4,X5) ) ) )
| r2_hidden(X3,X2) ) ) )
& ( ! [X3] :
( ( r2_hidden(X3,X2)
| ! [X4] :
( ~ m2_cat_1(X4,X0,X1)
| ! [X5] :
( ~ m2_cat_1(X5,X0,X1)
| ! [X6] :
( ~ m2_nattra_1(X6,X0,X1,X4,X5)
| k4_tarski(k4_tarski(X4,X5),X6) != X3
| ~ r2_nattra_1(X0,X1,X4,X5) ) ) ) )
& ( ? [X4] :
( m2_cat_1(X4,X0,X1)
& ? [X5] :
( m2_cat_1(X5,X0,X1)
& ? [X6] :
( m2_nattra_1(X6,X0,X1,X4,X5)
& X3 = k4_tarski(k4_tarski(X4,X5),X6)
& r2_nattra_1(X0,X1,X4,X5) ) ) )
| ~ r2_hidden(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f216]) ).
fof(f228,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ! [X4] :
( ~ m2_cat_1(X4,X1,X0)
| ! [X5] :
( ~ m2_cat_1(X5,X1,X0)
| ! [X6] :
( ~ m2_nattra_1(X6,X1,X0,X4,X5)
| k4_tarski(k4_tarski(X4,X5),X6) != X3
| ~ r2_nattra_1(X1,X0,X4,X5) ) ) )
| ~ r2_hidden(X3,X2) )
& ( ? [X7] :
( m2_cat_1(X7,X1,X0)
& ? [X8] :
( m2_cat_1(X8,X1,X0)
& ? [X9] :
( m2_nattra_1(X9,X1,X0,X7,X8)
& k4_tarski(k4_tarski(X7,X8),X9) = X3
& r2_nattra_1(X1,X0,X7,X8) ) ) )
| r2_hidden(X3,X2) ) ) )
& ( ! [X10] :
( ( r2_hidden(X10,X2)
| ! [X11] :
( ~ m2_cat_1(X11,X1,X0)
| ! [X12] :
( ~ m2_cat_1(X12,X1,X0)
| ! [X13] :
( ~ m2_nattra_1(X13,X1,X0,X11,X12)
| k4_tarski(k4_tarski(X11,X12),X13) != X10
| ~ r2_nattra_1(X1,X0,X11,X12) ) ) ) )
& ( ? [X14] :
( m2_cat_1(X14,X1,X0)
& ? [X15] :
( m2_cat_1(X15,X1,X0)
& ? [X16] :
( m2_nattra_1(X16,X1,X0,X14,X15)
& k4_tarski(k4_tarski(X14,X15),X16) = X10
& r2_nattra_1(X1,X0,X14,X15) ) ) )
| ~ r2_hidden(X10,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f227]) ).
fof(f229,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ! [X4] :
( ~ m2_cat_1(X4,X1,X0)
| ! [X5] :
( ~ m2_cat_1(X5,X1,X0)
| ! [X6] :
( ~ m2_nattra_1(X6,X1,X0,X4,X5)
| k4_tarski(k4_tarski(X4,X5),X6) != sK8(X0,X1,X2)
| ~ r2_nattra_1(X1,X0,X4,X5) ) ) )
| ~ r2_hidden(sK8(X0,X1,X2),X2) )
& ( ( m2_cat_1(sK9(X0,X1,X2),X1,X0)
& m2_cat_1(sK10(X0,X1,X2),X1,X0)
& m2_nattra_1(sK11(X0,X1,X2),X1,X0,sK9(X0,X1,X2),sK10(X0,X1,X2))
& sK8(X0,X1,X2) = k4_tarski(k4_tarski(sK9(X0,X1,X2),sK10(X0,X1,X2)),sK11(X0,X1,X2))
& r2_nattra_1(X1,X0,sK9(X0,X1,X2),sK10(X0,X1,X2)) )
| r2_hidden(sK8(X0,X1,X2),X2) ) ) )
& ( ! [X10] :
( ( r2_hidden(X10,X2)
| ! [X11] :
( ~ m2_cat_1(X11,X1,X0)
| ! [X12] :
( ~ m2_cat_1(X12,X1,X0)
| ! [X13] :
( ~ m2_nattra_1(X13,X1,X0,X11,X12)
| k4_tarski(k4_tarski(X11,X12),X13) != X10
| ~ r2_nattra_1(X1,X0,X11,X12) ) ) ) )
& ( ( m2_cat_1(sK12(X0,X1,X10),X1,X0)
& m2_cat_1(sK13(X0,X1,X10),X1,X0)
& m2_nattra_1(sK14(X0,X1,X10),X1,X0,sK12(X0,X1,X10),sK13(X0,X1,X10))
& k4_tarski(k4_tarski(sK12(X0,X1,X10),sK13(X0,X1,X10)),sK14(X0,X1,X10)) = X10
& r2_nattra_1(X1,X0,sK12(X0,X1,X10),sK13(X0,X1,X10)) )
| ~ r2_hidden(X10,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12,sK13,sK14]),skolemize(X3,sK8(X0,X1,X2)),skolemize(X7,sK9(X0,X1,X2)),skolemize(X8,sK10(X0,X1,X2)),skolemize(X9,sK11(X0,X1,X2)),skolemize(X14,sK12(X0,X1,X10)),skolemize(X15,sK13(X0,X1,X10)),skolemize(X16,sK14(X0,X1,X10))],[f228]) ).
fof(f230,plain,
! [X2,X0,X1] :
( ( ( X2 = k12_nattra_1(X0,X1)
| ~ sP4(X1,X0,X2) )
& ( sP4(X1,X0,X2)
| k12_nattra_1(X0,X1) != X2 ) )
| ~ sP5(X2,X0,X1) ),
inference(nnf_transformation,[],[f222]) ).
fof(f231,plain,
! [X0,X1,X2] :
( ( ( k12_nattra_1(X1,X2) = X0
| ~ sP4(X2,X1,X0) )
& ( sP4(X2,X1,X0)
| k12_nattra_1(X1,X2) != X0 ) )
| ~ sP5(X0,X1,X2) ),
inference(rectify,[],[f230]) ).
fof(f232,plain,
! [X1,X0,X2] :
( ( sP4(X1,X0,X2)
| u1_cat_1(X2) != k7_cat_2(X0,X1)
| k11_nattra_1(X0,X1) != u2_cat_1(X2)
| ? [X3] :
( ( k2_cat_1(X2,X3) != k1_mcart_1(k1_mcart_1(X3))
| k3_cat_1(X2,X3) != k2_mcart_1(k1_mcart_1(X3)) )
& m1_subset_1(X3,u2_cat_1(X2)) )
| ? [X4] :
( ? [X5] :
( ~ r2_hidden(k13_cat_2(X2,X2,X5,X4),k1_relat_1(u5_cat_1(X2)))
& k3_cat_1(X2,X4) = k2_cat_1(X2,X5)
& m1_subset_1(X5,u2_cat_1(X2)) )
& m1_subset_1(X4,u2_cat_1(X2)) )
| ~ sP3(X2,X1,X0)
| ~ sP2(X1,X0,X2) )
& ( ( u1_cat_1(X2) = k7_cat_2(X0,X1)
& u2_cat_1(X2) = k11_nattra_1(X0,X1)
& ! [X3] :
( ( k2_cat_1(X2,X3) = k1_mcart_1(k1_mcart_1(X3))
& k3_cat_1(X2,X3) = k2_mcart_1(k1_mcart_1(X3)) )
| ~ m1_subset_1(X3,u2_cat_1(X2)) )
& ! [X4] :
( ! [X5] :
( r2_hidden(k13_cat_2(X2,X2,X5,X4),k1_relat_1(u5_cat_1(X2)))
| k3_cat_1(X2,X4) != k2_cat_1(X2,X5)
| ~ m1_subset_1(X5,u2_cat_1(X2)) )
| ~ m1_subset_1(X4,u2_cat_1(X2)) )
& sP3(X2,X1,X0)
& sP2(X1,X0,X2) )
| ~ sP4(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f221]) ).
fof(f233,plain,
! [X1,X0,X2] :
( ( sP4(X1,X0,X2)
| u1_cat_1(X2) != k7_cat_2(X0,X1)
| k11_nattra_1(X0,X1) != u2_cat_1(X2)
| ? [X3] :
( ( k2_cat_1(X2,X3) != k1_mcart_1(k1_mcart_1(X3))
| k3_cat_1(X2,X3) != k2_mcart_1(k1_mcart_1(X3)) )
& m1_subset_1(X3,u2_cat_1(X2)) )
| ? [X4] :
( ? [X5] :
( ~ r2_hidden(k13_cat_2(X2,X2,X5,X4),k1_relat_1(u5_cat_1(X2)))
& k3_cat_1(X2,X4) = k2_cat_1(X2,X5)
& m1_subset_1(X5,u2_cat_1(X2)) )
& m1_subset_1(X4,u2_cat_1(X2)) )
| ~ sP3(X2,X1,X0)
| ~ sP2(X1,X0,X2) )
& ( ( u1_cat_1(X2) = k7_cat_2(X0,X1)
& u2_cat_1(X2) = k11_nattra_1(X0,X1)
& ! [X3] :
( ( k2_cat_1(X2,X3) = k1_mcart_1(k1_mcart_1(X3))
& k3_cat_1(X2,X3) = k2_mcart_1(k1_mcart_1(X3)) )
| ~ m1_subset_1(X3,u2_cat_1(X2)) )
& ! [X4] :
( ! [X5] :
( r2_hidden(k13_cat_2(X2,X2,X5,X4),k1_relat_1(u5_cat_1(X2)))
| k3_cat_1(X2,X4) != k2_cat_1(X2,X5)
| ~ m1_subset_1(X5,u2_cat_1(X2)) )
| ~ m1_subset_1(X4,u2_cat_1(X2)) )
& sP3(X2,X1,X0)
& sP2(X1,X0,X2) )
| ~ sP4(X1,X0,X2) ) ),
inference(flattening,[],[f232]) ).
fof(f234,plain,
! [X0,X1,X2] :
( ( sP4(X0,X1,X2)
| u1_cat_1(X2) != k7_cat_2(X1,X0)
| u2_cat_1(X2) != k11_nattra_1(X1,X0)
| ? [X3] :
( ( k2_cat_1(X2,X3) != k1_mcart_1(k1_mcart_1(X3))
| k3_cat_1(X2,X3) != k2_mcart_1(k1_mcart_1(X3)) )
& m1_subset_1(X3,u2_cat_1(X2)) )
| ? [X4] :
( ? [X5] :
( ~ r2_hidden(k13_cat_2(X2,X2,X5,X4),k1_relat_1(u5_cat_1(X2)))
& k3_cat_1(X2,X4) = k2_cat_1(X2,X5)
& m1_subset_1(X5,u2_cat_1(X2)) )
& m1_subset_1(X4,u2_cat_1(X2)) )
| ~ sP3(X2,X0,X1)
| ~ sP2(X0,X1,X2) )
& ( ( u1_cat_1(X2) = k7_cat_2(X1,X0)
& u2_cat_1(X2) = k11_nattra_1(X1,X0)
& ! [X6] :
( ( k2_cat_1(X2,X6) = k1_mcart_1(k1_mcart_1(X6))
& k3_cat_1(X2,X6) = k2_mcart_1(k1_mcart_1(X6)) )
| ~ m1_subset_1(X6,u2_cat_1(X2)) )
& ! [X7] :
( ! [X8] :
( r2_hidden(k13_cat_2(X2,X2,X8,X7),k1_relat_1(u5_cat_1(X2)))
| k3_cat_1(X2,X7) != k2_cat_1(X2,X8)
| ~ m1_subset_1(X8,u2_cat_1(X2)) )
| ~ m1_subset_1(X7,u2_cat_1(X2)) )
& sP3(X2,X0,X1)
& sP2(X0,X1,X2) )
| ~ sP4(X0,X1,X2) ) ),
inference(rectify,[],[f233]) ).
fof(f235,plain,
! [X0,X1,X2] :
( ( sP4(X0,X1,X2)
| u1_cat_1(X2) != k7_cat_2(X1,X0)
| u2_cat_1(X2) != k11_nattra_1(X1,X0)
| ( ( k2_cat_1(X2,sK15(X2)) != k1_mcart_1(k1_mcart_1(sK15(X2)))
| k3_cat_1(X2,sK15(X2)) != k2_mcart_1(k1_mcart_1(sK15(X2))) )
& m1_subset_1(sK15(X2),u2_cat_1(X2)) )
| ( ~ r2_hidden(k13_cat_2(X2,X2,sK17(X2),sK16(X2)),k1_relat_1(u5_cat_1(X2)))
& k3_cat_1(X2,sK16(X2)) = k2_cat_1(X2,sK17(X2))
& m1_subset_1(sK17(X2),u2_cat_1(X2))
& m1_subset_1(sK16(X2),u2_cat_1(X2)) )
| ~ sP3(X2,X0,X1)
| ~ sP2(X0,X1,X2) )
& ( ( u1_cat_1(X2) = k7_cat_2(X1,X0)
& u2_cat_1(X2) = k11_nattra_1(X1,X0)
& ! [X6] :
( ( k2_cat_1(X2,X6) = k1_mcart_1(k1_mcart_1(X6))
& k3_cat_1(X2,X6) = k2_mcart_1(k1_mcart_1(X6)) )
| ~ m1_subset_1(X6,u2_cat_1(X2)) )
& ! [X7] :
( ! [X8] :
( r2_hidden(k13_cat_2(X2,X2,X8,X7),k1_relat_1(u5_cat_1(X2)))
| k3_cat_1(X2,X7) != k2_cat_1(X2,X8)
| ~ m1_subset_1(X8,u2_cat_1(X2)) )
| ~ m1_subset_1(X7,u2_cat_1(X2)) )
& sP3(X2,X0,X1)
& sP2(X0,X1,X2) )
| ~ sP4(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16,sK17]),skolemize(X3,sK15(X2)),skolemize(X4,sK16(X2)),skolemize(X5,sK17(X2))],[f234]) ).
fof(f258,plain,
l1_cat_1(sK6),
inference(cnf_transformation,[],[f224]) ).
fof(f259,plain,
v2_cat_1(sK6),
inference(cnf_transformation,[],[f224]) ).
fof(f260,plain,
m1_subset_1(sK7,u2_cat_1(sK6)),
inference(cnf_transformation,[],[f224]) ).
fof(f261,plain,
~ m1_subset_1(k4_tarski(k4_tarski(k2_yoneda_1(sK6,k3_cat_1(sK6,sK7)),k2_yoneda_1(sK6,k2_cat_1(sK6,sK7))),k3_yoneda_1(sK6,sK7)),u2_cat_1(k12_nattra_1(sK6,k1_yoneda_1(sK6)))),
inference(cnf_transformation,[],[f224]) ).
fof(f269,plain,
! [X2,X0,X1] :
( sP0(X2,X1,X0)
| k11_nattra_1(X1,X2) != X0
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f226]) ).
fof(f276,plain,
! [X2,X10,X0,X11,X1,X12,X13] :
( r2_hidden(X10,X2)
| ~ m2_cat_1(X11,X1,X0)
| ~ m2_cat_1(X12,X1,X0)
| ~ m2_nattra_1(X13,X1,X0,X11,X12)
| k4_tarski(k4_tarski(X11,X12),X13) != X10
| ~ r2_nattra_1(X1,X0,X11,X12)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f229]) ).
fof(f283,plain,
! [X2,X0,X1] :
( ~ m4_nattra_1(X2,X0,X1)
| sP1(X2,X0,X1)
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1)
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(cnf_transformation,[],[f218]) ).
fof(f284,plain,
! [X2,X0,X1] :
( sP4(X2,X1,X0)
| k12_nattra_1(X1,X2) != X0
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f231]) ).
fof(f291,plain,
! [X2,X0,X1] :
( ~ sP4(X0,X1,X2)
| u2_cat_1(X2) = k11_nattra_1(X1,X0) ),
inference(cnf_transformation,[],[f235]) ).
fof(f318,plain,
! [X2,X0,X1] :
( sP5(X2,X0,X1)
| ~ v1_cat_1(X2)
| ~ v2_cat_1(X2)
| ~ l1_cat_1(X2)
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1)
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(cnf_transformation,[],[f223]) ).
fof(f321,plain,
! [X0,X1] : k4_tarski(X0,X1) = k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f327,plain,
! [X0,X1] :
( m4_nattra_1(k11_nattra_1(X0,X1),X0,X1)
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f329,plain,
! [X0,X1] :
( l1_cat_1(k12_nattra_1(X0,X1))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f330,plain,
! [X0,X1] :
( v2_cat_1(k12_nattra_1(X0,X1))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f331,plain,
! [X0,X1] :
( v1_cat_1(k12_nattra_1(X0,X1))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f333,plain,
! [X0] :
( l1_cat_1(k1_yoneda_1(X0))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f334,plain,
! [X0] :
( v2_cat_1(k1_yoneda_1(X0))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f338,plain,
! [X0,X1] :
( m1_subset_1(k2_cat_1(X0,X1),u1_cat_1(X0))
| ~ l1_cat_1(X0)
| ~ m1_subset_1(X1,u2_cat_1(X0)) ),
inference(cnf_transformation,[],[f138]) ).
fof(f339,plain,
! [X0,X1] :
( m2_cat_1(k2_yoneda_1(X0,X1),X0,k1_yoneda_1(X0))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| ~ m1_subset_1(X1,u1_cat_1(X0)) ),
inference(cnf_transformation,[],[f140]) ).
fof(f340,plain,
! [X0,X1] :
( m1_subset_1(k3_cat_1(X0,X1),u1_cat_1(X0))
| ~ l1_cat_1(X0)
| ~ m1_subset_1(X1,u2_cat_1(X0)) ),
inference(cnf_transformation,[],[f142]) ).
fof(f341,plain,
! [X0,X1] :
( m2_nattra_1(k3_yoneda_1(X0,X1),X0,k1_yoneda_1(X0),k2_yoneda_1(X0,k3_cat_1(X0,X1)),k2_yoneda_1(X0,k2_cat_1(X0,X1)))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| ~ m1_subset_1(X1,u2_cat_1(X0)) ),
inference(cnf_transformation,[],[f144]) ).
fof(f411,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f204]) ).
fof(f414,plain,
! [X0,X1] :
( r2_nattra_1(X0,k1_yoneda_1(X0),k2_yoneda_1(X0,k3_cat_1(X0,X1)),k2_yoneda_1(X0,k2_cat_1(X0,X1)))
| ~ m1_subset_1(X1,u2_cat_1(X0))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(cnf_transformation,[],[f209]) ).
fof(f420,plain,
~ m1_subset_1(k2_tarski(k2_tarski(k2_tarski(k2_tarski(k2_yoneda_1(sK6,k3_cat_1(sK6,sK7)),k2_yoneda_1(sK6,k2_cat_1(sK6,sK7))),k1_tarski(k2_yoneda_1(sK6,k3_cat_1(sK6,sK7)))),k3_yoneda_1(sK6,sK7)),k1_tarski(k2_tarski(k2_tarski(k2_yoneda_1(sK6,k3_cat_1(sK6,sK7)),k2_yoneda_1(sK6,k2_cat_1(sK6,sK7))),k1_tarski(k2_yoneda_1(sK6,k3_cat_1(sK6,sK7)))))),u2_cat_1(k12_nattra_1(sK6,k1_yoneda_1(sK6)))),
inference(definition_unfolding,[],[f261,f321,f321]) ).
fof(f423,plain,
! [X2,X10,X0,X11,X1,X12,X13] :
( r2_hidden(X10,X2)
| ~ m2_cat_1(X11,X1,X0)
| ~ m2_cat_1(X12,X1,X0)
| ~ m2_nattra_1(X13,X1,X0,X11,X12)
| k2_tarski(k2_tarski(k2_tarski(k2_tarski(X11,X12),k1_tarski(X11)),X13),k1_tarski(k2_tarski(k2_tarski(X11,X12),k1_tarski(X11)))) != X10
| ~ r2_nattra_1(X1,X0,X11,X12)
| ~ sP0(X0,X1,X2) ),
inference(definition_unfolding,[],[f276,f321,f321]) ).
fof(f432,plain,
! [X2,X1] :
( ~ sP1(k11_nattra_1(X1,X2),X1,X2)
| sP0(X2,X1,k11_nattra_1(X1,X2)) ),
inference(equality_resolution,[],[f269]) ).
fof(f433,plain,
! [X2,X0,X11,X1,X12,X13] :
( ~ m2_nattra_1(X13,X1,X0,X11,X12)
| ~ m2_cat_1(X11,X1,X0)
| ~ m2_cat_1(X12,X1,X0)
| r2_hidden(k2_tarski(k2_tarski(k2_tarski(k2_tarski(X11,X12),k1_tarski(X11)),X13),k1_tarski(k2_tarski(k2_tarski(X11,X12),k1_tarski(X11)))),X2)
| ~ r2_nattra_1(X1,X0,X11,X12)
| ~ sP0(X0,X1,X2) ),
inference(equality_resolution,[],[f423]) ).
fof(f434,plain,
! [X2,X1] :
( ~ sP5(k12_nattra_1(X1,X2),X1,X2)
| sP4(X2,X1,k12_nattra_1(X1,X2)) ),
inference(equality_resolution,[],[f284]) ).
fof(f436,definition,
sF42 = k3_cat_1(sK6,sK7),
introduced(definition,[new_symbols(definition,[sF42])],[function_definition]) ).
fof(f437,plain,
k3_cat_1(sK6,sK7) = sF42,
inference(reorient_equations,[],[f436]) ).
fof(f438,definition,
sF43 = k2_yoneda_1(sK6,sF42),
introduced(definition,[new_symbols(definition,[sF43])],[function_definition]) ).
fof(f439,plain,
k2_yoneda_1(sK6,sF42) = sF43,
inference(reorient_equations,[],[f438]) ).
fof(f440,definition,
sF44 = k2_cat_1(sK6,sK7),
introduced(definition,[new_symbols(definition,[sF44])],[function_definition]) ).
fof(f441,plain,
k2_cat_1(sK6,sK7) = sF44,
inference(reorient_equations,[],[f440]) ).
fof(f442,definition,
sF45 = k2_yoneda_1(sK6,sF44),
introduced(definition,[new_symbols(definition,[sF45])],[function_definition]) ).
fof(f443,plain,
k2_yoneda_1(sK6,sF44) = sF45,
inference(reorient_equations,[],[f442]) ).
fof(f444,definition,
sF46 = k2_tarski(sF43,sF45),
introduced(definition,[new_symbols(definition,[sF46])],[function_definition]) ).
fof(f445,plain,
k2_tarski(sF43,sF45) = sF46,
inference(reorient_equations,[],[f444]) ).
fof(f446,definition,
sF47 = k1_tarski(sF43),
introduced(definition,[new_symbols(definition,[sF47])],[function_definition]) ).
fof(f447,plain,
k1_tarski(sF43) = sF47,
inference(reorient_equations,[],[f446]) ).
fof(f448,definition,
sF48 = k2_tarski(sF46,sF47),
introduced(definition,[new_symbols(definition,[sF48])],[function_definition]) ).
fof(f449,plain,
k2_tarski(sF46,sF47) = sF48,
inference(reorient_equations,[],[f448]) ).
fof(f450,definition,
sF49 = k3_yoneda_1(sK6,sK7),
introduced(definition,[new_symbols(definition,[sF49])],[function_definition]) ).
fof(f451,plain,
k3_yoneda_1(sK6,sK7) = sF49,
inference(reorient_equations,[],[f450]) ).
fof(f452,definition,
sF50 = k2_tarski(sF48,sF49),
introduced(definition,[new_symbols(definition,[sF50])],[function_definition]) ).
fof(f453,plain,
k2_tarski(sF48,sF49) = sF50,
inference(reorient_equations,[],[f452]) ).
fof(f454,definition,
sF51 = k1_tarski(sF48),
introduced(definition,[new_symbols(definition,[sF51])],[function_definition]) ).
fof(f455,plain,
k1_tarski(sF48) = sF51,
inference(reorient_equations,[],[f454]) ).
fof(f456,definition,
sF52 = k2_tarski(sF50,sF51),
introduced(definition,[new_symbols(definition,[sF52])],[function_definition]) ).
fof(f457,plain,
k2_tarski(sF50,sF51) = sF52,
inference(reorient_equations,[],[f456]) ).
fof(f458,definition,
sF53 = k1_yoneda_1(sK6),
introduced(definition,[new_symbols(definition,[sF53])],[function_definition]) ).
fof(f459,plain,
k1_yoneda_1(sK6) = sF53,
inference(reorient_equations,[],[f458]) ).
fof(f460,definition,
sF54 = k12_nattra_1(sK6,sF53),
introduced(definition,[new_symbols(definition,[sF54])],[function_definition]) ).
fof(f461,plain,
k12_nattra_1(sK6,sF53) = sF54,
inference(reorient_equations,[],[f460]) ).
fof(f462,definition,
sF55 = u2_cat_1(sF54),
introduced(definition,[new_symbols(definition,[sF55])],[function_definition]) ).
fof(f463,plain,
u2_cat_1(sF54) = sF55,
inference(reorient_equations,[],[f462]) ).
fof(f464,plain,
~ m1_subset_1(sF52,sF55),
inference(definition_folding,[],[f420,f463,f461,f459,f457,f455,f449,f447,f439,f437,f445,f443,f441,f439,f437,f453,f451,f449,f447,f439,f437,f445,f443,f441,f439,f437]) ).
fof(f465,definition,
sF56 = u2_cat_1(sK6),
introduced(definition,[new_symbols(definition,[sF56])],[function_definition]) ).
fof(f466,plain,
u2_cat_1(sK6) = sF56,
inference(reorient_equations,[],[f465]) ).
fof(f467,plain,
m1_subset_1(sK7,sF56),
inference(definition_folding,[],[f260,f466]) ).
fof(f472,definition,
( spl57_1
<=> l1_cat_1(sF53) ),
introduced(definition,[new_symbols(definition,[spl57_1])],[avatar_definition]) ).
fof(f473,plain,
( l1_cat_1(sF53)
| ~ spl57_1 ),
inference(avatar_component_clause,[],[f472]) ).
fof(f474,plain,
( ~ l1_cat_1(sF53)
| spl57_1 ),
inference(avatar_component_clause,[],[f472]) ).
fof(f476,definition,
( spl57_2
<=> v2_cat_1(sF53) ),
introduced(definition,[new_symbols(definition,[spl57_2])],[avatar_definition]) ).
fof(f477,plain,
( v2_cat_1(sF53)
| ~ spl57_2 ),
inference(avatar_component_clause,[],[f476]) ).
fof(f518,plain,
( m2_nattra_1(k3_yoneda_1(sK6,sK7),sK6,k1_yoneda_1(sK6),k2_yoneda_1(sK6,k3_cat_1(sK6,sK7)),k2_yoneda_1(sK6,sF44))
| ~ v2_cat_1(sK6)
| ~ l1_cat_1(sK6)
| ~ m1_subset_1(sK7,u2_cat_1(sK6)) ),
inference(superposition,[],[f341,f441]) ).
fof(f519,plain,
( m2_nattra_1(k3_yoneda_1(sK6,sK7),sK6,k1_yoneda_1(sK6),k2_yoneda_1(sK6,k3_cat_1(sK6,sK7)),k2_yoneda_1(sK6,sF44))
| ~ l1_cat_1(sK6)
| ~ m1_subset_1(sK7,u2_cat_1(sK6)) ),
inference(forward_subsumption_resolution,[],[f518,f259]) ).
fof(f523,plain,
( m2_nattra_1(k3_yoneda_1(sK6,sK7),sK6,k1_yoneda_1(sK6),k2_yoneda_1(sK6,k3_cat_1(sK6,sK7)),k2_yoneda_1(sK6,sF44))
| ~ m1_subset_1(sK7,u2_cat_1(sK6)) ),
inference(forward_subsumption_resolution,[],[f519,f258]) ).
fof(f527,plain,
( m2_nattra_1(k3_yoneda_1(sK6,sK7),sK6,k1_yoneda_1(sK6),k2_yoneda_1(sK6,k3_cat_1(sK6,sK7)),sF45)
| ~ m1_subset_1(sK7,u2_cat_1(sK6)) ),
inference(forward_demodulation,[],[f523,f443]) ).
fof(f531,plain,
( m2_nattra_1(k3_yoneda_1(sK6,sK7),sK6,k1_yoneda_1(sK6),k2_yoneda_1(sK6,sF42),sF45)
| ~ m1_subset_1(sK7,u2_cat_1(sK6)) ),
inference(forward_demodulation,[],[f527,f437]) ).
fof(f534,plain,
( m2_nattra_1(k3_yoneda_1(sK6,sK7),sK6,k1_yoneda_1(sK6),sF43,sF45)
| ~ m1_subset_1(sK7,u2_cat_1(sK6)) ),
inference(forward_demodulation,[],[f531,f439]) ).
fof(f537,plain,
( m2_nattra_1(k3_yoneda_1(sK6,sK7),sK6,sF53,sF43,sF45)
| ~ m1_subset_1(sK7,u2_cat_1(sK6)) ),
inference(forward_demodulation,[],[f534,f459]) ).
fof(f540,plain,
( m2_nattra_1(sF49,sK6,sF53,sF43,sF45)
| ~ m1_subset_1(sK7,u2_cat_1(sK6)) ),
inference(forward_demodulation,[],[f537,f451]) ).
fof(f543,plain,
( ~ m1_subset_1(sK7,sF56)
| m2_nattra_1(sF49,sK6,sF53,sF43,sF45) ),
inference(forward_demodulation,[],[f540,f466]) ).
fof(f546,plain,
m2_nattra_1(sF49,sK6,sF53,sF43,sF45),
inference(forward_subsumption_resolution,[],[f543,f467]) ).
fof(f551,plain,
( r2_nattra_1(sK6,k1_yoneda_1(sK6),k2_yoneda_1(sK6,k3_cat_1(sK6,sK7)),k2_yoneda_1(sK6,sF44))
| ~ m1_subset_1(sK7,u2_cat_1(sK6))
| ~ v2_cat_1(sK6)
| ~ l1_cat_1(sK6) ),
inference(superposition,[],[f414,f441]) ).
fof(f552,plain,
( r2_nattra_1(sK6,k1_yoneda_1(sK6),k2_yoneda_1(sK6,k3_cat_1(sK6,sK7)),k2_yoneda_1(sK6,sF44))
| ~ m1_subset_1(sK7,u2_cat_1(sK6))
| ~ l1_cat_1(sK6) ),
inference(forward_subsumption_resolution,[],[f551,f259]) ).
fof(f555,plain,
( r2_nattra_1(sK6,k1_yoneda_1(sK6),k2_yoneda_1(sK6,k3_cat_1(sK6,sK7)),k2_yoneda_1(sK6,sF44))
| ~ m1_subset_1(sK7,u2_cat_1(sK6)) ),
inference(forward_subsumption_resolution,[],[f552,f258]) ).
fof(f558,plain,
( r2_nattra_1(sK6,k1_yoneda_1(sK6),k2_yoneda_1(sK6,k3_cat_1(sK6,sK7)),sF45)
| ~ m1_subset_1(sK7,u2_cat_1(sK6)) ),
inference(forward_demodulation,[],[f555,f443]) ).
fof(f561,plain,
( r2_nattra_1(sK6,k1_yoneda_1(sK6),k2_yoneda_1(sK6,sF42),sF45)
| ~ m1_subset_1(sK7,u2_cat_1(sK6)) ),
inference(forward_demodulation,[],[f558,f437]) ).
fof(f563,plain,
( r2_nattra_1(sK6,k1_yoneda_1(sK6),sF43,sF45)
| ~ m1_subset_1(sK7,u2_cat_1(sK6)) ),
inference(forward_demodulation,[],[f561,f439]) ).
fof(f565,plain,
( r2_nattra_1(sK6,sF53,sF43,sF45)
| ~ m1_subset_1(sK7,u2_cat_1(sK6)) ),
inference(forward_demodulation,[],[f563,f459]) ).
fof(f567,plain,
( ~ m1_subset_1(sK7,sF56)
| r2_nattra_1(sK6,sF53,sF43,sF45) ),
inference(forward_demodulation,[],[f565,f466]) ).
fof(f569,plain,
r2_nattra_1(sK6,sF53,sF43,sF45),
inference(forward_subsumption_resolution,[],[f567,f467]) ).
fof(f571,plain,
( v2_cat_1(sF53)
| ~ v2_cat_1(sK6)
| ~ l1_cat_1(sK6) ),
inference(superposition,[],[f334,f459]) ).
fof(f572,plain,
( v2_cat_1(sF53)
| ~ l1_cat_1(sK6) ),
inference(forward_subsumption_resolution,[],[f571,f259]) ).
fof(f573,plain,
v2_cat_1(sF53),
inference(forward_subsumption_resolution,[],[f572,f258]) ).
fof(f574,plain,
spl57_2,
inference(avatar_split_clause,[],[f573,f476]) ).
fof(f575,plain,
( l1_cat_1(sF53)
| ~ v2_cat_1(sK6)
| ~ l1_cat_1(sK6) ),
inference(superposition,[],[f333,f459]) ).
fof(f576,plain,
( ~ v2_cat_1(sK6)
| ~ l1_cat_1(sK6)
| spl57_1 ),
inference(forward_subsumption_resolution,[],[f575,f474]) ).
fof(f577,plain,
( ~ l1_cat_1(sK6)
| spl57_1 ),
inference(forward_subsumption_resolution,[],[f576,f259]) ).
fof(f578,plain,
( $false
| spl57_1 ),
inference(forward_subsumption_resolution,[],[f577,f258]) ).
fof(f579,plain,
spl57_1,
inference(avatar_contradiction_clause,[],[f578]) ).
fof(f611,plain,
! [X0] :
( ~ m2_cat_1(sF43,sK6,sF53)
| ~ m2_cat_1(sF45,sK6,sF53)
| r2_hidden(k2_tarski(k2_tarski(k2_tarski(k2_tarski(sF43,sF45),k1_tarski(sF43)),sF49),k1_tarski(k2_tarski(k2_tarski(sF43,sF45),k1_tarski(sF43)))),X0)
| ~ r2_nattra_1(sK6,sF53,sF43,sF45)
| ~ sP0(sF53,sK6,X0) ),
inference(resolution,[],[f433,f546]) ).
fof(f612,plain,
! [X0] :
( ~ m2_cat_1(sF43,sK6,sF53)
| ~ m2_cat_1(sF45,sK6,sF53)
| r2_hidden(k2_tarski(k2_tarski(k2_tarski(k2_tarski(sF43,sF45),k1_tarski(sF43)),sF49),k1_tarski(k2_tarski(k2_tarski(sF43,sF45),k1_tarski(sF43)))),X0)
| ~ sP0(sF53,sK6,X0) ),
inference(forward_subsumption_resolution,[],[f611,f569]) ).
fof(f615,plain,
! [X0] :
( r2_hidden(k2_tarski(k2_tarski(k2_tarski(k2_tarski(sF43,sF45),sF47),sF49),k1_tarski(k2_tarski(k2_tarski(sF43,sF45),sF47))),X0)
| ~ m2_cat_1(sF43,sK6,sF53)
| ~ m2_cat_1(sF45,sK6,sF53)
| ~ sP0(sF53,sK6,X0) ),
inference(forward_demodulation,[],[f612,f447]) ).
fof(f616,plain,
! [X0] :
( r2_hidden(k2_tarski(k2_tarski(k2_tarski(sF46,sF47),sF49),k1_tarski(k2_tarski(sF46,sF47))),X0)
| ~ m2_cat_1(sF43,sK6,sF53)
| ~ m2_cat_1(sF45,sK6,sF53)
| ~ sP0(sF53,sK6,X0) ),
inference(forward_demodulation,[],[f615,f445]) ).
fof(f617,plain,
! [X0] :
( r2_hidden(k2_tarski(k2_tarski(sF48,sF49),k1_tarski(sF48)),X0)
| ~ m2_cat_1(sF43,sK6,sF53)
| ~ m2_cat_1(sF45,sK6,sF53)
| ~ sP0(sF53,sK6,X0) ),
inference(forward_demodulation,[],[f616,f449]) ).
fof(f618,plain,
! [X0] :
( r2_hidden(k2_tarski(k2_tarski(sF48,sF49),sF51),X0)
| ~ m2_cat_1(sF43,sK6,sF53)
| ~ m2_cat_1(sF45,sK6,sF53)
| ~ sP0(sF53,sK6,X0) ),
inference(forward_demodulation,[],[f617,f455]) ).
fof(f619,plain,
! [X0] :
( r2_hidden(k2_tarski(sF50,sF51),X0)
| ~ m2_cat_1(sF43,sK6,sF53)
| ~ m2_cat_1(sF45,sK6,sF53)
| ~ sP0(sF53,sK6,X0) ),
inference(forward_demodulation,[],[f618,f453]) ).
fof(f620,plain,
! [X0] :
( r2_hidden(sF52,X0)
| ~ m2_cat_1(sF43,sK6,sF53)
| ~ m2_cat_1(sF45,sK6,sF53)
| ~ sP0(sF53,sK6,X0) ),
inference(forward_demodulation,[],[f619,f457]) ).
fof(f622,definition,
( spl57_9
<=> m2_cat_1(sF45,sK6,sF53) ),
introduced(definition,[new_symbols(definition,[spl57_9])],[avatar_definition]) ).
fof(f624,plain,
( ~ m2_cat_1(sF45,sK6,sF53)
| spl57_9 ),
inference(avatar_component_clause,[],[f622]) ).
fof(f626,definition,
( spl57_10
<=> m2_cat_1(sF43,sK6,sF53) ),
introduced(definition,[new_symbols(definition,[spl57_10])],[avatar_definition]) ).
fof(f630,definition,
( spl57_11
<=> ! [X0] :
( r2_hidden(sF52,X0)
| ~ sP0(sF53,sK6,X0) ) ),
introduced(definition,[new_symbols(definition,[spl57_11])],[avatar_definition]) ).
fof(f631,plain,
( ! [X0] :
( ~ sP0(sF53,sK6,X0)
| r2_hidden(sF52,X0) )
| ~ spl57_11 ),
inference(avatar_component_clause,[],[f630]) ).
fof(f632,plain,
( ~ spl57_9
| ~ spl57_10
| spl57_11 ),
inference(avatar_split_clause,[],[f620,f630,f626,f622]) ).
fof(f708,plain,
( m1_subset_1(sF44,u1_cat_1(sK6))
| ~ l1_cat_1(sK6)
| ~ m1_subset_1(sK7,u2_cat_1(sK6)) ),
inference(superposition,[],[f338,f441]) ).
fof(f709,plain,
( m1_subset_1(sF44,u1_cat_1(sK6))
| ~ m1_subset_1(sK7,u2_cat_1(sK6)) ),
inference(forward_subsumption_resolution,[],[f708,f258]) ).
fof(f710,plain,
( ~ m1_subset_1(sK7,sF56)
| m1_subset_1(sF44,u1_cat_1(sK6)) ),
inference(forward_demodulation,[],[f709,f466]) ).
fof(f711,plain,
m1_subset_1(sF44,u1_cat_1(sK6)),
inference(forward_subsumption_resolution,[],[f710,f467]) ).
fof(f712,plain,
( m1_subset_1(sF42,u1_cat_1(sK6))
| ~ l1_cat_1(sK6)
| ~ m1_subset_1(sK7,u2_cat_1(sK6)) ),
inference(superposition,[],[f340,f437]) ).
fof(f713,plain,
( m1_subset_1(sF42,u1_cat_1(sK6))
| ~ m1_subset_1(sK7,u2_cat_1(sK6)) ),
inference(forward_subsumption_resolution,[],[f712,f258]) ).
fof(f714,plain,
( ~ m1_subset_1(sK7,sF56)
| m1_subset_1(sF42,u1_cat_1(sK6)) ),
inference(forward_demodulation,[],[f713,f466]) ).
fof(f715,plain,
m1_subset_1(sF42,u1_cat_1(sK6)),
inference(forward_subsumption_resolution,[],[f714,f467]) ).
fof(f716,plain,
( m2_cat_1(sF43,sK6,k1_yoneda_1(sK6))
| ~ v2_cat_1(sK6)
| ~ l1_cat_1(sK6)
| ~ m1_subset_1(sF42,u1_cat_1(sK6)) ),
inference(superposition,[],[f339,f439]) ).
fof(f717,plain,
( m2_cat_1(sF45,sK6,k1_yoneda_1(sK6))
| ~ v2_cat_1(sK6)
| ~ l1_cat_1(sK6)
| ~ m1_subset_1(sF44,u1_cat_1(sK6)) ),
inference(superposition,[],[f339,f443]) ).
fof(f720,plain,
( m2_cat_1(sF45,sK6,k1_yoneda_1(sK6))
| ~ l1_cat_1(sK6)
| ~ m1_subset_1(sF44,u1_cat_1(sK6)) ),
inference(forward_subsumption_resolution,[],[f717,f259]) ).
fof(f721,plain,
( m2_cat_1(sF43,sK6,k1_yoneda_1(sK6))
| ~ l1_cat_1(sK6)
| ~ m1_subset_1(sF42,u1_cat_1(sK6)) ),
inference(forward_subsumption_resolution,[],[f716,f259]) ).
fof(f723,plain,
( m2_cat_1(sF45,sK6,k1_yoneda_1(sK6))
| ~ m1_subset_1(sF44,u1_cat_1(sK6)) ),
inference(forward_subsumption_resolution,[],[f720,f258]) ).
fof(f724,plain,
( m2_cat_1(sF43,sK6,k1_yoneda_1(sK6))
| ~ m1_subset_1(sF42,u1_cat_1(sK6)) ),
inference(forward_subsumption_resolution,[],[f721,f258]) ).
fof(f725,plain,
m2_cat_1(sF45,sK6,k1_yoneda_1(sK6)),
inference(forward_subsumption_resolution,[],[f723,f711]) ).
fof(f726,plain,
m2_cat_1(sF43,sK6,k1_yoneda_1(sK6)),
inference(forward_subsumption_resolution,[],[f724,f715]) ).
fof(f727,plain,
m2_cat_1(sF45,sK6,sF53),
inference(forward_demodulation,[],[f725,f459]) ).
fof(f728,plain,
m2_cat_1(sF43,sK6,sF53),
inference(forward_demodulation,[],[f726,f459]) ).
fof(f729,plain,
( $false
| spl57_9 ),
inference(forward_subsumption_resolution,[],[f727,f624]) ).
fof(f730,plain,
spl57_9,
inference(avatar_contradiction_clause,[],[f729]) ).
fof(f731,plain,
spl57_10,
inference(avatar_split_clause,[],[f728,f626]) ).
fof(f778,plain,
! [X0,X1] :
( ~ v1_cat_1(k12_nattra_1(X0,X1))
| ~ v2_cat_1(k12_nattra_1(X0,X1))
| ~ l1_cat_1(k12_nattra_1(X0,X1))
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1)
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| sP4(X1,X0,k12_nattra_1(X0,X1)) ),
inference(resolution,[],[f318,f434]) ).
fof(f779,plain,
! [X0,X1] :
( ~ v2_cat_1(k12_nattra_1(X0,X1))
| ~ l1_cat_1(k12_nattra_1(X0,X1))
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1)
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| sP4(X1,X0,k12_nattra_1(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f778,f331]) ).
fof(f780,plain,
! [X0,X1] :
( ~ l1_cat_1(k12_nattra_1(X0,X1))
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1)
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| sP4(X1,X0,k12_nattra_1(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f779,f330]) ).
fof(f781,plain,
! [X0,X1] :
( sP4(X1,X0,k12_nattra_1(X0,X1))
| ~ l1_cat_1(X1)
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| ~ v2_cat_1(X1) ),
inference(forward_subsumption_resolution,[],[f780,f329]) ).
fof(f784,plain,
! [X0,X1] :
( ~ l1_cat_1(X1)
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X0)
| ~ v2_cat_1(X0)
| k11_nattra_1(X1,X0) = u2_cat_1(k12_nattra_1(X1,X0)) ),
inference(resolution,[],[f781,f291]) ).
fof(f793,plain,
! [X0] :
( ~ v2_cat_1(sK6)
| ~ l1_cat_1(X0)
| ~ v2_cat_1(X0)
| k11_nattra_1(sK6,X0) = u2_cat_1(k12_nattra_1(sK6,X0)) ),
inference(resolution,[],[f784,f258]) ).
fof(f798,plain,
! [X0] :
( ~ l1_cat_1(X0)
| ~ v2_cat_1(X0)
| k11_nattra_1(sK6,X0) = u2_cat_1(k12_nattra_1(sK6,X0)) ),
inference(forward_subsumption_resolution,[],[f793,f259]) ).
fof(f804,plain,
( ~ v2_cat_1(sF53)
| k11_nattra_1(sK6,sF53) = u2_cat_1(k12_nattra_1(sK6,sF53))
| ~ spl57_1 ),
inference(resolution,[],[f798,f473]) ).
fof(f807,plain,
( k11_nattra_1(sK6,sF53) = u2_cat_1(k12_nattra_1(sK6,sF53))
| ~ spl57_1
| ~ spl57_2 ),
inference(forward_subsumption_resolution,[],[f804,f477]) ).
fof(f811,plain,
( u2_cat_1(sF54) = k11_nattra_1(sK6,sF53)
| ~ spl57_1
| ~ spl57_2 ),
inference(forward_demodulation,[],[f807,f461]) ).
fof(f812,plain,
( sF55 = k11_nattra_1(sK6,sF53)
| ~ spl57_1
| ~ spl57_2 ),
inference(forward_demodulation,[],[f811,f463]) ).
fof(f813,plain,
( ~ sP1(sF55,sK6,sF53)
| sP0(sF53,sK6,sF55)
| ~ spl57_1
| ~ spl57_2 ),
inference(superposition,[],[f432,f812]) ).
fof(f815,definition,
( spl57_12
<=> sP0(sF53,sK6,sF55) ),
introduced(definition,[new_symbols(definition,[spl57_12])],[avatar_definition]) ).
fof(f817,plain,
( sP0(sF53,sK6,sF55)
| ~ spl57_12 ),
inference(avatar_component_clause,[],[f815]) ).
fof(f819,definition,
( spl57_13
<=> sP1(sF55,sK6,sF53) ),
introduced(definition,[new_symbols(definition,[spl57_13])],[avatar_definition]) ).
fof(f821,plain,
( ~ sP1(sF55,sK6,sF53)
| spl57_13 ),
inference(avatar_component_clause,[],[f819]) ).
fof(f822,plain,
( spl57_12
| ~ spl57_13
| ~ spl57_1
| ~ spl57_2 ),
inference(avatar_split_clause,[],[f813,f476,f472,f819,f815]) ).
fof(f1258,plain,
( m4_nattra_1(sF55,sK6,sF53)
| ~ v2_cat_1(sK6)
| ~ l1_cat_1(sK6)
| ~ v2_cat_1(sF53)
| ~ l1_cat_1(sF53)
| ~ spl57_1
| ~ spl57_2 ),
inference(superposition,[],[f327,f812]) ).
fof(f1261,plain,
( m4_nattra_1(sF55,sK6,sF53)
| ~ l1_cat_1(sK6)
| ~ v2_cat_1(sF53)
| ~ l1_cat_1(sF53)
| ~ spl57_1
| ~ spl57_2 ),
inference(forward_subsumption_resolution,[],[f1258,f259]) ).
fof(f1262,plain,
( m4_nattra_1(sF55,sK6,sF53)
| ~ v2_cat_1(sF53)
| ~ l1_cat_1(sF53)
| ~ spl57_1
| ~ spl57_2 ),
inference(forward_subsumption_resolution,[],[f1261,f258]) ).
fof(f1263,plain,
( m4_nattra_1(sF55,sK6,sF53)
| ~ l1_cat_1(sF53)
| ~ spl57_1
| ~ spl57_2 ),
inference(forward_subsumption_resolution,[],[f1262,f477]) ).
fof(f1264,plain,
( m4_nattra_1(sF55,sK6,sF53)
| ~ spl57_1
| ~ spl57_2 ),
inference(forward_subsumption_resolution,[],[f1263,f473]) ).
fof(f1266,plain,
( sP1(sF55,sK6,sF53)
| ~ v2_cat_1(sF53)
| ~ l1_cat_1(sF53)
| ~ v2_cat_1(sK6)
| ~ l1_cat_1(sK6)
| ~ spl57_1
| ~ spl57_2 ),
inference(resolution,[],[f1264,f283]) ).
fof(f1267,plain,
( ~ v2_cat_1(sF53)
| ~ l1_cat_1(sF53)
| ~ v2_cat_1(sK6)
| ~ l1_cat_1(sK6)
| ~ spl57_1
| ~ spl57_2
| spl57_13 ),
inference(forward_subsumption_resolution,[],[f1266,f821]) ).
fof(f1268,plain,
( ~ l1_cat_1(sF53)
| ~ v2_cat_1(sK6)
| ~ l1_cat_1(sK6)
| ~ spl57_1
| ~ spl57_2
| spl57_13 ),
inference(forward_subsumption_resolution,[],[f1267,f477]) ).
fof(f1269,plain,
( ~ v2_cat_1(sK6)
| ~ l1_cat_1(sK6)
| ~ spl57_1
| ~ spl57_2
| spl57_13 ),
inference(forward_subsumption_resolution,[],[f1268,f473]) ).
fof(f1270,plain,
( ~ l1_cat_1(sK6)
| ~ spl57_1
| ~ spl57_2
| spl57_13 ),
inference(forward_subsumption_resolution,[],[f1269,f259]) ).
fof(f1271,plain,
( $false
| ~ spl57_1
| ~ spl57_2
| spl57_13 ),
inference(forward_subsumption_resolution,[],[f1270,f258]) ).
fof(f1272,plain,
( ~ spl57_1
| ~ spl57_2
| spl57_13 ),
inference(avatar_contradiction_clause,[],[f1271]) ).
fof(f1273,plain,
( r2_hidden(sF52,sF55)
| ~ spl57_11
| ~ spl57_12 ),
inference(resolution,[],[f817,f631]) ).
fof(f1275,plain,
( m1_subset_1(sF52,sF55)
| ~ spl57_11
| ~ spl57_12 ),
inference(resolution,[],[f1273,f411]) ).
fof(f1276,plain,
( $false
| ~ spl57_11
| ~ spl57_12 ),
inference(forward_subsumption_resolution,[],[f1275,f464]) ).
fof(f1277,plain,
( ~ spl57_11
| ~ spl57_12 ),
inference(avatar_contradiction_clause,[],[f1276]) ).
cnf(s5,plain,
spl57_2,
inference(sat_conversion,[],[f574]) ).
cnf(s6,plain,
spl57_1,
inference(sat_conversion,[],[f579]) ).
cnf(s8,plain,
( ~ spl57_9
| ~ spl57_10
| spl57_11 ),
inference(sat_conversion,[],[f632]) ).
cnf(s9,plain,
spl57_9,
inference(sat_conversion,[],[f730]) ).
cnf(s10,plain,
spl57_10,
inference(sat_conversion,[],[f731]) ).
cnf(s12,plain,
( ~ spl57_1
| ~ spl57_2
| spl57_12
| ~ spl57_13 ),
inference(sat_conversion,[],[f822]) ).
cnf(s38,plain,
( ~ spl57_1
| ~ spl57_2
| spl57_13 ),
inference(sat_conversion,[],[f1272]) ).
cnf(s39,plain,
( ~ spl57_11
| ~ spl57_12 ),
inference(sat_conversion,[],[f1277]) ).
cnf(s57,plain,
spl57_11,
inference(rat,[],[s8,s10,s9]) ).
cnf(s58,plain,
~ spl57_12,
inference(rat,[],[s39,s57]) ).
cnf(s59,plain,
spl57_13,
inference(rat,[],[s38,s6,s5]) ).
cnf(s60,plain,
$false,
inference(rat,[],[s12,s6,s58,s59,s5]) ).
fof(f1278,plain,
$false,
inference(avatar_sat_refutation,[],[s60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT034+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n017.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Mon Sep 28 21:16:21 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.20 Running first-order theorem proving
% 0.06/0.20 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.28/1.59 % (4045988)Detected formulas, will run a generic FOF schedule.
% 7.28/1.59 % (4045998)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1400940478:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 7.28/1.59 % (4045994)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2510205199:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 7.28/1.59 % (4045996)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3857311343:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 7.28/1.59 % (4045997)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1775992101:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 7.28/1.59 % (4045993)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1786725650:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 7.28/1.59 % (4045995)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=487180316:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 7.28/1.59 % (4045999)dis-21_1_sil=8000:lcm=predicate:random_seed=2021198640:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 7.28/1.59 % (4045997)Refutation not found, incomplete strategy
% 7.28/1.59 % (4045997)------------------------------
% 7.28/1.59 % (4045997)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.28/1.59 % (4045997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/1.59 % (4045996)Refutation not found, incomplete strategy
% 7.28/1.59 % (4045996)------------------------------
% 7.28/1.59 % (4045996)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.28/1.59 % (4045997)CaDiCaL version: 2.1.3
% 7.28/1.59 % (4045997)Termination reason: Refutation not found, incomplete strategy
% 7.28/1.59 % (4045997)Time elapsed: 0.002 s
% 7.28/1.59 % (4045997)Peak memory usage: 88 MB
% 7.28/1.59 % (4045997)Instructions burned: 1 (million)
% 7.28/1.59 % (4045996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/1.59 % (4045996)CaDiCaL version: 2.1.3
% 7.28/1.59 % (4045996)Termination reason: Refutation not found, incomplete strategy
% 7.28/1.59 % (4045996)Time elapsed: 0.002 s
% 7.28/1.59 % (4045996)Peak memory usage: 88 MB
% 7.28/1.59 % (4045996)Instructions burned: 1 (million)
% 7.28/1.59 % (4045998)Instruction limit reached!
% 7.28/1.59 % (4045998)------------------------------
% 7.28/1.59 % (4045998)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.28/1.59 % (4045998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/1.59 % (4045998)CaDiCaL version: 2.1.3
% 7.28/1.59 % (4045998)Termination reason: Instruction limit
% 7.28/1.59 % (4045998)Termination phase: Saturation
% 7.28/1.59 % (4045998)Time elapsed: 0.050 s
% 7.28/1.59 % (4045998)Peak memory usage: 90 MB
% 7.28/1.59 % (4045998)Instructions burned: 141 (million)
% 7.28/1.59 % (4045999)Instruction limit reached!
% 7.28/1.59 % (4045999)------------------------------
% 7.28/1.59 % (4045999)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.28/1.59 % (4045999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/1.59 % (4045999)CaDiCaL version: 2.1.3
% 7.28/1.59 % (4045999)Termination reason: Instruction limit
% 7.28/1.59 % (4045999)Termination phase: Saturation
% 7.28/1.59 % (4045999)Time elapsed: 0.074 s
% 7.28/1.59 % (4045999)Peak memory usage: 89 MB
% 7.28/1.59 % (4045999)Instructions burned: 130 (million)
% 7.28/1.59 % (4046007)lrs+10_1_sil=8000:sp=occurrence:random_seed=81753456:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 7.28/1.59 % (4046008)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1879055184:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 7.28/1.59 % (4045996)------------------------------
% 7.28/1.59 % (4045996)------------------------------
% 7.28/1.59 % (4045997)------------------------------
% 7.28/1.59 % (4045997)------------------------------
% 7.28/1.59 % (4046007)Instruction limit reached!
% 7.28/1.59 % (4046007)------------------------------
% 7.28/1.59 % (4046007)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.28/1.59 % (4046007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/1.59 % (4046007)CaDiCaL version: 2.1.3
% 7.28/1.59 % (4046007)Termination reason: Instruction limit
% 7.28/1.59 % (4046007)Termination phase: Saturation
% 7.28/1.59 % (4046007)Time elapsed: 0.095 s
% 7.28/1.59 % (4046007)Peak memory usage: 93 MB
% 7.28/1.59 % (4046007)Instructions burned: 285 (million)
% 7.28/1.59 % (4046008)Instruction limit reached!
% 7.28/1.59 % (4046008)------------------------------
% 7.28/1.59 % (4046008)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.28/1.59 % (4046008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/1.59 % (4046008)CaDiCaL version: 2.1.3
% 7.28/1.59 % (4046008)Termination reason: Instruction limit
% 7.28/1.59 % (4046008)Termination phase: Saturation
% 7.28/1.59 % (4046008)Time elapsed: 0.080 s
% 7.28/1.59 % (4046008)Peak memory usage: 91 MB
% 7.28/1.59 % (4046008)Instructions burned: 159 (million)
% 7.28/1.59 % (4046011)lrs+1011_1_sil=32000:sp=occurrence:random_seed=131842866:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 7.28/1.59 % (4046012)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=89294278:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 7.28/1.59 % (4046013)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2167875363:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 7.28/1.59 % (4046011)Instruction limit reached!
% 7.28/1.59 % (4046011)------------------------------
% 7.28/1.59 % (4046011)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.28/1.59 % (4046011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/1.59 % (4046011)CaDiCaL version: 2.1.3
% 7.28/1.59 % (4046011)Termination reason: Instruction limit
% 7.28/1.59 % (4046011)Termination phase: Saturation
% 7.28/1.59 % (4046011)Time elapsed: 0.109 s
% 7.28/1.59 % (4046011)Peak memory usage: 93 MB
% 7.28/1.59 % (4046011)Instructions burned: 326 (million)
% 7.28/1.59 % (4046014)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2954929286:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 7.28/1.59 % (4046012)Instruction limit reached!
% 7.28/1.59 % (4046012)------------------------------
% 7.28/1.59 % (4046012)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.28/1.59 % (4046012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/1.59 % (4046012)CaDiCaL version: 2.1.3
% 7.28/1.59 % (4046012)Termination reason: Instruction limit
% 7.28/1.59 % (4046012)Termination phase: Saturation
% 7.28/1.59 % (4046012)Time elapsed: 0.132 s
% 7.28/1.59 % (4046012)Peak memory usage: 93 MB
% 7.28/1.59 % (4046012)Instructions burned: 249 (million)
% 7.28/1.59 % (4046013)Instruction limit reached!
% 7.28/1.59 % (4046013)------------------------------
% 7.28/1.59 % (4046013)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.28/1.59 % (4046013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/1.59 % (4046013)CaDiCaL version: 2.1.3
% 7.28/1.59 % (4046013)Termination reason: Instruction limit
% 7.28/1.59 % (4046013)Termination phase: Saturation
% 7.28/1.59 % (4046013)Time elapsed: 0.149 s
% 7.28/1.59 % (4046013)Peak memory usage: 89 MB
% 7.28/1.59 % (4046013)Instructions burned: 296 (million)
% 7.28/1.59 % (4046019)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1423948370:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 7.28/1.59 % (4046019)Instruction limit reached!
% 7.28/1.59 % (4046019)------------------------------
% 7.28/1.59 % (4046019)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.28/1.59 % (4046019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/1.59 % (4046019)CaDiCaL version: 2.1.3
% 7.28/1.59 % (4046019)Termination reason: Instruction limit
% 7.28/1.59 % (4046019)Termination phase: Saturation
% 7.28/1.59 % (4046019)Time elapsed: 0.038 s
% 7.28/1.59 % (4046019)Peak memory usage: 91 MB
% 7.28/1.59 % (4046019)Instructions burned: 114 (million)
% 7.28/1.59 % (4046020)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1710828035:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 7.28/1.59 % (4046021)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3011661393:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 7.28/1.59 % (4046023)lrs+10_1_sil=8000:sp=occurrence:random_seed=3766918251:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 7.28/1.59 % (4046020)Instruction limit reached!
% 7.28/1.59 % (4046020)------------------------------
% 7.28/1.59 % (4046020)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.28/1.59 % (4046020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/1.59 % (4046020)CaDiCaL version: 2.1.3
% 7.28/1.59 % (4046020)Termination reason: Instruction limit
% 7.28/1.59 % (4046020)Termination phase: Saturation
% 7.28/1.59 % (4046020)Time elapsed: 0.064 s
% 7.28/1.59 % (4046020)Peak memory usage: 89 MB
% 7.28/1.59 % (4046020)Instructions burned: 127 (million)
% 7.28/1.59 % (4046021)Instruction limit reached!
% 7.28/1.59 % (4046021)------------------------------
% 7.28/1.59 % (4046021)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.28/1.59 % (4046021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/1.59 % (4046021)CaDiCaL version: 2.1.3
% 7.28/1.59 % (4046021)Termination reason: Instruction limit
% 7.28/1.59 % (4046021)Termination phase: Saturation
% 7.28/1.59 % (4046021)Time elapsed: 0.056 s
% 7.28/1.59 % (4046021)Peak memory usage: 89 MB
% 7.28/1.59 % (4046021)Instructions burned: 115 (million)
% 7.28/1.59 % (4045993)First to succeed.
% 7.28/1.59 % (4045993)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4045988"
% 7.28/1.59 % (4046027)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1629188122:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 7.28/1.59 % (4046027)Also succeeded, but the first one will report.
% 7.28/1.59 % (4046028)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=438820959:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 7.28/1.59 % (4045993)Refutation found. Thanks to Tanya!
% 7.28/1.59 % SZS status Theorem for theBenchmark
% 7.28/1.59 % SZS output start Proof for theBenchmark
% See solution above
% 8.72/1.78 % (4045993)------------------------------
% 8.72/1.78 % (4045993)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/1.78 % (4045993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/1.78 % (4045993)CaDiCaL version: 2.1.3
% 8.72/1.78 % (4045993)Termination reason: Refutation
% 8.72/1.78 % (4045993)Time elapsed: 0.761 s
% 8.72/1.78 % (4045993)Peak memory usage: 130 MB
% 8.72/1.78 % (4045993)Instructions burned: 1138 (million)
% 8.72/1.78 % (4045993)------------------------------
% 8.72/1.78 % (4045993)------------------------------
% 8.72/1.78 % (4045988)Success in time 1.186 s
% 8.72/1.78 % Vampire exiting
%------------------------------------------------------------------------------