%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP009_2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 11:27:55 AM UTC 2026
% Result : Theorem 5.90s 7.70s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 17
% Syntax : Number of formulae : 157 ( 32 unt; 0 typ; 9 def)
% Number of atoms : 2065 ( 50 equ)
% Maximal formula atoms : 18 ( 13 avg)
% Number of connectives : 1020 ( 446 ~; 441 |; 79 &)
% ( 14 <=>; 38 =>; 0 <=; 2 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of FOOLs : 1334 (1334 fml; 0 var)
% Number of types : 4 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 22 ( 20 usr; 18 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 8 con; 0-4 aty)
% Number of variables : 398 ( 0 sgn 350 !; 48 ?; 398 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
del: $tType ).
tff(type_def_6,type,
tp__o: $tType ).
tff(func_def_0,type,
bool: del ).
tff(func_def_1,type,
ind: del ).
tff(func_def_2,type,
arr: ( del * del ) > del ).
tff(func_def_4,type,
k: ( del * $i ) > $i ).
tff(func_def_5,type,
i: del > $i ).
tff(func_def_6,type,
inj__o: tp__o > $i ).
tff(func_def_7,type,
surj__o: $i > tp__o ).
tff(func_def_9,type,
fo__c_2Ebool_2E_7E: tp__o > tp__o ).
tff(func_def_11,type,
fo__c_2Ebool_2EF: tp__o ).
tff(func_def_13,type,
fo__c_2Ebool_2ET: tp__o ).
tff(func_def_15,type,
fo__c_2Ebool_2E_2F_5C: ( tp__o * tp__o ) > tp__o ).
tff(func_def_16,type,
c_2Equotient_2E_2D_2D_3E: ( del * del * del * del ) > $i ).
tff(func_def_17,type,
c_2Equotient_2E_3D_3D_3D_3E: ( del * del ) > $i ).
tff(func_def_18,type,
c_2Equotient_2EQUOTIENT: ( del * del ) > $i ).
tff(func_def_20,type,
fo__c_2Emin_2E_3D_3D_3E: ( tp__o * tp__o ) > tp__o ).
tff(func_def_21,type,
c_2Ebool_2E_21: del > $i ).
tff(func_def_22,type,
c_2Ecombin_2EW: ( del * del ) > $i ).
tff(func_def_23,type,
c_2Equotient_2Erespects: ( del * del ) > $i ).
tff(func_def_24,type,
c_2Emin_2E_3D: del > $i ).
tff(func_def_25,type,
sK0: ( del * $i ) > $i ).
tff(func_def_26,type,
sK1: del ).
tff(func_def_27,type,
sK2: del ).
tff(func_def_28,type,
sK3: del ).
tff(func_def_29,type,
sK4: del ).
tff(func_def_38,type,
sK13: ( del * $i * $i ) > $i ).
tff(pred_def_1,type,
mem: ( $i * del ) > $o ).
tff(f1,axiom,
! [X0: del,X1: del,X2: $i] :
( mem(X2,arr(X0,X1))
=> ! [X3: $i] :
( mem(X3,X0)
=> mem(ap(X2,X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_tp) ).
tff(f21,axiom,
! [X0: del,X1: del,X2: del,X3: del] : mem(c_2Equotient_2E_2D_2D_3E(X0,X1,X2,X3),arr(arr(X0,X2),arr(arr(X1,X3),arr(arr(X2,X1),arr(X0,X3))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Equotient_2E_2D_2D_3E) ).
tff(f22,axiom,
! [X0: del,X1: del] : mem(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),arr(arr(X0,arr(X0,bool)),arr(arr(X1,arr(X1,bool)),arr(arr(X0,X1),arr(arr(X0,X1),bool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Equotient_2E_3D_3D_3D_3E) ).
tff(f38,axiom,
! [X0: del,X1: del,X2: $i] :
( mem(X2,arr(X0,arr(X0,X1)))
=> ! [X3: $i] :
( mem(X3,X0)
=> ( ap(ap(c_2Ecombin_2EW(X0,X1),X2),X3) = ap(ap(X2,X3),X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ecombin_2EW__THM) ).
tff(f39,axiom,
! [X0: del,X1: del,X2: $i] :
( mem(X2,arr(X0,arr(X0,bool)))
=> ! [X3: $i] :
( mem(X3,arr(X0,X1))
=> ! [X4: $i] :
( mem(X4,arr(X1,X0))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X1),X2),X3),X4))
=> ! [X5: $i] :
( mem(X5,X0)
=> ! [X6: $i] :
( mem(X6,X0)
=> ( p(ap(ap(X2,X5),X6))
<=> ( p(ap(ap(X2,X5),X5))
& p(ap(ap(X2,X6),X6))
& ( ap(X3,X5) = ap(X3,X6) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Equotient_2EQUOTIENT__REL) ).
tff(f40,axiom,
! [X0: del,X1: del,X2: del,X3: del,X4: $i] :
( mem(X4,arr(X0,arr(X0,bool)))
=> ! [X5: $i] :
( mem(X5,arr(X0,X2))
=> ! [X6: $i] :
( mem(X6,arr(X2,X0))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X2),X4),X5),X6))
=> ! [X7: $i] :
( mem(X7,arr(X1,arr(X1,bool)))
=> ! [X8: $i] :
( mem(X8,arr(X1,X3))
=> ! [X9: $i] :
( mem(X9,arr(X3,X1))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X1,X3),X7),X8),X9))
=> p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(X0,X1),arr(X2,X3)),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8)),ap(ap(c_2Equotient_2E_2D_2D_3E(X0,X3,X2,X1),X5),X9))) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Equotient_2EFUN__QUOTIENT) ).
tff(f41,axiom,
! [X0: del,X1: del] : ( c_2Equotient_2Erespects(X0,X1) = c_2Ecombin_2EW(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Equotient_2Erespects__def) ).
tff(f42,conjecture,
! [X0: del,X1: del,X2: del,X3: del,X4: $i] :
( mem(X4,arr(X0,arr(X0,bool)))
=> ! [X5: $i] :
( mem(X5,arr(X0,X2))
=> ! [X6: $i] :
( mem(X6,arr(X2,X0))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X2),X4),X5),X6))
=> ! [X7: $i] :
( mem(X7,arr(X1,arr(X1,bool)))
=> ! [X8: $i] :
( mem(X8,arr(X1,X3))
=> ! [X9: $i] :
( mem(X9,arr(X3,X1))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X1,X3),X7),X8),X9))
=> ! [X10: $i] :
( mem(X10,arr(X0,X1))
=> ! [X11: $i] :
( mem(X11,arr(X0,X1))
=> ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7),X10),X11))
<=> ( p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X10))
& p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X11))
& ( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X10) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X11) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Equotient_2EFUN__REL__EQ__REL) ).
tff(f43,negated_conjecture,
~ ! [X0: del,X1: del,X2: del,X3: del,X4: $i] :
( mem(X4,arr(X0,arr(X0,bool)))
=> ! [X5: $i] :
( mem(X5,arr(X0,X2))
=> ! [X6: $i] :
( mem(X6,arr(X2,X0))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X2),X4),X5),X6))
=> ! [X7: $i] :
( mem(X7,arr(X1,arr(X1,bool)))
=> ! [X8: $i] :
( mem(X8,arr(X1,X3))
=> ! [X9: $i] :
( mem(X9,arr(X3,X1))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X1,X3),X7),X8),X9))
=> ! [X10: $i] :
( mem(X10,arr(X0,X1))
=> ! [X11: $i] :
( mem(X11,arr(X0,X1))
=> ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7),X10),X11))
<=> ( p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X10))
& p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X11))
& ( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X10) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X11) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
tff(f57,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( ( ap(ap(c_2Ecombin_2EW(X0,X1),X2),X3) = ap(ap(X2,X3),X3) )
| ~ mem(X3,X0) )
| ~ mem(X2,arr(X0,arr(X0,X1))) ),
inference(ennf_transformation,[],[f38]) ).
tff(f58,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ! [X5: $i] :
( ! [X6: $i] :
( ( p(ap(ap(X2,X5),X6))
<=> ( p(ap(ap(X2,X5),X5))
& p(ap(ap(X2,X6),X6))
& ( ap(X3,X5) = ap(X3,X6) ) ) )
| ~ mem(X6,X0) )
| ~ mem(X5,X0) )
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X1),X2),X3),X4))
| ~ mem(X4,arr(X1,X0)) )
| ~ mem(X3,arr(X0,X1)) )
| ~ mem(X2,arr(X0,arr(X0,bool))) ),
inference(ennf_transformation,[],[f39]) ).
tff(f59,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ! [X5: $i] :
( ! [X6: $i] :
( ( p(ap(ap(X2,X5),X6))
<=> ( p(ap(ap(X2,X5),X5))
& p(ap(ap(X2,X6),X6))
& ( ap(X3,X5) = ap(X3,X6) ) ) )
| ~ mem(X6,X0) )
| ~ mem(X5,X0) )
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X1),X2),X3),X4))
| ~ mem(X4,arr(X1,X0)) )
| ~ mem(X3,arr(X0,X1)) )
| ~ mem(X2,arr(X0,arr(X0,bool))) ),
inference(flattening,[],[f58]) ).
tff(f60,plain,
! [X0: del,X1: del,X2: del,X3: del,X4: $i] :
( ! [X5: $i] :
( ! [X6: $i] :
( ! [X7: $i] :
( ! [X8: $i] :
( ! [X9: $i] :
( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(X0,X1),arr(X2,X3)),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8)),ap(ap(c_2Equotient_2E_2D_2D_3E(X0,X3,X2,X1),X5),X9)))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X1,X3),X7),X8),X9))
| ~ mem(X9,arr(X3,X1)) )
| ~ mem(X8,arr(X1,X3)) )
| ~ mem(X7,arr(X1,arr(X1,bool))) )
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X2),X4),X5),X6))
| ~ mem(X6,arr(X2,X0)) )
| ~ mem(X5,arr(X0,X2)) )
| ~ mem(X4,arr(X0,arr(X0,bool))) ),
inference(ennf_transformation,[],[f40]) ).
tff(f61,plain,
! [X0: del,X1: del,X2: del,X3: del,X4: $i] :
( ! [X5: $i] :
( ! [X6: $i] :
( ! [X7: $i] :
( ! [X8: $i] :
( ! [X9: $i] :
( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(X0,X1),arr(X2,X3)),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8)),ap(ap(c_2Equotient_2E_2D_2D_3E(X0,X3,X2,X1),X5),X9)))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X1,X3),X7),X8),X9))
| ~ mem(X9,arr(X3,X1)) )
| ~ mem(X8,arr(X1,X3)) )
| ~ mem(X7,arr(X1,arr(X1,bool))) )
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X2),X4),X5),X6))
| ~ mem(X6,arr(X2,X0)) )
| ~ mem(X5,arr(X0,X2)) )
| ~ mem(X4,arr(X0,arr(X0,bool))) ),
inference(flattening,[],[f60]) ).
tff(f62,plain,
? [X0: del,X1: del,X2: del,X3: del,X4: $i] :
( ? [X5: $i] :
( ? [X6: $i] :
( ? [X7: $i] :
( ? [X8: $i] :
( ? [X9: $i] :
( ? [X10: $i] :
( ? [X11: $i] :
( ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7),X10),X11))
<~> ( p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X10))
& p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X11))
& ( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X10) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X11) ) ) )
& mem(X11,arr(X0,X1)) )
& mem(X10,arr(X0,X1)) )
& p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X1,X3),X7),X8),X9))
& mem(X9,arr(X3,X1)) )
& mem(X8,arr(X1,X3)) )
& mem(X7,arr(X1,arr(X1,bool))) )
& p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X2),X4),X5),X6))
& mem(X6,arr(X2,X0)) )
& mem(X5,arr(X0,X2)) )
& mem(X4,arr(X0,arr(X0,bool))) ),
inference(ennf_transformation,[],[f43]) ).
tff(f63,plain,
? [X0: del,X1: del,X2: del,X3: del,X4: $i] :
( ? [X5: $i] :
( ? [X6: $i] :
( ? [X7: $i] :
( ? [X8: $i] :
( ? [X9: $i] :
( ? [X10: $i] :
( ? [X11: $i] :
( ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7),X10),X11))
<~> ( p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X10))
& p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X11))
& ( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X10) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X11) ) ) )
& mem(X11,arr(X0,X1)) )
& mem(X10,arr(X0,X1)) )
& p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X1,X3),X7),X8),X9))
& mem(X9,arr(X3,X1)) )
& mem(X8,arr(X1,X3)) )
& mem(X7,arr(X1,arr(X1,bool))) )
& p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X2),X4),X5),X6))
& mem(X6,arr(X2,X0)) )
& mem(X5,arr(X0,X2)) )
& mem(X4,arr(X0,arr(X0,bool))) ),
inference(flattening,[],[f62]) ).
tff(f66,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( mem(ap(X2,X3),X1)
| ~ mem(X3,X0) )
| ~ mem(X2,arr(X0,X1)) ),
inference(ennf_transformation,[],[f1]) ).
tff(f85,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ! [X5: $i] :
( ! [X6: $i] :
( ( ( p(ap(ap(X2,X5),X6))
| ~ p(ap(ap(X2,X5),X5))
| ~ p(ap(ap(X2,X6),X6))
| ( ap(X3,X5) != ap(X3,X6) ) )
& ( ( p(ap(ap(X2,X5),X5))
& p(ap(ap(X2,X6),X6))
& ( ap(X3,X5) = ap(X3,X6) ) )
| ~ p(ap(ap(X2,X5),X6)) ) )
| ~ mem(X6,X0) )
| ~ mem(X5,X0) )
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X1),X2),X3),X4))
| ~ mem(X4,arr(X1,X0)) )
| ~ mem(X3,arr(X0,X1)) )
| ~ mem(X2,arr(X0,arr(X0,bool))) ),
inference(nnf_transformation,[],[f59]) ).
tff(f86,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ! [X5: $i] :
( ! [X6: $i] :
( ( ( p(ap(ap(X2,X5),X6))
| ~ p(ap(ap(X2,X5),X5))
| ~ p(ap(ap(X2,X6),X6))
| ( ap(X3,X5) != ap(X3,X6) ) )
& ( ( p(ap(ap(X2,X5),X5))
& p(ap(ap(X2,X6),X6))
& ( ap(X3,X5) = ap(X3,X6) ) )
| ~ p(ap(ap(X2,X5),X6)) ) )
| ~ mem(X6,X0) )
| ~ mem(X5,X0) )
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X1),X2),X3),X4))
| ~ mem(X4,arr(X1,X0)) )
| ~ mem(X3,arr(X0,X1)) )
| ~ mem(X2,arr(X0,arr(X0,bool))) ),
inference(flattening,[],[f85]) ).
tff(f87,plain,
? [X0: del,X1: del,X2: del,X3: del,X4: $i] :
( ? [X5: $i] :
( ? [X6: $i] :
( ? [X7: $i] :
( ? [X8: $i] :
( ? [X9: $i] :
( ? [X10: $i] :
( ? [X11: $i] :
( ( ~ p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X10))
| ~ p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X11))
| ( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X10) != ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X11) )
| ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7),X10),X11)) )
& ( ( p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X10))
& p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X11))
& ( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X10) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X11) ) )
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7),X10),X11)) )
& mem(X11,arr(X0,X1)) )
& mem(X10,arr(X0,X1)) )
& p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X1,X3),X7),X8),X9))
& mem(X9,arr(X3,X1)) )
& mem(X8,arr(X1,X3)) )
& mem(X7,arr(X1,arr(X1,bool))) )
& p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X2),X4),X5),X6))
& mem(X6,arr(X2,X0)) )
& mem(X5,arr(X0,X2)) )
& mem(X4,arr(X0,arr(X0,bool))) ),
inference(nnf_transformation,[],[f63]) ).
tff(f88,plain,
? [X0: del,X1: del,X2: del,X3: del,X4: $i] :
( ? [X5: $i] :
( ? [X6: $i] :
( ? [X7: $i] :
( ? [X8: $i] :
( ? [X9: $i] :
( ? [X10: $i] :
( ? [X11: $i] :
( ( ~ p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X10))
| ~ p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X11))
| ( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X10) != ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X11) )
| ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7),X10),X11)) )
& ( ( p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X10))
& p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X11))
& ( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X10) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X11) ) )
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7),X10),X11)) )
& mem(X11,arr(X0,X1)) )
& mem(X10,arr(X0,X1)) )
& p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X1,X3),X7),X8),X9))
& mem(X9,arr(X3,X1)) )
& mem(X8,arr(X1,X3)) )
& mem(X7,arr(X1,arr(X1,bool))) )
& p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X2),X4),X5),X6))
& mem(X6,arr(X2,X0)) )
& mem(X5,arr(X0,X2)) )
& mem(X4,arr(X0,arr(X0,bool))) ),
inference(flattening,[],[f87]) ).
tff(f89,plain,
( ( ~ p(ap(ap(c_2Equotient_2Erespects(arr(sK1,sK2),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),sK11))
| ~ p(ap(ap(c_2Equotient_2Erespects(arr(sK1,sK2),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),sK12))
| ( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK3,sK2,sK1,sK4),sK7),sK9),sK11) != ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK3,sK2,sK1,sK4),sK7),sK9),sK12) )
| ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),sK11),sK12)) )
& ( ( p(ap(ap(c_2Equotient_2Erespects(arr(sK1,sK2),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),sK11))
& p(ap(ap(c_2Equotient_2Erespects(arr(sK1,sK2),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),sK12))
& ( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK3,sK2,sK1,sK4),sK7),sK9),sK11) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK3,sK2,sK1,sK4),sK7),sK9),sK12) ) )
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),sK11),sK12)) )
& mem(sK12,arr(sK1,sK2))
& mem(sK11,arr(sK1,sK2))
& p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK2,sK4),sK8),sK9),sK10))
& mem(sK10,arr(sK4,sK2))
& mem(sK9,arr(sK2,sK4))
& mem(sK8,arr(sK2,arr(sK2,bool)))
& p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK1,sK3),sK5),sK6),sK7))
& mem(sK7,arr(sK3,sK1))
& mem(sK6,arr(sK1,sK3))
& mem(sK5,arr(sK1,arr(sK1,bool))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4),skolemize(X4,sK5),skolemize(X5,sK6),skolemize(X6,sK7),skolemize(X7,sK8),skolemize(X8,sK9),skolemize(X9,sK10),skolemize(X10,sK11),skolemize(X11,sK12)],[f88]) ).
tff(f110,plain,
! [X2: del,X3: del,X0: del,X1: del] : mem(c_2Equotient_2E_2D_2D_3E(X0,X1,X2,X3),arr(arr(X0,X2),arr(arr(X1,X3),arr(arr(X2,X1),arr(X0,X3))))),
inference(cnf_transformation,[],[f21]) ).
tff(f111,plain,
! [X0: del,X1: del] : mem(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),arr(arr(X0,arr(X0,bool)),arr(arr(X1,arr(X1,bool)),arr(arr(X0,X1),arr(arr(X0,X1),bool))))),
inference(cnf_transformation,[],[f22]) ).
tff(f156,plain,
! [X2: $i,X3: $i,X0: del,X1: del] :
( ( ap(ap(c_2Ecombin_2EW(X0,X1),X2),X3) = ap(ap(X2,X3),X3) )
| ~ mem(X3,X0)
| ~ mem(X2,arr(X0,arr(X0,X1))) ),
inference(cnf_transformation,[],[f57]) ).
tff(f157,plain,
! [X2: $i,X3: $i,X0: del,X1: del,X6: $i,X4: $i,X5: $i] :
( ~ mem(X2,arr(X0,arr(X0,bool)))
| ~ p(ap(ap(X2,X5),X6))
| ~ mem(X6,X0)
| ~ mem(X5,X0)
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X1),X2),X3),X4))
| ~ mem(X4,arr(X1,X0))
| ~ mem(X3,arr(X0,X1))
| ( ap(X3,X5) = ap(X3,X6) ) ),
inference(cnf_transformation,[],[f86]) ).
tff(f158,plain,
! [X2: $i,X3: $i,X0: del,X1: del,X6: $i,X4: $i,X5: $i] :
( ~ mem(X2,arr(X0,arr(X0,bool)))
| ~ p(ap(ap(X2,X5),X6))
| ~ mem(X6,X0)
| ~ mem(X5,X0)
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X1),X2),X3),X4))
| ~ mem(X4,arr(X1,X0))
| ~ mem(X3,arr(X0,X1))
| p(ap(ap(X2,X6),X6)) ),
inference(cnf_transformation,[],[f86]) ).
tff(f159,plain,
! [X2: $i,X3: $i,X0: del,X1: del,X6: $i,X4: $i,X5: $i] :
( ~ mem(X2,arr(X0,arr(X0,bool)))
| ~ p(ap(ap(X2,X5),X6))
| ~ mem(X6,X0)
| ~ mem(X5,X0)
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X1),X2),X3),X4))
| ~ mem(X4,arr(X1,X0))
| ~ mem(X3,arr(X0,X1))
| p(ap(ap(X2,X5),X5)) ),
inference(cnf_transformation,[],[f86]) ).
tff(f160,plain,
! [X2: $i,X3: $i,X0: del,X1: del,X6: $i,X4: $i,X5: $i] :
( ~ mem(X2,arr(X0,arr(X0,bool)))
| ~ p(ap(ap(X2,X5),X5))
| ~ p(ap(ap(X2,X6),X6))
| ( ap(X3,X5) != ap(X3,X6) )
| ~ mem(X6,X0)
| ~ mem(X5,X0)
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X1),X2),X3),X4))
| ~ mem(X4,arr(X1,X0))
| ~ mem(X3,arr(X0,X1))
| p(ap(ap(X2,X5),X6)) ),
inference(cnf_transformation,[],[f86]) ).
tff(f161,plain,
! [X2: del,X3: del,X0: del,X1: del,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i] :
( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(X0,X1),arr(X2,X3)),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8)),ap(ap(c_2Equotient_2E_2D_2D_3E(X0,X3,X2,X1),X5),X9)))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X1,X3),X7),X8),X9))
| ~ mem(X9,arr(X3,X1))
| ~ mem(X8,arr(X1,X3))
| ~ mem(X7,arr(X1,arr(X1,bool)))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X2),X4),X5),X6))
| ~ mem(X6,arr(X2,X0))
| ~ mem(X5,arr(X0,X2))
| ~ mem(X4,arr(X0,arr(X0,bool))) ),
inference(cnf_transformation,[],[f61]) ).
tff(f162,plain,
! [X0: del,X1: del] : ( c_2Ecombin_2EW(X0,X1) = c_2Equotient_2Erespects(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
tff(f163,plain,
mem(sK5,arr(sK1,arr(sK1,bool))),
inference(cnf_transformation,[],[f89]) ).
tff(f164,plain,
mem(sK6,arr(sK1,sK3)),
inference(cnf_transformation,[],[f89]) ).
tff(f165,plain,
mem(sK7,arr(sK3,sK1)),
inference(cnf_transformation,[],[f89]) ).
tff(f166,plain,
p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK1,sK3),sK5),sK6),sK7)),
inference(cnf_transformation,[],[f89]) ).
tff(f167,plain,
mem(sK8,arr(sK2,arr(sK2,bool))),
inference(cnf_transformation,[],[f89]) ).
tff(f168,plain,
mem(sK9,arr(sK2,sK4)),
inference(cnf_transformation,[],[f89]) ).
tff(f169,plain,
mem(sK10,arr(sK4,sK2)),
inference(cnf_transformation,[],[f89]) ).
tff(f170,plain,
p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK2,sK4),sK8),sK9),sK10)),
inference(cnf_transformation,[],[f89]) ).
tff(f171,plain,
mem(sK11,arr(sK1,sK2)),
inference(cnf_transformation,[],[f89]) ).
tff(f172,plain,
mem(sK12,arr(sK1,sK2)),
inference(cnf_transformation,[],[f89]) ).
tff(f173,plain,
( ( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK3,sK2,sK1,sK4),sK7),sK9),sK11) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK3,sK2,sK1,sK4),sK7),sK9),sK12) )
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),sK11),sK12)) ),
inference(cnf_transformation,[],[f89]) ).
tff(f174,plain,
( p(ap(ap(c_2Equotient_2Erespects(arr(sK1,sK2),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),sK12))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),sK11),sK12)) ),
inference(cnf_transformation,[],[f89]) ).
tff(f175,plain,
( p(ap(ap(c_2Equotient_2Erespects(arr(sK1,sK2),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),sK11))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),sK11),sK12)) ),
inference(cnf_transformation,[],[f89]) ).
tff(f176,plain,
( ~ p(ap(ap(c_2Equotient_2Erespects(arr(sK1,sK2),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),sK11))
| ~ p(ap(ap(c_2Equotient_2Erespects(arr(sK1,sK2),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),sK12))
| ( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK3,sK2,sK1,sK4),sK7),sK9),sK11) != ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK3,sK2,sK1,sK4),sK7),sK9),sK12) )
| ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),sK11),sK12)) ),
inference(cnf_transformation,[],[f89]) ).
tff(f179,plain,
! [X2: $i,X3: $i,X0: del,X1: del] :
( ~ mem(X2,arr(X0,X1))
| ~ mem(X3,X0)
| mem(ap(X2,X3),X1) ),
inference(cnf_transformation,[],[f66]) ).
tff(f183,plain,
! [X2: $i,X3: $i,X0: del,X1: del] :
( ~ mem(X2,arr(X0,arr(X0,X1)))
| ~ mem(X3,X0)
| ( ap(ap(X2,X3),X3) = ap(ap(c_2Equotient_2Erespects(X0,X1),X2),X3) ) ),
inference(definition_unfolding,[],[f156,f162]) ).
tff(f196,definition,
( spl14_1
<=> p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),sK11),sK12)) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
tff(f197,plain,
( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),sK11),sK12))
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f196]) ).
tff(f199,definition,
( spl14_2
<=> ( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK3,sK2,sK1,sK4),sK7),sK9),sK11) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK3,sK2,sK1,sK4),sK7),sK9),sK12) ) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
tff(f200,plain,
( ( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK3,sK2,sK1,sK4),sK7),sK9),sK11) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK3,sK2,sK1,sK4),sK7),sK9),sK12) )
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f199]) ).
tff(f201,plain,
( spl14_1
| spl14_2 ),
inference(avatar_split_clause,[],[f173,f199,f196]) ).
tff(f203,definition,
( spl14_3
<=> p(ap(ap(c_2Equotient_2Erespects(arr(sK1,sK2),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),sK12)) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
tff(f204,plain,
( p(ap(ap(c_2Equotient_2Erespects(arr(sK1,sK2),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),sK12))
| ~ spl14_3 ),
inference(avatar_component_clause,[],[f203]) ).
tff(f205,plain,
( spl14_1
| spl14_3 ),
inference(avatar_split_clause,[],[f174,f203,f196]) ).
tff(f207,definition,
( spl14_4
<=> p(ap(ap(c_2Equotient_2Erespects(arr(sK1,sK2),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),sK11)) ),
introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition]) ).
tff(f208,plain,
( p(ap(ap(c_2Equotient_2Erespects(arr(sK1,sK2),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),sK11))
| ~ spl14_4 ),
inference(avatar_component_clause,[],[f207]) ).
tff(f209,plain,
( spl14_1
| spl14_4 ),
inference(avatar_split_clause,[],[f175,f207,f196]) ).
tff(f210,plain,
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),sK11),sK12))
| spl14_1 ),
inference(avatar_component_clause,[],[f196]) ).
tff(f211,plain,
( ( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK3,sK2,sK1,sK4),sK7),sK9),sK11) != ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK3,sK2,sK1,sK4),sK7),sK9),sK12) )
| spl14_2 ),
inference(avatar_component_clause,[],[f199]) ).
tff(f212,plain,
( ~ p(ap(ap(c_2Equotient_2Erespects(arr(sK1,sK2),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),sK12))
| spl14_3 ),
inference(avatar_component_clause,[],[f203]) ).
tff(f213,plain,
( ~ p(ap(ap(c_2Equotient_2Erespects(arr(sK1,sK2),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),sK11))
| spl14_4 ),
inference(avatar_component_clause,[],[f207]) ).
tff(f214,plain,
( ~ spl14_1
| ~ spl14_2
| ~ spl14_3
| ~ spl14_4 ),
inference(avatar_split_clause,[],[f176,f207,f203,f199,f196]) ).
tff(f221,definition,
( spl14_5
<=> ! [X4: $i,X2: del,X3: $i] :
( ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK2,X2),sK8),X3),X4))
| ~ mem(X3,arr(sK2,X2))
| ~ mem(X4,arr(X2,sK2)) ) ),
introduced(definition,[new_symbols(definition,[spl14_5])],[avatar_definition]) ).
tff(f222,plain,
( ! [X2: del,X3: $i,X4: $i] :
( ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK2,X2),sK8),X3),X4))
| ~ mem(X3,arr(sK2,X2))
| ~ mem(X4,arr(X2,sK2)) )
| ~ spl14_5 ),
inference(avatar_component_clause,[],[f221]) ).
tff(f232,plain,
( ~ mem(sK9,arr(sK2,sK4))
| ~ mem(sK10,arr(sK4,sK2))
| ~ spl14_5 ),
inference(resolution,[],[f222,f170]) ).
tff(f234,plain,
( ~ mem(sK10,arr(sK4,sK2))
| ~ spl14_5 ),
inference(forward_subsumption_resolution,[],[f232,f168]) ).
tff(f235,plain,
( $false
| ~ spl14_5 ),
inference(forward_subsumption_resolution,[],[f234,f169]) ).
tff(f236,plain,
~ spl14_5,
inference(avatar_contradiction_clause,[],[f235]) ).
tff(f243,definition,
( spl14_8
<=> ! [X4: $i,X2: del,X3: $i] :
( ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK1,X2),sK5),X3),X4))
| ~ mem(X3,arr(sK1,X2))
| ~ mem(X4,arr(X2,sK1)) ) ),
introduced(definition,[new_symbols(definition,[spl14_8])],[avatar_definition]) ).
tff(f244,plain,
( ! [X2: del,X3: $i,X4: $i] :
( ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK1,X2),sK5),X3),X4))
| ~ mem(X3,arr(sK1,X2))
| ~ mem(X4,arr(X2,sK1)) )
| ~ spl14_8 ),
inference(avatar_component_clause,[],[f243]) ).
tff(f254,plain,
( ~ mem(sK6,arr(sK1,sK3))
| ~ mem(sK7,arr(sK3,sK1))
| ~ spl14_8 ),
inference(resolution,[],[f244,f166]) ).
tff(f256,plain,
( ~ mem(sK7,arr(sK3,sK1))
| ~ spl14_8 ),
inference(forward_subsumption_resolution,[],[f254,f164]) ).
tff(f257,plain,
( $false
| ~ spl14_8 ),
inference(forward_subsumption_resolution,[],[f256,f165]) ).
tff(f258,plain,
~ spl14_8,
inference(avatar_contradiction_clause,[],[f257]) ).
tff(f268,plain,
! [X2: del,X3: del,X0: $i,X1: del,X4: del] :
( mem(ap(c_2Equotient_2E_2D_2D_3E(X1,X3,X2,X4),X0),arr(arr(X3,X4),arr(arr(X2,X3),arr(X1,X4))))
| ~ mem(X0,arr(X1,X2)) ),
inference(resolution,[],[f110,f179]) ).
tff(f270,plain,
! [X2: del,X3: $i,X0: $i,X1: del,X4: del,X5: del] :
( mem(ap(ap(c_2Equotient_2E_2D_2D_3E(X1,X4,X2,X5),X0),X3),arr(arr(X2,X4),arr(X1,X5)))
| ~ mem(X3,arr(X4,X5))
| ~ mem(X0,arr(X1,X2)) ),
inference(resolution,[],[f268,f179]) ).
tff(f272,plain,
! [X2: del,X0: $i,X1: del] :
( mem(ap(c_2Equotient_2E_3D_3D_3D_3E(X1,X2),X0),arr(arr(X2,arr(X2,bool)),arr(arr(X1,X2),arr(arr(X1,X2),bool))))
| ~ mem(X0,arr(X1,arr(X1,bool))) ),
inference(resolution,[],[f111,f179]) ).
tff(f273,plain,
! [X2: $i,X3: del,X0: $i,X1: del] :
( ~ mem(X2,arr(X3,arr(X3,bool)))
| ~ mem(X0,arr(X1,arr(X1,bool)))
| mem(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X1,X3),X0),X2),arr(arr(X1,X3),arr(arr(X1,X3),bool))) ),
inference(resolution,[],[f272,f179]) ).
tff(f275,plain,
! [X0: $i,X1: del] :
( ~ mem(X0,arr(X1,arr(X1,bool)))
| mem(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X1,sK2),X0),sK8),arr(arr(X1,sK2),arr(arr(X1,sK2),bool))) ),
inference(resolution,[],[f273,f167]) ).
tff(f444,plain,
mem(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),arr(arr(sK1,sK2),arr(arr(sK1,sK2),bool))),
inference(resolution,[],[f275,f163]) ).
tff(f446,plain,
! [X2: del,X3: $i,X0: $i,X1: $i,X4: $i] :
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),X0),X1))
| ~ mem(X1,arr(sK1,sK2))
| ~ mem(X0,arr(sK1,sK2))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(sK1,sK2),X2),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),X3),X4))
| ~ mem(X4,arr(X2,arr(sK1,sK2)))
| ~ mem(X3,arr(arr(sK1,sK2),X2))
| ( ap(X3,X0) = ap(X3,X1) ) ),
inference(resolution,[],[f444,f157]) ).
tff(f447,plain,
! [X2: del,X3: $i,X0: $i,X1: $i,X4: $i] :
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),X0),X1))
| ~ mem(X1,arr(sK1,sK2))
| ~ mem(X0,arr(sK1,sK2))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(sK1,sK2),X2),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),X3),X4))
| ~ mem(X4,arr(X2,arr(sK1,sK2)))
| ~ mem(X3,arr(arr(sK1,sK2),X2))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),X1),X1)) ),
inference(resolution,[],[f444,f158]) ).
tff(f448,plain,
! [X2: del,X3: $i,X0: $i,X1: $i,X4: $i] :
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),X0),X1))
| ~ mem(X1,arr(sK1,sK2))
| ~ mem(X0,arr(sK1,sK2))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(sK1,sK2),X2),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),X3),X4))
| ~ mem(X4,arr(X2,arr(sK1,sK2)))
| ~ mem(X3,arr(arr(sK1,sK2),X2))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),X0),X0)) ),
inference(resolution,[],[f444,f159]) ).
tff(f449,plain,
! [X2: $i,X3: del,X0: $i,X1: $i,X4: $i] :
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),X0),X0))
| ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),X1),X1))
| ( ap(X2,X0) != ap(X2,X1) )
| ~ mem(X1,arr(sK1,sK2))
| ~ mem(X0,arr(sK1,sK2))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(sK1,sK2),X3),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),X2),X4))
| ~ mem(X4,arr(X3,arr(sK1,sK2)))
| ~ mem(X2,arr(arr(sK1,sK2),X3))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),X0),X1)) ),
inference(resolution,[],[f444,f160]) ).
tff(f456,plain,
! [X0: $i] :
( ~ mem(X0,arr(sK1,sK2))
| ( ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),X0),X0) = ap(ap(c_2Equotient_2Erespects(arr(sK1,sK2),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),X0) ) ),
inference(resolution,[],[f444,f183]) ).
tff(f460,definition,
( spl14_23
<=> ! [X4: $i,X2: del,X3: $i] :
( ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(sK1,sK2),X2),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),X3),X4))
| ~ mem(X3,arr(arr(sK1,sK2),X2))
| ~ mem(X4,arr(X2,arr(sK1,sK2))) ) ),
introduced(definition,[new_symbols(definition,[spl14_23])],[avatar_definition]) ).
tff(f461,plain,
( ! [X2: del,X3: $i,X4: $i] :
( ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(sK1,sK2),X2),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),X3),X4))
| ~ mem(X3,arr(arr(sK1,sK2),X2))
| ~ mem(X4,arr(X2,arr(sK1,sK2))) )
| ~ spl14_23 ),
inference(avatar_component_clause,[],[f460]) ).
tff(f463,definition,
( spl14_24
<=> ! [X0: $i,X1: $i] :
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),X0),X1))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),X0),X0))
| ~ mem(X0,arr(sK1,sK2))
| ~ mem(X1,arr(sK1,sK2)) ) ),
introduced(definition,[new_symbols(definition,[spl14_24])],[avatar_definition]) ).
tff(f464,plain,
( ! [X0: $i,X1: $i] :
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),X0),X1))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),X0),X0))
| ~ mem(X0,arr(sK1,sK2))
| ~ mem(X1,arr(sK1,sK2)) )
| ~ spl14_24 ),
inference(avatar_component_clause,[],[f463]) ).
tff(f465,plain,
( spl14_23
| spl14_24 ),
inference(avatar_split_clause,[],[f448,f463,f460]) ).
tff(f467,definition,
( spl14_25
<=> ! [X0: $i,X1: $i] :
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),X0),X1))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),X1),X1))
| ~ mem(X0,arr(sK1,sK2))
| ~ mem(X1,arr(sK1,sK2)) ) ),
introduced(definition,[new_symbols(definition,[spl14_25])],[avatar_definition]) ).
tff(f468,plain,
( ! [X0: $i,X1: $i] :
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),X0),X1))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),X1),X1))
| ~ mem(X0,arr(sK1,sK2))
| ~ mem(X1,arr(sK1,sK2)) )
| ~ spl14_25 ),
inference(avatar_component_clause,[],[f467]) ).
tff(f469,plain,
( spl14_23
| spl14_25 ),
inference(avatar_split_clause,[],[f447,f467,f460]) ).
tff(f470,plain,
( ! [X2: $i,X3: $i,X0: del,X1: del,X4: $i,X5: $i] :
( ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(X0,sK2,sK1,X1),X2),X3),arr(arr(sK1,sK2),arr(X0,X1)))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK1,X1,X0,sK2),X4),X5),arr(arr(X0,X1),arr(sK1,sK2)))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK2,X1),sK8),X3),X5))
| ~ mem(X5,arr(X1,sK2))
| ~ mem(X3,arr(sK2,X1))
| ~ mem(sK8,arr(sK2,arr(sK2,bool)))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK1,X0),sK5),X4),X2))
| ~ mem(X2,arr(X0,sK1))
| ~ mem(X4,arr(sK1,X0))
| ~ mem(sK5,arr(sK1,arr(sK1,bool))) )
| ~ spl14_23 ),
inference(resolution,[],[f461,f161]) ).
tff(f471,plain,
( ! [X2: $i,X3: $i,X0: del,X1: del,X4: $i,X5: $i] :
( ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(X0,sK2,sK1,X1),X2),X3),arr(arr(sK1,sK2),arr(X0,X1)))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK1,X1,X0,sK2),X4),X5),arr(arr(X0,X1),arr(sK1,sK2)))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK2,X1),sK8),X3),X5))
| ~ mem(X5,arr(X1,sK2))
| ~ mem(X3,arr(sK2,X1))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK1,X0),sK5),X4),X2))
| ~ mem(X2,arr(X0,sK1))
| ~ mem(X4,arr(sK1,X0))
| ~ mem(sK5,arr(sK1,arr(sK1,bool))) )
| ~ spl14_23 ),
inference(forward_subsumption_resolution,[],[f470,f167]) ).
tff(f472,plain,
( ! [X2: $i,X3: $i,X0: del,X1: del,X4: $i,X5: $i] :
( ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(X0,sK2,sK1,X1),X2),X3),arr(arr(sK1,sK2),arr(X0,X1)))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK1,X1,X0,sK2),X4),X5),arr(arr(X0,X1),arr(sK1,sK2)))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK2,X1),sK8),X3),X5))
| ~ mem(X5,arr(X1,sK2))
| ~ mem(X3,arr(sK2,X1))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK1,X0),sK5),X4),X2))
| ~ mem(X2,arr(X0,sK1))
| ~ mem(X4,arr(sK1,X0)) )
| ~ spl14_23 ),
inference(forward_subsumption_resolution,[],[f471,f163]) ).
tff(f473,plain,
( ! [X2: $i,X3: $i,X0: del,X1: del,X4: $i,X5: $i] :
( ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK1,X1,X0,sK2),X4),X5),arr(arr(X0,X1),arr(sK1,sK2)))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK2,X1),sK8),X3),X5))
| ~ mem(X5,arr(X1,sK2))
| ~ mem(X3,arr(sK2,X1))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK1,X0),sK5),X4),X2))
| ~ mem(X2,arr(X0,sK1))
| ~ mem(X4,arr(sK1,X0)) )
| ~ spl14_23 ),
inference(forward_subsumption_resolution,[],[f472,f270]) ).
tff(f474,plain,
( ! [X2: $i,X3: $i,X0: del,X1: del,X4: $i,X5: $i] :
( ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK2,X1),sK8),X3),X5))
| ~ mem(X5,arr(X1,sK2))
| ~ mem(X3,arr(sK2,X1))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK1,X0),sK5),X4),X2))
| ~ mem(X2,arr(X0,sK1))
| ~ mem(X4,arr(sK1,X0)) )
| ~ spl14_23 ),
inference(forward_subsumption_resolution,[],[f473,f270]) ).
tff(f475,plain,
( spl14_8
| spl14_5
| ~ spl14_23 ),
inference(avatar_split_clause,[],[f474,f460,f221,f243]) ).
tff(f575,plain,
ap(ap(c_2Equotient_2Erespects(arr(sK1,sK2),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),sK11) = ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),sK11),sK11),
inference(resolution,[],[f456,f171]) ).
tff(f576,plain,
ap(ap(c_2Equotient_2Erespects(arr(sK1,sK2),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),sK12) = ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),sK12),sK12),
inference(resolution,[],[f456,f172]) ).
tff(f578,plain,
( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),sK12),sK12))
| ~ spl14_3 ),
inference(superposition,[],[f204,f576]) ).
tff(f589,plain,
( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),sK11),sK11))
| ~ spl14_4 ),
inference(superposition,[],[f208,f575]) ).
tff(f607,plain,
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),sK12),sK12))
| spl14_3 ),
inference(forward_demodulation,[],[f212,f576]) ).
tff(f609,plain,
( ! [X2: $i,X0: del,X1: $i] :
( ~ mem(sK12,arr(sK1,sK2))
| ~ mem(sK11,arr(sK1,sK2))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(sK1,sK2),X0),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),X1),X2))
| ~ mem(X2,arr(X0,arr(sK1,sK2)))
| ~ mem(X1,arr(arr(sK1,sK2),X0))
| ( ap(X1,sK12) = ap(X1,sK11) ) )
| ~ spl14_1 ),
inference(resolution,[],[f197,f446]) ).
tff(f610,plain,
( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),sK11),sK11))
| ~ mem(sK11,arr(sK1,sK2))
| ~ mem(sK12,arr(sK1,sK2))
| ~ spl14_1
| ~ spl14_24 ),
inference(resolution,[],[f197,f464]) ).
tff(f611,plain,
( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),sK12),sK12))
| ~ mem(sK11,arr(sK1,sK2))
| ~ mem(sK12,arr(sK1,sK2))
| ~ spl14_1
| ~ spl14_25 ),
inference(resolution,[],[f197,f468]) ).
tff(f613,plain,
( ~ mem(sK11,arr(sK1,sK2))
| ~ mem(sK12,arr(sK1,sK2))
| ~ spl14_1
| spl14_3
| ~ spl14_25 ),
inference(forward_subsumption_resolution,[],[f611,f607]) ).
tff(f614,plain,
( ! [X2: $i,X0: del,X1: $i] :
( ~ mem(sK11,arr(sK1,sK2))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(sK1,sK2),X0),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),X1),X2))
| ~ mem(X2,arr(X0,arr(sK1,sK2)))
| ~ mem(X1,arr(arr(sK1,sK2),X0))
| ( ap(X1,sK12) = ap(X1,sK11) ) )
| ~ spl14_1 ),
inference(forward_subsumption_resolution,[],[f609,f172]) ).
tff(f615,plain,
( ~ mem(sK12,arr(sK1,sK2))
| ~ spl14_1
| spl14_3
| ~ spl14_25 ),
inference(forward_subsumption_resolution,[],[f613,f171]) ).
tff(f616,plain,
( ! [X2: $i,X0: del,X1: $i] :
( ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(sK1,sK2),X0),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),X1),X2))
| ~ mem(X2,arr(X0,arr(sK1,sK2)))
| ~ mem(X1,arr(arr(sK1,sK2),X0))
| ( ap(X1,sK12) = ap(X1,sK11) ) )
| ~ spl14_1 ),
inference(forward_subsumption_resolution,[],[f614,f171]) ).
tff(f617,plain,
( $false
| ~ spl14_1
| spl14_3
| ~ spl14_25 ),
inference(forward_subsumption_resolution,[],[f615,f172]) ).
tff(f618,plain,
( ~ spl14_1
| spl14_3
| ~ spl14_25 ),
inference(avatar_contradiction_clause,[],[f617]) ).
tff(f622,plain,
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),sK11),sK11))
| spl14_4 ),
inference(forward_demodulation,[],[f213,f575]) ).
tff(f623,plain,
( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),sK11),sK11))
| ~ mem(sK12,arr(sK1,sK2))
| ~ spl14_1
| ~ spl14_24 ),
inference(forward_subsumption_resolution,[],[f610,f171]) ).
tff(f624,plain,
( ~ mem(sK12,arr(sK1,sK2))
| ~ spl14_1
| spl14_4
| ~ spl14_24 ),
inference(forward_subsumption_resolution,[],[f623,f622]) ).
tff(f625,plain,
( $false
| ~ spl14_1
| spl14_4
| ~ spl14_24 ),
inference(forward_subsumption_resolution,[],[f624,f172]) ).
tff(f626,plain,
( ~ spl14_1
| spl14_4
| ~ spl14_24 ),
inference(avatar_contradiction_clause,[],[f625]) ).
tff(f638,plain,
( ! [X2: del,X3: $i,X0: $i,X1: $i] :
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),X0),X0))
| ( ap(X1,X0) != ap(X1,sK11) )
| ~ mem(X0,arr(sK1,sK2))
| ~ mem(sK11,arr(sK1,sK2))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(sK1,sK2),X2),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),X1),X3))
| ~ mem(X3,arr(X2,arr(sK1,sK2)))
| ~ mem(X1,arr(arr(sK1,sK2),X2))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),sK11),X0)) )
| ~ spl14_4 ),
inference(resolution,[],[f589,f449]) ).
tff(f642,plain,
( ! [X2: del,X3: $i,X0: $i,X1: $i] :
( ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(sK1,sK2),X2),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8)),X1),X3))
| ( ap(X1,X0) != ap(X1,sK11) )
| ~ mem(X0,arr(sK1,sK2))
| ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),X0),X0))
| ~ mem(X3,arr(X2,arr(sK1,sK2)))
| ~ mem(X1,arr(arr(sK1,sK2),X2))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),sK11),X0)) )
| ~ spl14_4 ),
inference(forward_subsumption_resolution,[],[f638,f171]) ).
tff(f651,plain,
( ! [X2: $i,X3: $i,X0: del,X1: del,X4: $i,X5: $i] :
( ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK1,X0,X1,sK2),X2),X3),arr(arr(X1,X0),arr(sK1,sK2)))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(X1,sK2,sK1,X0),X4),X5),arr(arr(sK1,sK2),arr(X1,X0)))
| ( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X1,sK2,sK1,X0),X4),X5),sK12) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X1,sK2,sK1,X0),X4),X5),sK11) )
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK2,X0),sK8),X5),X3))
| ~ mem(X3,arr(X0,sK2))
| ~ mem(X5,arr(sK2,X0))
| ~ mem(sK8,arr(sK2,arr(sK2,bool)))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK1,X1),sK5),X2),X4))
| ~ mem(X4,arr(X1,sK1))
| ~ mem(X2,arr(sK1,X1))
| ~ mem(sK5,arr(sK1,arr(sK1,bool))) )
| ~ spl14_1 ),
inference(resolution,[],[f616,f161]) ).
tff(f652,plain,
( ! [X2: $i,X3: $i,X0: del,X1: del,X4: $i,X5: $i] :
( ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK1,X0,X1,sK2),X2),X3),arr(arr(X1,X0),arr(sK1,sK2)))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(X1,sK2,sK1,X0),X4),X5),arr(arr(sK1,sK2),arr(X1,X0)))
| ( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X1,sK2,sK1,X0),X4),X5),sK12) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X1,sK2,sK1,X0),X4),X5),sK11) )
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK2,X0),sK8),X5),X3))
| ~ mem(X3,arr(X0,sK2))
| ~ mem(X5,arr(sK2,X0))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK1,X1),sK5),X2),X4))
| ~ mem(X4,arr(X1,sK1))
| ~ mem(X2,arr(sK1,X1))
| ~ mem(sK5,arr(sK1,arr(sK1,bool))) )
| ~ spl14_1 ),
inference(forward_subsumption_resolution,[],[f651,f167]) ).
tff(f653,plain,
( ! [X2: $i,X3: $i,X0: del,X1: del,X4: $i,X5: $i] :
( ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK1,X0,X1,sK2),X2),X3),arr(arr(X1,X0),arr(sK1,sK2)))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(X1,sK2,sK1,X0),X4),X5),arr(arr(sK1,sK2),arr(X1,X0)))
| ( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X1,sK2,sK1,X0),X4),X5),sK12) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X1,sK2,sK1,X0),X4),X5),sK11) )
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK2,X0),sK8),X5),X3))
| ~ mem(X3,arr(X0,sK2))
| ~ mem(X5,arr(sK2,X0))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK1,X1),sK5),X2),X4))
| ~ mem(X4,arr(X1,sK1))
| ~ mem(X2,arr(sK1,X1)) )
| ~ spl14_1 ),
inference(forward_subsumption_resolution,[],[f652,f163]) ).
tff(f654,plain,
( ! [X2: $i,X3: $i,X0: del,X1: del,X4: $i,X5: $i] :
( ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(X1,sK2,sK1,X0),X4),X5),arr(arr(sK1,sK2),arr(X1,X0)))
| ( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X1,sK2,sK1,X0),X4),X5),sK12) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X1,sK2,sK1,X0),X4),X5),sK11) )
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK2,X0),sK8),X5),X3))
| ~ mem(X3,arr(X0,sK2))
| ~ mem(X5,arr(sK2,X0))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK1,X1),sK5),X2),X4))
| ~ mem(X4,arr(X1,sK1))
| ~ mem(X2,arr(sK1,X1)) )
| ~ spl14_1 ),
inference(forward_subsumption_resolution,[],[f653,f270]) ).
tff(f655,plain,
( ! [X2: $i,X3: $i,X0: del,X1: del,X4: $i,X5: $i] :
( ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK2,X0),sK8),X5),X3))
| ( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X1,sK2,sK1,X0),X4),X5),sK12) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X1,sK2,sK1,X0),X4),X5),sK11) )
| ~ mem(X3,arr(X0,sK2))
| ~ mem(X5,arr(sK2,X0))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK1,X1),sK5),X2),X4))
| ~ mem(X4,arr(X1,sK1))
| ~ mem(X2,arr(sK1,X1)) )
| ~ spl14_1 ),
inference(forward_subsumption_resolution,[],[f654,f270]) ).
tff(f656,plain,
( $false
| ~ spl14_1
| spl14_2 ),
inference(unit_resulting_resolution,[],[f655,f164,f165,f169,f168,f166,f170,f211]) ).
tff(f658,plain,
( ~ spl14_1
| spl14_2 ),
inference(avatar_contradiction_clause,[],[f656]) ).
tff(f675,plain,
( ! [X2: $i,X3: $i,X0: del,X1: del,X6: $i,X4: $i,X5: $i] :
( ( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X0,sK2,sK1,X1),X2),X3),sK11) != ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X0,sK2,sK1,X1),X2),X3),X4) )
| ~ mem(X4,arr(sK1,sK2))
| ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),X4),X4))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK1,X1,X0,sK2),X5),X6),arr(arr(X0,X1),arr(sK1,sK2)))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(X0,sK2,sK1,X1),X2),X3),arr(arr(sK1,sK2),arr(X0,X1)))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),sK11),X4))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK2,X1),sK8),X3),X6))
| ~ mem(X6,arr(X1,sK2))
| ~ mem(X3,arr(sK2,X1))
| ~ mem(sK8,arr(sK2,arr(sK2,bool)))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK1,X0),sK5),X5),X2))
| ~ mem(X2,arr(X0,sK1))
| ~ mem(X5,arr(sK1,X0))
| ~ mem(sK5,arr(sK1,arr(sK1,bool))) )
| ~ spl14_4 ),
inference(resolution,[],[f642,f161]) ).
tff(f676,plain,
( ! [X2: $i,X3: $i,X0: del,X1: del,X6: $i,X4: $i,X5: $i] :
( ( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X0,sK2,sK1,X1),X2),X3),sK11) != ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X0,sK2,sK1,X1),X2),X3),X4) )
| ~ mem(X4,arr(sK1,sK2))
| ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),X4),X4))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK1,X1,X0,sK2),X5),X6),arr(arr(X0,X1),arr(sK1,sK2)))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(X0,sK2,sK1,X1),X2),X3),arr(arr(sK1,sK2),arr(X0,X1)))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),sK11),X4))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK2,X1),sK8),X3),X6))
| ~ mem(X6,arr(X1,sK2))
| ~ mem(X3,arr(sK2,X1))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK1,X0),sK5),X5),X2))
| ~ mem(X2,arr(X0,sK1))
| ~ mem(X5,arr(sK1,X0))
| ~ mem(sK5,arr(sK1,arr(sK1,bool))) )
| ~ spl14_4 ),
inference(forward_subsumption_resolution,[],[f675,f167]) ).
tff(f677,plain,
( ! [X2: $i,X3: $i,X0: del,X1: del,X6: $i,X4: $i,X5: $i] :
( ( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X0,sK2,sK1,X1),X2),X3),sK11) != ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X0,sK2,sK1,X1),X2),X3),X4) )
| ~ mem(X4,arr(sK1,sK2))
| ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),X4),X4))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK1,X1,X0,sK2),X5),X6),arr(arr(X0,X1),arr(sK1,sK2)))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(X0,sK2,sK1,X1),X2),X3),arr(arr(sK1,sK2),arr(X0,X1)))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),sK11),X4))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK2,X1),sK8),X3),X6))
| ~ mem(X6,arr(X1,sK2))
| ~ mem(X3,arr(sK2,X1))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK1,X0),sK5),X5),X2))
| ~ mem(X2,arr(X0,sK1))
| ~ mem(X5,arr(sK1,X0)) )
| ~ spl14_4 ),
inference(forward_subsumption_resolution,[],[f676,f163]) ).
tff(f678,plain,
( ! [X2: $i,X3: $i,X0: del,X1: del,X6: $i,X4: $i,X5: $i] :
( ( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X0,sK2,sK1,X1),X2),X3),sK11) != ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X0,sK2,sK1,X1),X2),X3),X4) )
| ~ mem(X4,arr(sK1,sK2))
| ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),X4),X4))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(X0,sK2,sK1,X1),X2),X3),arr(arr(sK1,sK2),arr(X0,X1)))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),sK11),X4))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK2,X1),sK8),X3),X6))
| ~ mem(X6,arr(X1,sK2))
| ~ mem(X3,arr(sK2,X1))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK1,X0),sK5),X5),X2))
| ~ mem(X2,arr(X0,sK1))
| ~ mem(X5,arr(sK1,X0)) )
| ~ spl14_4 ),
inference(forward_subsumption_resolution,[],[f677,f270]) ).
tff(f679,plain,
( ! [X2: $i,X3: $i,X0: del,X1: del,X6: $i,X4: $i,X5: $i] :
( ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK2,X1),sK8),X3),X6))
| ~ mem(X4,arr(sK1,sK2))
| ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),X4),X4))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK1,sK2),sK5),sK8),sK11),X4))
| ( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X0,sK2,sK1,X1),X2),X3),sK11) != ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X0,sK2,sK1,X1),X2),X3),X4) )
| ~ mem(X6,arr(X1,sK2))
| ~ mem(X3,arr(sK2,X1))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK1,X0),sK5),X5),X2))
| ~ mem(X2,arr(X0,sK1))
| ~ mem(X5,arr(sK1,X0)) )
| ~ spl14_4 ),
inference(forward_subsumption_resolution,[],[f678,f270]) ).
tff(f680,plain,
( $false
| spl14_1
| ~ spl14_2
| ~ spl14_3
| ~ spl14_4 ),
inference(unit_resulting_resolution,[],[f679,f164,f165,f172,f168,f169,f166,f170,f210,f578,f200]) ).
tff(f682,plain,
( spl14_1
| ~ spl14_2
| ~ spl14_3
| ~ spl14_4 ),
inference(avatar_contradiction_clause,[],[f680]) ).
cnf(s1,plain,
( spl14_1
| spl14_2 ),
inference(sat_conversion,[],[f201]) ).
cnf(s2,plain,
( spl14_1
| spl14_3 ),
inference(sat_conversion,[],[f205]) ).
cnf(s3,plain,
( spl14_1
| spl14_4 ),
inference(sat_conversion,[],[f209]) ).
cnf(s4,plain,
( ~ spl14_1
| ~ spl14_2
| ~ spl14_3
| ~ spl14_4 ),
inference(sat_conversion,[],[f214]) ).
cnf(s8,plain,
~ spl14_5,
inference(sat_conversion,[],[f236]) ).
cnf(s12,plain,
~ spl14_8,
inference(sat_conversion,[],[f258]) ).
cnf(s24,plain,
( spl14_23
| spl14_24 ),
inference(sat_conversion,[],[f465]) ).
cnf(s25,plain,
( spl14_23
| spl14_25 ),
inference(sat_conversion,[],[f469]) ).
cnf(s26,plain,
( spl14_5
| spl14_8
| ~ spl14_23 ),
inference(sat_conversion,[],[f475]) ).
cnf(s33,plain,
( ~ spl14_1
| spl14_3
| ~ spl14_25 ),
inference(sat_conversion,[],[f618]) ).
cnf(s34,plain,
( ~ spl14_1
| spl14_4
| ~ spl14_24 ),
inference(sat_conversion,[],[f626]) ).
cnf(s36,plain,
( ~ spl14_1
| spl14_2 ),
inference(sat_conversion,[],[f658]) ).
cnf(s37,plain,
( spl14_1
| ~ spl14_2
| ~ spl14_3
| ~ spl14_4 ),
inference(sat_conversion,[],[f682]) ).
cnf(s44,plain,
~ spl14_23,
inference(rat,[],[s26,s12,s8]) ).
cnf(s48,plain,
spl14_25,
inference(rat,[],[s25,s44]) ).
cnf(s49,plain,
spl14_24,
inference(rat,[],[s24,s44]) ).
cnf(s54,plain,
spl14_1,
inference(rat,[],[s37,s1,s2,s3]) ).
cnf(s55,plain,
spl14_2,
inference(rat,[],[s36,s54]) ).
cnf(s57,plain,
spl14_4,
inference(rat,[],[s34,s49,s54]) ).
cnf(s58,plain,
spl14_3,
inference(rat,[],[s33,s48,s54]) ).
cnf(s59,plain,
$false,
inference(rat,[],[s4,s57,s58,s55,s54]) ).
tff(f685,plain,
$false,
inference(avatar_sat_refutation,[],[s59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP009_2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/5.99 % Computer : n015.cluster.edu
% 0.12/5.99 % Model : x86_64 x86_64
% 0.12/5.99 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.99 % Memory : 8046.5625MB
% 0.12/5.99 % OS : Linux 6.8.0-71-generic
% 0.12/6.00 % CPULimit : 300
% 0.12/6.00 % WCLimit : 300
% 0.12/6.00 % DateTime : Sun Sep 27 11:59:07 UTC 2026
% 0.12/6.00 % CPUTime :
% 0.12/6.00 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/6.03 Running first-order theorem proving
% 0.17/6.03 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
% 5.90/7.70 % (1531435)Detected formulas, will run a generic FOF schedule.
% 5.90/7.70 % (1531446)dis-21_1_sil=8000:lcm=predicate:random_seed=4286284603: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)
% 5.90/7.70 % (1531445)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1391611537:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.90/7.70 % (1531442)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=2465144350:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.90/7.70 % (1531444)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=764783952:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.90/7.70 % (1531441)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=2860803365:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.90/7.70 % (1531443)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=327552603:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.90/7.70 % (1531440)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=715850601:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.90/7.70 % (1531446)Instruction limit reached!
% 5.90/7.70 % (1531446)------------------------------
% 5.90/7.70 % (1531446)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.90/7.70 % (1531446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.90/7.70 % (1531446)CaDiCaL version: 2.1.3
% 5.90/7.70 % (1531446)Termination reason: Instruction limit
% 5.90/7.70 % (1531446)Termination phase: Saturation
% 5.90/7.70 % (1531446)Time elapsed: 0.045 s
% 5.90/7.70 % (1531446)Peak memory usage: 90 MB
% 5.90/7.70 % (1531446)Instructions burned: 129 (million)
% 5.90/7.70 % (1531443)Instruction limit reached!
% 5.90/7.70 % (1531443)------------------------------
% 5.90/7.70 % (1531443)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.90/7.70 % (1531443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.90/7.70 % (1531443)CaDiCaL version: 2.1.3
% 5.90/7.70 % (1531443)Termination reason: Instruction limit
% 5.90/7.70 % (1531443)Termination phase: Saturation
% 5.90/7.70 % (1531443)Time elapsed: 0.061 s
% 5.90/7.70 % (1531443)Peak memory usage: 89 MB
% 5.90/7.70 % (1531443)Instructions burned: 109 (million)
% 5.90/7.70 % (1531444)Instruction limit reached!
% 5.90/7.70 % (1531444)------------------------------
% 5.90/7.70 % (1531444)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.90/7.70 % (1531444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.90/7.70 % (1531444)CaDiCaL version: 2.1.3
% 5.90/7.70 % (1531444)Termination reason: Instruction limit
% 5.90/7.70 % (1531444)Termination phase: Saturation
% 5.90/7.70 % (1531444)Time elapsed: 0.069 s
% 5.90/7.70 % (1531444)Peak memory usage: 88 MB
% 5.90/7.70 % (1531444)Instructions burned: 119 (million)
% 5.90/7.70 % (1531445)Instruction limit reached!
% 5.90/7.70 % (1531445)------------------------------
% 5.90/7.70 % (1531445)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.90/7.70 % (1531445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.90/7.70 % (1531445)CaDiCaL version: 2.1.3
% 5.90/7.70 % (1531445)Termination reason: Instruction limit
% 5.90/7.70 % (1531445)Termination phase: Saturation
% 5.90/7.70 % (1531445)Time elapsed: 0.093 s
% 5.90/7.70 % (1531445)Peak memory usage: 90 MB
% 5.90/7.70 % (1531445)Instructions burned: 139 (million)
% 5.90/7.70 % (1531454)lrs+10_1_sil=8000:sp=occurrence:random_seed=1636937441:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 5.90/7.70 % (1531456)lrs+1011_1_sil=32000:sp=occurrence:random_seed=706346182:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.90/7.70 % (1531455)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4014415016:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.90/7.70 % (1531454)Instruction limit reached!
% 5.90/7.70 % (1531454)------------------------------
% 5.90/7.70 % (1531454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.90/7.70 % (1531454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.90/7.70 % (1531454)CaDiCaL version: 2.1.3
% 5.90/7.70 % (1531454)Termination reason: Instruction limit
% 5.90/7.70 % (1531454)Termination phase: Saturation
% 5.90/7.70 % (1531454)Time elapsed: 0.087 s
% 5.90/7.70 % (1531454)Peak memory usage: 92 MB
% 5.90/7.70 % (1531454)Instructions burned: 286 (million)
% 5.90/7.70 % (1531457)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=1870777425:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 5.90/7.70 % (1531455)Instruction limit reached!
% 5.90/7.70 % (1531455)------------------------------
% 5.90/7.70 % (1531455)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.90/7.70 % (1531455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.90/7.70 % (1531455)CaDiCaL version: 2.1.3
% 5.90/7.70 % (1531455)Termination reason: Instruction limit
% 5.90/7.70 % (1531455)Termination phase: Saturation
% 5.90/7.70 % (1531455)Time elapsed: 0.088 s
% 5.90/7.70 % (1531455)Peak memory usage: 90 MB
% 5.90/7.70 % (1531455)Instructions burned: 159 (million)
% 5.90/7.70 % (1531461)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2864717454:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 5.90/7.70 % (1531461)Instruction limit reached!
% 5.90/7.70 % (1531461)------------------------------
% 5.90/7.70 % (1531461)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.90/7.70 % (1531461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.90/7.70 % (1531461)CaDiCaL version: 2.1.3
% 5.90/7.70 % (1531461)Termination reason: Instruction limit
% 5.90/7.70 % (1531461)Termination phase: Saturation
% 5.90/7.70 % (1531461)Time elapsed: 0.068 s
% 5.90/7.70 % (1531461)Peak memory usage: 88 MB
% 5.90/7.70 % (1531461)Instructions burned: 297 (million)
% 5.90/7.70 % (1531457)Instruction limit reached!
% 5.90/7.70 % (1531457)------------------------------
% 5.90/7.70 % (1531457)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.90/7.70 % (1531457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.90/7.70 % (1531457)CaDiCaL version: 2.1.3
% 5.90/7.70 % (1531457)Termination reason: Instruction limit
% 5.90/7.70 % (1531457)Termination phase: Saturation
% 5.90/7.70 % (1531457)Time elapsed: 0.142 s
% 5.90/7.70 % (1531457)Peak memory usage: 90 MB
% 5.90/7.70 % (1531457)Instructions burned: 248 (million)
% 5.90/7.70 % (1531456)Instruction limit reached!
% 5.90/7.70 % (1531456)------------------------------
% 5.90/7.70 % (1531456)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.90/7.70 % (1531456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.90/7.70 % (1531456)CaDiCaL version: 2.1.3
% 5.90/7.70 % (1531456)Termination reason: Instruction limit
% 5.90/7.70 % (1531456)Termination phase: Saturation
% 5.90/7.70 % (1531456)Time elapsed: 0.206 s
% 5.90/7.70 % (1531456)Peak memory usage: 92 MB
% 5.90/7.70 % (1531456)Instructions burned: 325 (million)
% 5.90/7.70 % (1531463)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=85072775:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 5.90/7.70 % (1531465)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=450200659:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 5.90/7.70 % (1531466)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3354445365:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 5.90/7.70 % (1531468)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=699568401:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2994 on theBenchmark for (2994ds/114Mi)
% 5.90/7.70 % (1531465)Instruction limit reached!
% 5.90/7.70 % (1531465)------------------------------
% 5.90/7.70 % (1531465)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.90/7.70 % (1531465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.90/7.70 % (1531465)CaDiCaL version: 2.1.3
% 5.90/7.70 % (1531465)Termination reason: Instruction limit
% 5.90/7.70 % (1531465)Termination phase: Saturation
% 5.90/7.70 % (1531465)Time elapsed: 0.072 s
% 5.90/7.70 % (1531465)Peak memory usage: 90 MB
% 5.90/7.70 % (1531465)Instructions burned: 114 (million)
% 5.90/7.70 % (1531466)Instruction limit reached!
% 5.90/7.70 % (1531466)------------------------------
% 5.90/7.70 % (1531466)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.90/7.70 % (1531466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.90/7.70 % (1531466)CaDiCaL version: 2.1.3
% 5.90/7.70 % (1531466)Termination reason: Instruction limit
% 5.90/7.70 % (1531466)Termination phase: Saturation
% 5.90/7.70 % (1531466)Time elapsed: 0.065 s
% 5.90/7.70 % (1531466)Peak memory usage: 89 MB
% 5.90/7.70 % (1531466)Instructions burned: 128 (million)
% 5.90/7.70 % (1531468)Instruction limit reached!
% 5.90/7.70 % (1531468)------------------------------
% 5.90/7.70 % (1531468)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.90/7.70 % (1531468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.90/7.70 % (1531468)CaDiCaL version: 2.1.3
% 5.90/7.70 % (1531468)Termination reason: Instruction limit
% 5.90/7.70 % (1531468)Termination phase: Saturation
% 5.90/7.70 % (1531468)Time elapsed: 0.061 s
% 5.90/7.70 % (1531468)Peak memory usage: 89 MB
% 5.90/7.70 % (1531468)Instructions burned: 115 (million)
% 5.90/7.70 % (1531472)lrs+10_1_sil=8000:sp=occurrence:random_seed=1447543138:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 5.90/7.70 % (1531473)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2731238607:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 5.90/7.70 % (1531474)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=187015830:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 5.90/7.70 % (1531441)First to succeed.
% 5.90/7.70 % (1531441)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1531435"
% 5.90/7.70 % (1531473)Instruction limit reached!
% 5.90/7.70 % (1531473)------------------------------
% 5.90/7.70 % (1531473)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.90/7.70 % (1531473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.90/7.70 % (1531473)CaDiCaL version: 2.1.3
% 5.90/7.70 % (1531473)Termination reason: Instruction limit
% 5.90/7.70 % (1531473)Termination phase: Saturation
% 5.90/7.70 % (1531473)Time elapsed: 0.209 s
% 5.90/7.70 % (1531473)Peak memory usage: 90 MB
% 5.90/7.70 % (1531473)Instructions burned: 438 (million)
% 5.90/7.70 % (1531478)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=348304428:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2989 on theBenchmark for (2989ds/134Mi)
% 5.90/7.70 % (1531441)Refutation found. Thanks to Tanya!
% 5.90/7.70 % SZS status Theorem for theBenchmark
% 5.90/7.70 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/7.80 % (1531441)------------------------------
% 0.19/7.80 % (1531441)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/7.80 % (1531441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/7.80 % (1531441)CaDiCaL version: 2.1.3
% 0.19/7.80 % (1531441)Termination reason: Refutation
% 0.19/7.80 % (1531441)Time elapsed: 0.828 s
% 0.19/7.80 % (1531441)Peak memory usage: 133 MB
% 0.19/7.80 % (1531441)Instructions burned: 1251 (million)
% 0.19/7.80 % (1531441)------------------------------
% 0.19/7.80 % (1531441)------------------------------
% 0.19/7.80 % (1531435)Success in time 1.229 s
% 0.19/7.80 % Vampire exiting
%------------------------------------------------------------------------------