%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ITP006+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:47:33 PM UTC 2026
% Result : Theorem 8.29s 6.87s
% Output : CNFRefutation 8.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 30 ( 5 unt; 0 def)
% Number of atoms : 213 ( 20 equ)
% Maximal formula atoms : 32 ( 7 avg)
% Number of connectives : 279 ( 96 ~; 85 |; 76 &)
% ( 12 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 6 con; 0-4 aty)
% Number of variables : 220 ( 0 sgn 172 !; 48 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
fof(f37,axiom,
! [X0,X1,X2,X3] :
( ! [X18,X19] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X18),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X19))))
<=> ! [X20] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X19),s(X1,X20))))
=> ? [X21] : s(X1,X20) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X18),s(X0,X21))) ) )
& ! [X14,X15] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X14),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X15))))
<=> ! [X16] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X15),s(X1,X16))))
=> ? [X17] : s(X1,X16) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X14),s(X0,X17))) ) )
& ! [X11,X12] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X11),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X12))))
<=> ! [X13] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X12),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X11),s(X0,X13)))))) )
& ! [X8,X9] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X8),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X9))))
<=> ! [X10] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X9),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X8),s(X0,X10)))))) )
& ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))
<=> ! [X6] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X6))))
=> ? [X7] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X7)))))) ) )
& ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))
<=> ! [X4] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X4))))
=> ? [X5] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X5)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EquantHeuristics_2EGUESS__REWRITES) ).
fof(f49,conjecture,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4),s(X0,X5))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3),s(X0,X5)))) )
=> ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X1,X0),X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3))))
=> p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X1,X0),X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT) ).
fof(f50,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ! [X5] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4),s(X0,X5))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3),s(X0,X5)))) )
=> ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X1,X0),X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3))))
=> p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X1,X0),X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4)))) ) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
fof(f60,plain,
! [X0,X1,X2,X3] :
( ! [X18,X19] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X18),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X19))))
<=> ! [X20] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X19),s(X1,X20))))
| ? [X21] : s(X1,X20) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X18),s(X0,X21))) ) )
& ! [X14,X15] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X14),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X15))))
<=> ! [X16] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X15),s(X1,X16))))
| ? [X17] : s(X1,X16) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X14),s(X0,X17))) ) )
& ! [X11,X12] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X11),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X12))))
<=> ! [X13] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X12),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X11),s(X0,X13)))))) )
& ! [X8,X9] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X8),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X9))))
<=> ! [X10] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X9),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X8),s(X0,X10)))))) )
& ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))
<=> ! [X6] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X6))))
| ? [X7] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X7)))))) ) )
& ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))
<=> ! [X4] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X4))))
| ? [X5] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X5)))))) ) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f74,plain,
? [X0,X1,X2,X3,X4] :
( ! [X5] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4),s(X0,X5))))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3),s(X0,X5)))) )
& p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X1,X0),X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3))))
& ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X1,X0),X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4)))) ),
inference(ennf_transformation,[],[f50]) ).
fof(f75,plain,
? [X0,X1,X2,X3,X4] :
( ! [X5] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4),s(X0,X5))))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3),s(X0,X5)))) )
& p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X1,X0),X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3))))
& ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X1,X0),X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4)))) ),
inference(flattening,[],[f74]) ).
fof(f126,plain,
! [X0,X1,X2,X3] :
( ! [X18,X19] :
( ( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X18),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X19))))
| ! [X20] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X19),s(X1,X20))))
| ? [X21] : s(X1,X20) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X18),s(X0,X21))) ) )
& ( ? [X20] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X19),s(X1,X20))))
& ! [X21] : s(X1,X20) != s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X18),s(X0,X21))) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X18),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X19)))) ) )
& ! [X14,X15] :
( ( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X14),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X15))))
| ! [X16] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X15),s(X1,X16))))
| ? [X17] : s(X1,X16) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X14),s(X0,X17))) ) )
& ( ? [X16] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X15),s(X1,X16))))
& ! [X17] : s(X1,X16) != s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X14),s(X0,X17))) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X14),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X15)))) ) )
& ! [X11,X12] :
( ( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X11),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X12))))
| ! [X13] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X12),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X11),s(X0,X13)))))) )
& ( ? [X13] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X12),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X11),s(X0,X13))))))
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X11),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X12)))) ) )
& ! [X8,X9] :
( ( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X8),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X9))))
| ! [X10] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X9),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X8),s(X0,X10)))))) )
& ( ? [X10] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X9),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X8),s(X0,X10))))))
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X8),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X9)))) ) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))
| ! [X6] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X6))))
| ? [X7] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X7)))))) ) )
& ( ? [X6] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X6))))
& ! [X7] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X7)))))) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))
| ! [X4] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X4))))
| ? [X5] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X5)))))) ) )
& ( ? [X4] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X4))))
& ! [X5] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X5)))))) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))) ) ),
inference(nnf_transformation,[],[f60]) ).
fof(f127,plain,
! [X0,X1,X2,X3] :
( ! [X18,X19] :
( ( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X18),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X19))))
| ! [X20] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X19),s(X1,X20))))
| ? [X21] : s(X1,X20) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X18),s(X0,X21))) ) )
& ( ? [X20] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X19),s(X1,X20))))
& ! [X21] : s(X1,X20) != s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X18),s(X0,X21))) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X18),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X19)))) ) )
& ! [X14,X15] :
( ( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X14),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X15))))
| ! [X16] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X15),s(X1,X16))))
| ? [X17] : s(X1,X16) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X14),s(X0,X17))) ) )
& ( ? [X16] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X15),s(X1,X16))))
& ! [X17] : s(X1,X16) != s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X14),s(X0,X17))) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X14),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X15)))) ) )
& ! [X11,X12] :
( ( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X11),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X12))))
| ! [X13] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X12),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X11),s(X0,X13)))))) )
& ( ? [X13] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X12),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X11),s(X0,X13))))))
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X11),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X12)))) ) )
& ! [X8,X9] :
( ( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X8),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X9))))
| ! [X10] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X9),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X8),s(X0,X10)))))) )
& ( ? [X10] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X9),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X8),s(X0,X10))))))
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X8),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X9)))) ) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))
| ! [X6] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X6))))
| ? [X7] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X7)))))) ) )
& ( ? [X6] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X6))))
& ! [X7] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X7)))))) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))
| ! [X4] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X4))))
| ? [X5] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X5)))))) ) )
& ( ? [X4] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X4))))
& ! [X5] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X5)))))) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))) ) ),
inference(flattening,[],[f126]) ).
fof(f128,plain,
! [X0,X1,X2,X3] :
( ! [X26,X27] :
( ( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X26),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X27))))
| ! [X30] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X27),s(X1,X30))))
| ? [X31] : s(X1,X30) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X26),s(X0,X31))) ) )
& ( ? [X28] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X27),s(X1,X28))))
& ! [X29] : s(X1,X28) != s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X26),s(X0,X29))) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X26),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X27)))) ) )
& ! [X20,X21] :
( ( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X20),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X21))))
| ! [X24] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X21),s(X1,X24))))
| ? [X25] : s(X1,X24) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X20),s(X0,X25))) ) )
& ( ? [X22] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X21),s(X1,X22))))
& ! [X23] : s(X1,X22) != s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X20),s(X0,X23))) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X20),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X21)))) ) )
& ! [X16,X17] :
( ( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X16),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17))))
| ! [X19] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X16),s(X0,X19)))))) )
& ( ? [X18] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X16),s(X0,X18))))))
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X16),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17)))) ) )
& ! [X12,X13] :
( ( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X12),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X13))))
| ! [X15] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X13),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X12),s(X0,X15)))))) )
& ( ? [X14] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X13),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X12),s(X0,X14))))))
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X12),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X13)))) ) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))
| ! [X10] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X10))))
| ? [X11] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X11)))))) ) )
& ( ? [X8] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X8))))
& ! [X9] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X9)))))) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))
| ! [X6] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X6))))
| ? [X7] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X7)))))) ) )
& ( ? [X4] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X4))))
& ! [X5] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X5)))))) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))) ) ),
inference(rectify,[],[f127]) ).
fof(f129,plain,
! [X0,X1,X2,X3] :
( ! [X26,X27] :
( ( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X26),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X27))))
| ! [X30] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X27),s(X1,X30))))
| s(X1,X30) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X26),s(X0,sK22(X0,X1,X26,X30)))) ) )
& ( ( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X27),s(X1,sK21(X0,X1,X26,X27)))))
& ! [X29] : s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X26),s(X0,X29))) != s(X1,sK21(X0,X1,X26,X27)) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X26),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X27)))) ) )
& ! [X20,X21] :
( ( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X20),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X21))))
| ! [X24] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X21),s(X1,X24))))
| s(X1,X24) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X20),s(X0,sK20(X0,X1,X20,X24)))) ) )
& ( ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X21),s(X1,sK19(X0,X1,X20,X21)))))
& ! [X23] : s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X20),s(X0,X23))) != s(X1,sK19(X0,X1,X20,X21)) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X20),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X21)))) ) )
& ! [X16,X17] :
( ( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X16),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17))))
| ! [X19] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X16),s(X0,X19)))))) )
& ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X16),s(X0,sK18(X0,X1,X16,X17)))))))
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X16),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17)))) ) )
& ! [X12,X13] :
( ( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X12),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X13))))
| ! [X15] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X13),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X12),s(X0,X15)))))) )
& ( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X13),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X12),s(X0,sK17(X0,X1,X12,X13)))))))
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X12),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X13)))) ) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))
| ! [X10] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X10))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,sK16(X0,X1,X2,X3))))))) ) )
& ( ( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,sK15(X0,X1,X2,X3)))))
& ! [X9] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X9)))))) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))
| ! [X6] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X6))))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,sK14(X0,X1,X2,X3))))))) ) )
& ( ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,sK13(X0,X1,X2,X3)))))
& ! [X5] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X5)))))) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16,sK17,sK18,sK19,sK20,sK21,sK22]),skolemize(X4,sK13(X0,X1,X2,X3)),skolemize(X7,sK14(X0,X1,X2,X3)),skolemize(X8,sK15(X0,X1,X2,X3)),skolemize(X11,sK16(X0,X1,X2,X3)),skolemize(X14,sK17(X0,X1,X12,X13)),skolemize(X18,sK18(X0,X1,X16,X17)),skolemize(X22,sK19(X0,X1,X20,X21)),skolemize(X25,sK20(X0,X1,X20,X24)),skolemize(X28,sK21(X0,X1,X26,X27)),skolemize(X31,sK22(X0,X1,X26,X30))],[f128]) ).
fof(f170,plain,
( ! [X5] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK27),s(sK23,X5))))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK26),s(sK23,X5)))) )
& p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK24,sK23),sK25),s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK26))))
& ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK24,sK23),sK25),s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK27)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23,sK24,sK25,sK26,sK27]),skolemize(X0,sK23),skolemize(X1,sK24),skolemize(X2,sK25),skolemize(X3,sK26),skolemize(X4,sK27)],[f75]) ).
fof(f271,plain,
! [X0,X1,X19,X16,X17] :
( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X16),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X16),s(X0,X19)))))) ),
inference(cnf_transformation,[],[f129]) ).
fof(f272,plain,
! [X0,X1,X16,X17] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X16),s(X0,sK18(X0,X1,X16,X17)))))))
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X16),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17)))) ),
inference(cnf_transformation,[],[f129]) ).
fof(f372,plain,
! [X5] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK27),s(sK23,X5))))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK26),s(sK23,X5)))) ),
inference(cnf_transformation,[],[f170]) ).
fof(f373,plain,
p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK24,sK23),sK25),s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK26)))),
inference(cnf_transformation,[],[f170]) ).
fof(f374,plain,
~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK24,sK23),sK25),s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK27)))),
inference(cnf_transformation,[],[f170]) ).
tcf(c_132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X2,X0),X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,app_2E2(s(tyop_2Emin_2Efun(X2,X0),X3),s(X2,sK18(X2,X0,X3,X1))))))) ),
inference(cnf_transformation,[],[f272]) ).
tcf(c_133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X2,X0),X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,app_2E2(s(tyop_2Emin_2Efun(X2,X0),X3),s(X2,X4)))))) ),
inference(cnf_transformation,[],[f271]) ).
tcf(c_214,negated_conjecture,
~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK24,sK23),sK25),s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK27)))),
inference(cnf_transformation,[],[f374]) ).
tcf(c_215,negated_conjecture,
p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK24,sK23),sK25),s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK26)))),
inference(cnf_transformation,[],[f373]) ).
tcf(c_216,negated_conjecture,
! [X0: $i] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK26),s(sK23,X0))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK27),s(sK23,X0)))) ),
inference(cnf_transformation,[],[f372]) ).
tcf(c_1701,negated_conjecture,
! [X0_iProver_sP7_2: iProver_sP7_2] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK26),s(sK23,X0_iProver_sP7_2))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK27),s(sK23,X0_iProver_sP7_2)))) ),
inference(subtyping,[status(esa)],[c_216]) ).
tcf(c_1718,plain,
! [X0_iProver_sP7_2: iProver_sP7_2,X0_iProver_s_1: iProver_s_1,X1_iProver_sP7_2: iProver_sP7_2,X1_iProver_s_1: iProver_s_1,X2_iProver_sP7_2: iProver_sP7_2] :
( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X1_iProver_s_1,X0_iProver_s_1),X1_iProver_sP7_2),s(tyop_2Emin_2Efun(X0_iProver_s_1,tyop_2Emin_2Ebool),X0_iProver_sP7_2))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0_iProver_s_1,tyop_2Emin_2Ebool),X0_iProver_sP7_2),s(X0_iProver_s_1,app_2E2(s(tyop_2Emin_2Efun(X1_iProver_s_1,X0_iProver_s_1),X1_iProver_sP7_2),s(X1_iProver_s_1,X2_iProver_sP7_2)))))) ),
inference(subtyping,[status(esa)],[c_133]) ).
tcf(c_1719,plain,
! [X0_iProver_sP7_2: iProver_sP7_2,X0_iProver_s_1: iProver_s_1,X1_iProver_sP7_2: iProver_sP7_2,X1_iProver_s_1: iProver_s_1] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X1_iProver_s_1,X0_iProver_s_1),X1_iProver_sP7_2),s(tyop_2Emin_2Efun(X0_iProver_s_1,tyop_2Emin_2Ebool),X0_iProver_sP7_2))))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0_iProver_s_1,tyop_2Emin_2Ebool),X0_iProver_sP7_2),s(X0_iProver_s_1,app_2E2(s(tyop_2Emin_2Efun(X1_iProver_s_1,X0_iProver_s_1),X1_iProver_sP7_2),s(X1_iProver_s_1,sK18(X1_iProver_s_1,X0_iProver_s_1,X1_iProver_sP7_2,X0_iProver_sP7_2))))))) ),
inference(subtyping,[status(esa)],[c_132]) ).
tcf(c_2643,plain,
! [X0_iProver_sP7_2: iProver_sP7_2] :
( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK24,sK23),sK25),s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK26))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK26),s(sK23,app_2E2(s(tyop_2Emin_2Efun(sK24,sK23),sK25),s(sK24,X0_iProver_sP7_2)))))) ),
inference(instantiation,[status(thm)],[c_1718]) ).
tcf(c_2723,plain,
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK24,sK23),sK25),s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK27))))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK27),s(sK23,app_2E2(s(tyop_2Emin_2Efun(sK24,sK23),sK25),s(sK24,sK18(sK24,sK23,sK25,sK27))))))) ),
inference(instantiation,[status(thm)],[c_1719]) ).
tcf(c_3358,plain,
! [X0_iProver_sP7_2: iProver_sP7_2,X0_iProver_s_1: iProver_s_1] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK26),s(sK23,app_2E2(s(tyop_2Emin_2Efun(X0_iProver_s_1,sK23),X0_iProver_sP7_2),s(X0_iProver_s_1,sK18(X0_iProver_s_1,sK23,X0_iProver_sP7_2,sK27)))))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK27),s(sK23,app_2E2(s(tyop_2Emin_2Efun(X0_iProver_s_1,sK23),X0_iProver_sP7_2),s(X0_iProver_s_1,sK18(X0_iProver_s_1,sK23,X0_iProver_sP7_2,sK27))))))) ),
inference(instantiation,[status(thm)],[c_1701]) ).
tcf(c_9196,plain,
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK26),s(sK23,app_2E2(s(tyop_2Emin_2Efun(sK24,sK23),sK25),s(sK24,sK18(sK24,sK23,sK25,sK27)))))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK27),s(sK23,app_2E2(s(tyop_2Emin_2Efun(sK24,sK23),sK25),s(sK24,sK18(sK24,sK23,sK25,sK27))))))) ),
inference(instantiation,[status(thm)],[c_3358]) ).
tcf(c_21730,plain,
( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK24,sK23),sK25),s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK26))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK26),s(sK23,app_2E2(s(tyop_2Emin_2Efun(sK24,sK23),sK25),s(sK24,sK18(sK24,sK23,sK25,sK27))))))) ),
inference(instantiation,[status(thm)],[c_2643]) ).
tcf(c_21731,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_21730,c_9196,c_2723,c_214,c_215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP006+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.58 % Computer : n006.cluster.edu
% 0.10/5.58 % Model : x86_64 x86_64
% 0.10/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.58 % Memory : 8046.5625MB
% 0.10/5.58 % OS : Linux 6.8.0-71-generic
% 0.10/5.58 % CPULimit : 300
% 0.10/5.58 % WCLimit : 300
% 0.10/5.58 % DateTime : Wed Sep 23 17:30:36 UTC 2026
% 0.10/5.58 % CPUTime :
% 0.10/5.58 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.62 Running first-order theorem proving
% 0.14/5.62 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/5.63
% 0.14/5.63 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.63
% 0.14/5.63 % Detected problem language: tptp
% 0.14/5.64 % Proving...
% 8.29/6.87 % SZS status Started for theBenchmark.p
% 8.29/6.87 % SZS status Theorem for theBenchmark.p
% 8.29/6.87
% 8.29/6.87 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.29/6.87
% 8.29/6.87 % ------ iProver source info
% 8.29/6.87
% 8.29/6.87 % git: date: 2026-07-19 20:42:38 +0200
% 8.29/6.87 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.29/6.87 % git: non_committed_changes: false
% 8.29/6.87
% 8.29/6.87 % ------ Parsing...
% 8.29/6.87 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.29/6.87
% 8.29/6.87 % ------ Preprocessing... sup_sim: 4 pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 pe_s pe_e %
% 8.29/6.87
% 8.29/6.87 % ------ Preprocessing... gs_s sp: 10 0s gs_e scvd_s sp: 2 0s scvd_e snvd_s sp: 0 0s snvd_e %
% 8.29/6.87
% 8.29/6.87 % ------ Preprocessing...
% 8.29/6.87 % ------ Proving...
% 8.29/6.87 % ------ Problem Properties
% 8.29/6.87
% 8.29/6.87 %
% 8.29/6.87 % clauses 140
% 8.29/6.87 % conjectures 3
% 8.29/6.87 % EPR 9
% 8.29/6.87 % Horn 91
% 8.29/6.87 % unary 15
% 8.29/6.87 % binary 101
% 8.29/6.87 % lits 298
% 8.29/6.87 % lits eq 40
% 8.29/6.87 % fd_pure 0
% 8.29/6.87 % fd_pseudo 0
% 8.29/6.87 % fd_cond 0
% 8.29/6.87 % fd_pseudo_cond 0
% 8.29/6.87 % AC symbols 0
% 8.29/6.87
% 8.29/6.87 % ------ Input Options Time Limit: Unbounded
% 8.29/6.87
% 8.29/6.87
% 8.29/6.87 % ------
% 8.29/6.87 % Current options:
% 8.29/6.87 % ------
% 8.29/6.87
% 8.29/6.87
% 8.29/6.87 %
% 8.29/6.87
% 8.29/6.87 % ------ Proving...
% 8.29/6.87 %
% 8.29/6.87
% 8.29/6.87 % SZS status Theorem for theBenchmark.p
% 8.29/6.87
% 8.29/6.87 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.29/6.87
% 8.29/6.87
%------------------------------------------------------------------------------