%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ITP006+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 : Thu Sep 24 12:50:02 PM UTC 2026
% Result : Theorem 54.02s 7.26s
% Output : CNFRefutation 54.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 160 ( 16 equ)
% Maximal formula atoms : 32 ( 8 avg)
% Number of connectives : 209 ( 68 ~; 58 |; 61 &)
% ( 12 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 6 con; 0-5 aty)
% Number of variables : 238 ( 200 !; 38 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f37,axiom,
! [A_27a,A_27b,V0i_2E0,V1P_2E0] :
( ! [V16i_2E0,V17P_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V16i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V17P_2E0))))
<=> ! [V18v_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V17P_2E0),s(A_27b,V18v_2E0))))
=> ? [V19fv_2E0] : s(A_27b,V18v_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V16i_2E0),s(A_27a,V19fv_2E0))) ) )
& ! [V12i_2E0,V13P_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V12i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V13P_2E0))))
<=> ! [V14v_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V13P_2E0),s(A_27b,V14v_2E0))))
=> ? [V15fv_2E0] : s(A_27b,V14v_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V12i_2E0),s(A_27a,V15fv_2E0))) ) )
& ! [V9i_2E0,V10P_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V9i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V10P_2E0))))
<=> ! [V11fv_2E0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V10P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V9i_2E0),s(A_27a,V11fv_2E0)))))) )
& ! [V6i_2E0,V7P_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V7P_2E0))))
<=> ! [V8fv_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V7P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6i_2E0),s(A_27a,V8fv_2E0)))))) )
& ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0))))
<=> ! [V4v_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V4v_2E0))))
=> ? [V5fv_2E0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(A_27a,V5fv_2E0)))))) ) )
& ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0))))
<=> ! [V2v_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V2v_2E0))))
=> ? [V3fv_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(A_27a,V3fv_2E0)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,conjecture,
! [A_27a,A_27b,V0i_2E0,V1P_2E0,V2Q_2E0] :
( ! [V3x_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V3x_2E0))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3x_2E0)))) )
=> ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0i_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0i_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
~ ! [A_27a,A_27b,V0i_2E0,V1P_2E0,V2Q_2E0] :
( ! [V3x_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V3x_2E0))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3x_2E0)))) )
=> ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0i_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0i_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0)))) ) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
fof(f189,plain,
! [A_27a,A_27b,V0i_2E0,V1P_2E0] :
( ! [V16i_2E0,V17P_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V16i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V17P_2E0))))
<=> ! [V18v_2E0] :
( ? [V19fv_2E0] : s(A_27b,V18v_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V16i_2E0),s(A_27a,V19fv_2E0)))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V17P_2E0),s(A_27b,V18v_2E0)))) ) )
& ! [V12i_2E0,V13P_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V12i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V13P_2E0))))
<=> ! [V14v_2E0] :
( ? [V15fv_2E0] : s(A_27b,V14v_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V12i_2E0),s(A_27a,V15fv_2E0)))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V13P_2E0),s(A_27b,V14v_2E0)))) ) )
& ! [V9i_2E0,V10P_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V9i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V10P_2E0))))
<=> ! [V11fv_2E0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V10P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V9i_2E0),s(A_27a,V11fv_2E0)))))) )
& ! [V6i_2E0,V7P_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V7P_2E0))))
<=> ! [V8fv_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V7P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6i_2E0),s(A_27a,V8fv_2E0)))))) )
& ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0))))
<=> ! [V4v_2E0] :
( ? [V5fv_2E0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(A_27a,V5fv_2E0))))))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V4v_2E0)))) ) )
& ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0))))
<=> ! [V2v_2E0] :
( ? [V3fv_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(A_27a,V3fv_2E0))))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V2v_2E0)))) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f190,plain,
! [A_27a,A_27b,V0i_2E0,V1P_2E0] :
( ! [V16i_2E0,V17P_2E0] :
( ( ? [V18v_2E0] :
( ! [V19fv_2E0] : s(A_27b,V18v_2E0) != s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V16i_2E0),s(A_27a,V19fv_2E0)))
& ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V17P_2E0),s(A_27b,V18v_2E0)))) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V16i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V17P_2E0)))) )
& ( ! [V18v_2E0] :
( ? [V19fv_2E0] : s(A_27b,V18v_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V16i_2E0),s(A_27a,V19fv_2E0)))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V17P_2E0),s(A_27b,V18v_2E0)))) )
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V16i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V17P_2E0)))) ) )
& ! [V12i_2E0,V13P_2E0] :
( ( ? [V14v_2E0] :
( ! [V15fv_2E0] : s(A_27b,V14v_2E0) != s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V12i_2E0),s(A_27a,V15fv_2E0)))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V13P_2E0),s(A_27b,V14v_2E0)))) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V12i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V13P_2E0)))) )
& ( ! [V14v_2E0] :
( ? [V15fv_2E0] : s(A_27b,V14v_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V12i_2E0),s(A_27a,V15fv_2E0)))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V13P_2E0),s(A_27b,V14v_2E0)))) )
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V12i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V13P_2E0)))) ) )
& ! [V9i_2E0,V10P_2E0] :
( ( ? [V11fv_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V10P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V9i_2E0),s(A_27a,V11fv_2E0))))))
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V9i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V10P_2E0)))) )
& ( ! [V11fv_2E0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V10P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V9i_2E0),s(A_27a,V11fv_2E0))))))
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V9i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V10P_2E0)))) ) )
& ! [V6i_2E0,V7P_2E0] :
( ( ? [V8fv_2E0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V7P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6i_2E0),s(A_27a,V8fv_2E0))))))
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V7P_2E0)))) )
& ( ! [V8fv_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V7P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6i_2E0),s(A_27a,V8fv_2E0))))))
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V7P_2E0)))) ) )
& ( ? [V4v_2E0] :
( ! [V5fv_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(A_27a,V5fv_2E0))))))
& ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V4v_2E0)))) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0)))) )
& ( ! [V4v_2E0] :
( ? [V5fv_2E0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(A_27a,V5fv_2E0))))))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V4v_2E0)))) )
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0)))) )
& ( ? [V2v_2E0] :
( ! [V3fv_2E0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(A_27a,V3fv_2E0))))))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V2v_2E0)))) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0)))) )
& ( ! [V2v_2E0] :
( ? [V3fv_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(A_27a,V3fv_2E0))))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V2v_2E0)))) )
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0)))) ) ),
inference(NNF_transformation,[status(thm)],[f189]) ).
fof(f191,plain,
( ! [A_27a,A_27b,V16i_2E0,V17P_2E0] :
( ? [V18v_2E0] :
( ! [V19fv_2E0] : s(A_27b,V18v_2E0) != s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V16i_2E0),s(A_27a,V19fv_2E0)))
& ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V17P_2E0),s(A_27b,V18v_2E0)))) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V16i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V17P_2E0)))) )
& ! [A_27a,A_27b,V16i_2E0,V17P_2E0] :
( ! [V18v_2E0] :
( ? [V19fv_2E0] : s(A_27b,V18v_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V16i_2E0),s(A_27a,V19fv_2E0)))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V17P_2E0),s(A_27b,V18v_2E0)))) )
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V16i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V17P_2E0)))) )
& ! [A_27a,A_27b,V12i_2E0,V13P_2E0] :
( ? [V14v_2E0] :
( ! [V15fv_2E0] : s(A_27b,V14v_2E0) != s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V12i_2E0),s(A_27a,V15fv_2E0)))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V13P_2E0),s(A_27b,V14v_2E0)))) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V12i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V13P_2E0)))) )
& ! [A_27a,A_27b,V12i_2E0,V13P_2E0] :
( ! [V14v_2E0] :
( ? [V15fv_2E0] : s(A_27b,V14v_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V12i_2E0),s(A_27a,V15fv_2E0)))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V13P_2E0),s(A_27b,V14v_2E0)))) )
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V12i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V13P_2E0)))) )
& ! [A_27a,A_27b,V9i_2E0,V10P_2E0] :
( ? [V11fv_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V10P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V9i_2E0),s(A_27a,V11fv_2E0))))))
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V9i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V10P_2E0)))) )
& ! [A_27a,A_27b,V9i_2E0,V10P_2E0] :
( ! [V11fv_2E0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V10P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V9i_2E0),s(A_27a,V11fv_2E0))))))
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V9i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V10P_2E0)))) )
& ! [A_27a,A_27b,V6i_2E0,V7P_2E0] :
( ? [V8fv_2E0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V7P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6i_2E0),s(A_27a,V8fv_2E0))))))
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V7P_2E0)))) )
& ! [A_27a,A_27b,V6i_2E0,V7P_2E0] :
( ! [V8fv_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V7P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6i_2E0),s(A_27a,V8fv_2E0))))))
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V7P_2E0)))) )
& ! [A_27a,A_27b,V0i_2E0,V1P_2E0] :
( ( ! [V5fv_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(A_27a,V5fv_2E0))))))
& ? [V4v_2E0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V4v_2E0)))) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0)))) )
& ! [A_27a,A_27b,V0i_2E0,V1P_2E0] :
( ? [V5fv_2E0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(A_27a,V5fv_2E0))))))
| ! [V4v_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V4v_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0)))) )
& ! [A_27a,A_27b,V0i_2E0,V1P_2E0] :
( ( ! [V3fv_2E0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(A_27a,V3fv_2E0))))))
& ? [V2v_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V2v_2E0)))) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0)))) )
& ! [A_27a,A_27b,V0i_2E0,V1P_2E0] :
( ? [V3fv_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(A_27a,V3fv_2E0))))))
| ! [V2v_2E0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V2v_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0)))) ) ),
inference(miniscoping,[status(thm)],[f190]) ).
fof(f192,plain,
( ! [A_27a,A_27b,V16i_2E0,V17P_2E0] :
( ( ! [V19fv_2E0] : s(A_27b,sK12_skl(V17P_2E0,V16i_2E0,A_27b,A_27a)) != s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V16i_2E0),s(A_27a,V19fv_2E0)))
& ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V17P_2E0),s(A_27b,sK12_skl(V17P_2E0,V16i_2E0,A_27b,A_27a))))) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V16i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V17P_2E0)))) )
& ! [A_27a,A_27b,V16i_2E0,V17P_2E0] :
( ! [V18v_2E0] :
( s(A_27b,V18v_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V16i_2E0),s(A_27a,sK11_skl(V18v_2E0,V17P_2E0,V16i_2E0,A_27b,A_27a))))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V17P_2E0),s(A_27b,V18v_2E0)))) )
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V16i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V17P_2E0)))) )
& ! [A_27a,A_27b,V12i_2E0,V13P_2E0] :
( ( ! [V15fv_2E0] : s(A_27b,sK10_skl(V13P_2E0,V12i_2E0,A_27b,A_27a)) != s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V12i_2E0),s(A_27a,V15fv_2E0)))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V13P_2E0),s(A_27b,sK10_skl(V13P_2E0,V12i_2E0,A_27b,A_27a))))) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V12i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V13P_2E0)))) )
& ! [A_27a,A_27b,V12i_2E0,V13P_2E0] :
( ! [V14v_2E0] :
( s(A_27b,V14v_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V12i_2E0),s(A_27a,sK9_skl(V14v_2E0,V13P_2E0,V12i_2E0,A_27b,A_27a))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V13P_2E0),s(A_27b,V14v_2E0)))) )
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V12i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V13P_2E0)))) )
& ! [A_27a,A_27b,V9i_2E0,V10P_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V10P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V9i_2E0),s(A_27a,sK8_skl(V10P_2E0,V9i_2E0,A_27b,A_27a)))))))
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V9i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V10P_2E0)))) )
& ! [A_27a,A_27b,V9i_2E0,V10P_2E0] :
( ! [V11fv_2E0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V10P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V9i_2E0),s(A_27a,V11fv_2E0))))))
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V9i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V10P_2E0)))) )
& ! [A_27a,A_27b,V6i_2E0,V7P_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V7P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6i_2E0),s(A_27a,sK7_skl(V7P_2E0,V6i_2E0,A_27b,A_27a)))))))
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V7P_2E0)))) )
& ! [A_27a,A_27b,V6i_2E0,V7P_2E0] :
( ! [V8fv_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V7P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6i_2E0),s(A_27a,V8fv_2E0))))))
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V7P_2E0)))) )
& ! [A_27a,A_27b,V0i_2E0,V1P_2E0] :
( ( ! [V5fv_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(A_27a,V5fv_2E0))))))
& ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,sK6_skl(V1P_2E0,V0i_2E0,A_27b,A_27a))))) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0)))) )
& ! [A_27a,A_27b,V0i_2E0,V1P_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(A_27a,sK5_skl(V1P_2E0,V0i_2E0,A_27b,A_27a)))))))
| ! [V4v_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V4v_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0)))) )
& ! [A_27a,A_27b,V0i_2E0,V1P_2E0] :
( ( ! [V3fv_2E0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(A_27a,V3fv_2E0))))))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,sK4_skl(V1P_2E0,V0i_2E0,A_27b,A_27a))))) )
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0)))) )
& ! [A_27a,A_27b,V0i_2E0,V1P_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(A_27a,sK3_skl(V1P_2E0,V0i_2E0,A_27b,A_27a)))))))
| ! [V2v_2E0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V2v_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl,sK6_skl,sK7_skl,sK8_skl,sK9_skl,sK10_skl,sK11_skl,sK12_skl]),skolemize(V3fv_2E0,sK3_skl(V1P_2E0,V0i_2E0,A_27b,A_27a)),skolemize(V2v_2E0,sK4_skl(V1P_2E0,V0i_2E0,A_27b,A_27a)),skolemize(V5fv_2E0,sK5_skl(V1P_2E0,V0i_2E0,A_27b,A_27a)),skolemize(V4v_2E0,sK6_skl(V1P_2E0,V0i_2E0,A_27b,A_27a)),skolemize(V8fv_2E0,sK7_skl(V7P_2E0,V6i_2E0,A_27b,A_27a)),skolemize(V11fv_2E0,sK8_skl(V10P_2E0,V9i_2E0,A_27b,A_27a)),skolemize(V15fv_2E0,sK9_skl(V14v_2E0,V13P_2E0,V12i_2E0,A_27b,A_27a)),skolemize(V14v_2E0,sK10_skl(V13P_2E0,V12i_2E0,A_27b,A_27a)),skolemize(V19fv_2E0,sK11_skl(V18v_2E0,V17P_2E0,V16i_2E0,A_27b,A_27a)),skolemize(V18v_2E0,sK12_skl(V17P_2E0,V16i_2E0,A_27b,A_27a))],[f191]) ).
fof(f201,plain,
! [X0,X1,X2,X3,X4] :
( ~ 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,X4))))))
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f202,plain,
! [X0,X1,X2,X3] :
( 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,sK8_skl(X1,X3,X0,X2))))))) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f288,plain,
? [A_27a,A_27b,V0i_2E0,V1P_2E0,V2Q_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0i_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0i_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))))
& ! [V3x_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3x_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V3x_2E0)))) ) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f289,plain,
? [A_27a,V1P_2E0,V2Q_2E0] :
( ? [A_27b,V0i_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0i_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0i_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)))) )
& ! [V3x_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3x_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V3x_2E0)))) ) ),
inference(miniscoping,[status(thm)],[f288]) ).
fof(f290,plain,
( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK16_skl,sK13_skl),sK17_skl),s(tyop_2Emin_2Efun(sK13_skl,tyop_2Emin_2Ebool),sK15_skl))))
& p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK16_skl,sK13_skl),sK17_skl),s(tyop_2Emin_2Efun(sK13_skl,tyop_2Emin_2Ebool),sK14_skl))))
& ! [V3x_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK13_skl,tyop_2Emin_2Ebool),sK14_skl),s(sK13_skl,V3x_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK13_skl,tyop_2Emin_2Ebool),sK15_skl),s(sK13_skl,V3x_2E0)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl,sK15_skl,sK16_skl,sK17_skl]),skolemize(A_27a,sK13_skl),skolemize(V1P_2E0,sK14_skl),skolemize(V2Q_2E0,sK15_skl),skolemize(A_27b,sK16_skl),skolemize(V0i_2E0,sK17_skl)],[f289]) ).
fof(f291,plain,
! [X0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK13_skl,tyop_2Emin_2Ebool),sK14_skl),s(sK13_skl,X0))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK13_skl,tyop_2Emin_2Ebool),sK15_skl),s(sK13_skl,X0)))) ),
inference(cnf_transformation,[status(thm)],[f290]) ).
fof(f292,plain,
p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK16_skl,sK13_skl),sK17_skl),s(tyop_2Emin_2Efun(sK13_skl,tyop_2Emin_2Ebool),sK14_skl)))),
inference(cnf_transformation,[status(thm)],[f290]) ).
fof(f293,plain,
~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK16_skl,sK13_skl),sK17_skl),s(tyop_2Emin_2Efun(sK13_skl,tyop_2Emin_2Ebool),sK15_skl)))),
inference(cnf_transformation,[status(thm)],[f290]) ).
fof(f474,plain,
! [X0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK13_skl,tyop_2Emin_2Ebool),sK14_skl),s(sK13_skl,app_2E2(s(tyop_2Emin_2Efun(sK16_skl,sK13_skl),sK17_skl),s(sK16_skl,X0)))))),
inference(resolution,[status(thm)],[f292,f201]) ).
fof(f1287,plain,
p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK13_skl,tyop_2Emin_2Ebool),sK15_skl),s(sK13_skl,app_2E2(s(tyop_2Emin_2Efun(sK16_skl,sK13_skl),sK17_skl),s(sK16_skl,sK8_skl(sK15_skl,sK17_skl,sK13_skl,sK16_skl))))))),
inference(resolution,[status(thm)],[f202,f293]) ).
fof(f3033,plain,
p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK13_skl,tyop_2Emin_2Ebool),sK14_skl),s(sK13_skl,app_2E2(s(tyop_2Emin_2Efun(sK16_skl,sK13_skl),sK17_skl),s(sK16_skl,sK8_skl(sK15_skl,sK17_skl,sK13_skl,sK16_skl))))))),
inference(resolution,[status(thm)],[f1287,f291]) ).
fof(f3039,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3033,f474]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP006+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 21:40:51 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 54.02/7.26 % Refutation found
% 54.02/7.26 % SZS status Theorem for theBenchmark: Theorem is valid
% 54.02/7.26 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 38.03/8.46 % Elapsed time: 7.891127 seconds
% 38.03/8.46 % CPU time: 49.915849 seconds
% 38.03/8.46 % Total memory used: 567.344 MB
% 38.03/8.46 % Net memory used: 540.199 MB
%------------------------------------------------------------------------------