%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP006_3 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 11:34:00 AM UTC 2026
% Result : Theorem 0.77s 0.59s
% Output : Refutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 356 ( 51 equ)
% Maximal formula atoms : 32 ( 7 avg)
% Number of connectives : 458 ( 147 ~; 137 |; 130 &)
% ( 27 <=>; 16 =>; 0 <=; 1 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 49 ( 49 usr; 9 con; 0-4 aty)
% Number of variables : 235 ( 187 !; 48 ?; 235 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
tyop_2Emin_2Ebool: $tType ).
tff(type_def_6,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(type_def_7,type,
sK23: $tType ).
tff(type_def_8,type,
sK24: $tType ).
tff(func_def_0,type,
app_2E2:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_1,type,
combin_i_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(X0,X0) ).
tff(func_def_2,type,
combin_k_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X0)) ).
tff(func_def_3,type,
combin_s_2E0:
!>[X0: $tType,X1: $tType,X2: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2))) ).
tff(func_def_4,type,
c_2Ebool_2E_21_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(func_def_5,type,
c_2Ebool_2E_21_2E1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(func_def_6,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(func_def_7,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_8,type,
c_2Emin_2E_3D_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)) ).
tff(func_def_9,type,
c_2Emin_2E_3D_2E2:
!>[X0: $tType] : ( ( X0 * X0 ) > tyop_2Emin_2Ebool ) ).
tff(func_def_10,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(func_def_11,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_12,type,
c_2Ebool_2E_3F_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(func_def_13,type,
c_2Ebool_2E_3F_2E1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(func_def_14,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(func_def_15,type,
c_2EquantHeuristics_2EGUESS__EXISTS_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(func_def_16,type,
c_2EquantHeuristics_2EGUESS__EXISTS_2E2:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(func_def_17,type,
c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(func_def_18,type,
c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(func_def_19,type,
c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(func_def_20,type,
c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(func_def_21,type,
c_2EquantHeuristics_2EGUESS__FORALL_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(func_def_22,type,
c_2EquantHeuristics_2EGUESS__FORALL_2E2:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(func_def_23,type,
c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(func_def_24,type,
c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(func_def_25,type,
c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(func_def_26,type,
c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(func_def_27,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(func_def_28,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(func_def_29,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_30,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(func_def_31,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(func_def_32,type,
sK10:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X0,X1) ) > X0 ) ).
tff(func_def_33,type,
sK11:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_34,type,
sK12:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_35,type,
sK13:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > X1 ) ).
tff(func_def_36,type,
sK14:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > X0 ) ).
tff(func_def_37,type,
sK15:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > X1 ) ).
tff(func_def_38,type,
sK16:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > X0 ) ).
tff(func_def_39,type,
sK17:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > X0 ) ).
tff(func_def_40,type,
sK18:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > X0 ) ).
tff(func_def_41,type,
sK19:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > X1 ) ).
tff(func_def_42,type,
sK20:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * X1 ) > X0 ) ).
tff(func_def_43,type,
sK21:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > X1 ) ).
tff(func_def_44,type,
sK22:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * X1 ) > X0 ) ).
tff(func_def_45,type,
sK25: tyop_2Emin_2Efun(sK24,sK23) ).
tff(func_def_46,type,
sK26: tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool) ).
tff(func_def_47,type,
sK27: tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool) ).
tff(pred_def_1,type,
p: tyop_2Emin_2Ebool > $o ).
tff(pred_def_2,type,
sP0: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_3,type,
sP1: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_4,type,
sP2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_5,type,
sP3: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_6,type,
sP4: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_7,type,
sP5: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_8,type,
sP6: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_9,type,
sP7: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_10,type,
sP8: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_11,type,
sP9: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(f2,axiom,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X0)
<=> p(X1) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Eboolext) ).
tff(f26,axiom,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] : ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(X0,X1,X2,X3) = app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E0(X0,X1),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2_2Emono_2EA_27a_20mono_2EA_27b) ).
tff(f31,axiom,
! [X0: tyop_2Emin_2Ebool] :
( ( ( p(c_2Ebool_2ET_2E0)
=> p(X0) )
<=> p(X0) )
& ( ( p(X0)
=> p(c_2Ebool_2ET_2E0) )
<=> p(c_2Ebool_2ET_2E0) )
& ( ( p(c_2Ebool_2EF_2E0)
=> p(X0) )
<=> p(c_2Ebool_2ET_2E0) )
& ( ( p(X0)
=> p(X0) )
<=> p(c_2Ebool_2ET_2E0) )
& ( ( p(X0)
=> p(c_2Ebool_2EF_2E0) )
<=> ~ p(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CLAUSES) ).
tff(f34,axiom,
! [X0: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2ET_2E0 = X0 )
<=> p(X0) )
& ( ( X0 = c_2Ebool_2ET_2E0 )
<=> p(X0) )
& ( ( c_2Ebool_2EF_2E0 = X0 )
<=> ~ p(X0) )
& ( ( X0 = c_2Ebool_2EF_2E0 )
<=> ~ p(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
tff(f37,axiom,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( p(c_2EquantHeuristics_2EGUESS__EXISTS_2E2(X0,X1,X2,X3))
<=> ! [X4: X1] :
( p(app_2E2(X1,tyop_2Emin_2Ebool,X3,X4))
=> ? [X5: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,X3,app_2E2(X0,X1,X2,X5))) ) )
& ( p(c_2EquantHeuristics_2EGUESS__FORALL_2E2(X0,X1,X2,X3))
<=> ! [X6: X1] :
( ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X3,X6))
=> ? [X7: X0] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X3,app_2E2(X0,X1,X2,X7))) ) )
& ! [X8: tyop_2Emin_2Efun(X0,X1),X9: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( p(c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(X0,X1,X8,X9))
<=> ! [X10: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,X9,app_2E2(X0,X1,X8,X10))) )
& ! [X11: tyop_2Emin_2Efun(X0,X1),X12: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( p(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(X0,X1,X11,X12))
<=> ! [X13: X0] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X12,app_2E2(X0,X1,X11,X13))) )
& ! [X14: tyop_2Emin_2Efun(X0,X1),X15: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( p(c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(X0,X1,X14,X15))
<=> ! [X16: X1] :
( p(app_2E2(X1,tyop_2Emin_2Ebool,X15,X16))
=> ? [X17: X0] : ( X16 = app_2E2(X0,X1,X14,X17) ) ) )
& ! [X18: tyop_2Emin_2Efun(X0,X1),X19: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( p(c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(X0,X1,X18,X19))
<=> ! [X20: X1] :
( ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X19,X20))
=> ? [X21: X0] : ( X20 = app_2E2(X0,X1,X18,X21) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EquantHeuristics_2EGUESS__REWRITES) ).
tff(f49,conjecture,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X1,X0),X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ! [X5: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X4,X5))
=> p(app_2E2(X0,tyop_2Emin_2Ebool,X3,X5)) )
=> ( p(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(X1,X0,X2,X3))
=> p(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(X1,X0,X2,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT) ).
tff(f50,negated_conjecture,
~ ! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X1,X0),X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ! [X5: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X4,X5))
=> p(app_2E2(X0,tyop_2Emin_2Ebool,X3,X5)) )
=> ( p(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(X1,X0,X2,X3))
=> p(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(X1,X0,X2,X4)) ) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
tff(f53,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| ( p(X0)
<~> p(X1) ) ),
inference(ennf_transformation,[],[f2]) ).
tff(f56,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( ( p(X0)
| ~ p(c_2Ebool_2ET_2E0) )
<=> p(X0) )
& ( ( p(c_2Ebool_2ET_2E0)
| ~ p(X0) )
<=> p(c_2Ebool_2ET_2E0) )
& ( ( p(X0)
| ~ p(c_2Ebool_2EF_2E0) )
<=> p(c_2Ebool_2ET_2E0) )
& ( ( p(X0)
| ~ p(X0) )
<=> p(c_2Ebool_2ET_2E0) )
& ( ( p(c_2Ebool_2EF_2E0)
| ~ p(X0) )
<=> ~ p(X0) ) ),
inference(ennf_transformation,[],[f31]) ).
tff(f61,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( p(c_2EquantHeuristics_2EGUESS__EXISTS_2E2(X0,X1,X2,X3))
<=> ! [X4: X1] :
( ? [X5: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,X3,app_2E2(X0,X1,X2,X5)))
| ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X3,X4)) ) )
& ( p(c_2EquantHeuristics_2EGUESS__FORALL_2E2(X0,X1,X2,X3))
<=> ! [X6: X1] :
( ? [X7: X0] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X3,app_2E2(X0,X1,X2,X7)))
| p(app_2E2(X1,tyop_2Emin_2Ebool,X3,X6)) ) )
& ! [X8: tyop_2Emin_2Efun(X0,X1),X9: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( p(c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(X0,X1,X8,X9))
<=> ! [X10: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,X9,app_2E2(X0,X1,X8,X10))) )
& ! [X11: tyop_2Emin_2Efun(X0,X1),X12: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( p(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(X0,X1,X11,X12))
<=> ! [X13: X0] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X12,app_2E2(X0,X1,X11,X13))) )
& ! [X14: tyop_2Emin_2Efun(X0,X1),X15: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( p(c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(X0,X1,X14,X15))
<=> ! [X16: X1] :
( ? [X17: X0] : ( X16 = app_2E2(X0,X1,X14,X17) )
| ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X15,X16)) ) )
& ! [X18: tyop_2Emin_2Efun(X0,X1),X19: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( p(c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(X0,X1,X18,X19))
<=> ! [X20: X1] :
( ? [X21: X0] : ( X20 = app_2E2(X0,X1,X18,X21) )
| p(app_2E2(X1,tyop_2Emin_2Ebool,X19,X20)) ) ) ),
inference(ennf_transformation,[],[f37]) ).
tff(f75,plain,
? [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X1,X0),X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ~ p(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(X1,X0,X2,X4))
& p(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(X1,X0,X2,X3))
& ! [X5: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X3,X5))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X4,X5)) ) ),
inference(ennf_transformation,[],[f50]) ).
tff(f76,plain,
? [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X1,X0),X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ~ p(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(X1,X0,X2,X4))
& p(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(X1,X0,X2,X3))
& ! [X5: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X3,X5))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X4,X5)) ) ),
inference(flattening,[],[f75]) ).
tff(f93,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| ( ( ~ p(X1)
| ~ p(X0) )
& ( p(X1)
| p(X0) ) ) ),
inference(nnf_transformation,[],[f53]) ).
tff(f116,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( p(X0)
| ~ p(c_2Ebool_2ET_2E0)
| ~ p(X0) )
& ( p(X0)
| ( ~ p(X0)
& p(c_2Ebool_2ET_2E0) ) )
& ( p(c_2Ebool_2ET_2E0)
| ~ p(X0)
| ~ p(c_2Ebool_2ET_2E0) )
& ( p(c_2Ebool_2ET_2E0)
| ( ~ p(c_2Ebool_2ET_2E0)
& p(X0) ) )
& ( p(X0)
| ~ p(c_2Ebool_2EF_2E0)
| ~ p(c_2Ebool_2ET_2E0) )
& ( p(c_2Ebool_2ET_2E0)
| ( ~ p(X0)
& p(c_2Ebool_2EF_2E0) ) )
& ( p(X0)
| ~ p(X0)
| ~ p(c_2Ebool_2ET_2E0) )
& ( p(c_2Ebool_2ET_2E0)
| ( ~ p(X0)
& p(X0) ) )
& ( p(c_2Ebool_2EF_2E0)
| ~ p(X0)
| p(X0) )
& ( ~ p(X0)
| ( ~ p(c_2Ebool_2EF_2E0)
& p(X0) ) ) ),
inference(nnf_transformation,[],[f56]) ).
tff(f117,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( p(X0)
| ~ p(c_2Ebool_2ET_2E0)
| ~ p(X0) )
& ( p(X0)
| ( ~ p(X0)
& p(c_2Ebool_2ET_2E0) ) )
& ( p(c_2Ebool_2ET_2E0)
| ~ p(X0)
| ~ p(c_2Ebool_2ET_2E0) )
& ( p(c_2Ebool_2ET_2E0)
| ( ~ p(c_2Ebool_2ET_2E0)
& p(X0) ) )
& ( p(X0)
| ~ p(c_2Ebool_2EF_2E0)
| ~ p(c_2Ebool_2ET_2E0) )
& ( p(c_2Ebool_2ET_2E0)
| ( ~ p(X0)
& p(c_2Ebool_2EF_2E0) ) )
& ( p(X0)
| ~ p(X0)
| ~ p(c_2Ebool_2ET_2E0) )
& ( p(c_2Ebool_2ET_2E0)
| ( ~ p(X0)
& p(X0) ) )
& ( p(c_2Ebool_2EF_2E0)
| ~ p(X0)
| p(X0) )
& ( ~ p(X0)
| ( ~ p(c_2Ebool_2EF_2E0)
& p(X0) ) ) ),
inference(flattening,[],[f116]) ).
tff(f121,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2ET_2E0 = X0 )
| ~ p(X0) )
& ( p(X0)
| ( c_2Ebool_2ET_2E0 != X0 ) )
& ( ( X0 = c_2Ebool_2ET_2E0 )
| ~ p(X0) )
& ( p(X0)
| ( c_2Ebool_2ET_2E0 != X0 ) )
& ( ( c_2Ebool_2EF_2E0 = X0 )
| p(X0) )
& ( ~ p(X0)
| ( c_2Ebool_2EF_2E0 != X0 ) )
& ( ( X0 = c_2Ebool_2EF_2E0 )
| p(X0) )
& ( ~ p(X0)
| ( c_2Ebool_2EF_2E0 != X0 ) ) ),
inference(nnf_transformation,[],[f34]) ).
tff(f122,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2ET_2E0 = X0 )
| ~ p(X0) )
& ( p(X0)
| ( c_2Ebool_2ET_2E0 != X0 ) )
& ( ( X0 = c_2Ebool_2ET_2E0 )
| ~ p(X0) )
& ( p(X0)
| ( c_2Ebool_2ET_2E0 != X0 ) )
& ( ( c_2Ebool_2EF_2E0 = X0 )
| p(X0) )
& ( ~ p(X0)
| ( c_2Ebool_2EF_2E0 != X0 ) )
& ( ( X0 = c_2Ebool_2EF_2E0 )
| p(X0) )
& ( ~ p(X0)
| ( c_2Ebool_2EF_2E0 != X0 ) ) ),
inference(flattening,[],[f121]) ).
tff(f127,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( p(c_2EquantHeuristics_2EGUESS__EXISTS_2E2(X0,X1,X2,X3))
| ? [X4: X1] :
( ! [X5: X0] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X3,app_2E2(X0,X1,X2,X5)))
& p(app_2E2(X1,tyop_2Emin_2Ebool,X3,X4)) ) )
& ( ! [X4: X1] :
( ? [X5: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,X3,app_2E2(X0,X1,X2,X5)))
| ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X3,X4)) )
| ~ p(c_2EquantHeuristics_2EGUESS__EXISTS_2E2(X0,X1,X2,X3)) )
& ( p(c_2EquantHeuristics_2EGUESS__FORALL_2E2(X0,X1,X2,X3))
| ? [X6: X1] :
( ! [X7: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,X3,app_2E2(X0,X1,X2,X7)))
& ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X3,X6)) ) )
& ( ! [X6: X1] :
( ? [X7: X0] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X3,app_2E2(X0,X1,X2,X7)))
| p(app_2E2(X1,tyop_2Emin_2Ebool,X3,X6)) )
| ~ p(c_2EquantHeuristics_2EGUESS__FORALL_2E2(X0,X1,X2,X3)) )
& ! [X8: tyop_2Emin_2Efun(X0,X1),X9: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( p(c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(X0,X1,X8,X9))
| ? [X10: X0] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X9,app_2E2(X0,X1,X8,X10))) )
& ( ! [X10: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,X9,app_2E2(X0,X1,X8,X10)))
| ~ p(c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(X0,X1,X8,X9)) ) )
& ! [X11: tyop_2Emin_2Efun(X0,X1),X12: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( p(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(X0,X1,X11,X12))
| ? [X13: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,X12,app_2E2(X0,X1,X11,X13))) )
& ( ! [X13: X0] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X12,app_2E2(X0,X1,X11,X13)))
| ~ p(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(X0,X1,X11,X12)) ) )
& ! [X14: tyop_2Emin_2Efun(X0,X1),X15: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( p(c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(X0,X1,X14,X15))
| ? [X16: X1] :
( ! [X17: X0] : ( app_2E2(X0,X1,X14,X17) != X16 )
& p(app_2E2(X1,tyop_2Emin_2Ebool,X15,X16)) ) )
& ( ! [X16: X1] :
( ? [X17: X0] : ( X16 = app_2E2(X0,X1,X14,X17) )
| ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X15,X16)) )
| ~ p(c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(X0,X1,X14,X15)) ) )
& ! [X18: tyop_2Emin_2Efun(X0,X1),X19: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( p(c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(X0,X1,X18,X19))
| ? [X20: X1] :
( ! [X21: X0] : ( app_2E2(X0,X1,X18,X21) != X20 )
& ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X19,X20)) ) )
& ( ! [X20: X1] :
( ? [X21: X0] : ( X20 = app_2E2(X0,X1,X18,X21) )
| p(app_2E2(X1,tyop_2Emin_2Ebool,X19,X20)) )
| ~ p(c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(X0,X1,X18,X19)) ) ) ),
inference(nnf_transformation,[],[f61]) ).
tff(f128,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( p(c_2EquantHeuristics_2EGUESS__EXISTS_2E2(X0,X1,X2,X3))
| ? [X4: X1] :
( ! [X5: X0] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X3,app_2E2(X0,X1,X2,X5)))
& p(app_2E2(X1,tyop_2Emin_2Ebool,X3,X4)) ) )
& ( ! [X4: X1] :
( ? [X5: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,X3,app_2E2(X0,X1,X2,X5)))
| ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X3,X4)) )
| ~ p(c_2EquantHeuristics_2EGUESS__EXISTS_2E2(X0,X1,X2,X3)) )
& ( p(c_2EquantHeuristics_2EGUESS__FORALL_2E2(X0,X1,X2,X3))
| ? [X6: X1] :
( ! [X7: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,X3,app_2E2(X0,X1,X2,X7)))
& ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X3,X6)) ) )
& ( ! [X6: X1] :
( ? [X7: X0] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X3,app_2E2(X0,X1,X2,X7)))
| p(app_2E2(X1,tyop_2Emin_2Ebool,X3,X6)) )
| ~ p(c_2EquantHeuristics_2EGUESS__FORALL_2E2(X0,X1,X2,X3)) )
& ! [X8: tyop_2Emin_2Efun(X0,X1),X9: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( p(c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(X0,X1,X8,X9))
| ? [X10: X0] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X9,app_2E2(X0,X1,X8,X10))) )
& ( ! [X10: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,X9,app_2E2(X0,X1,X8,X10)))
| ~ p(c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(X0,X1,X8,X9)) ) )
& ! [X11: tyop_2Emin_2Efun(X0,X1),X12: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( p(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(X0,X1,X11,X12))
| ? [X13: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,X12,app_2E2(X0,X1,X11,X13))) )
& ( ! [X13: X0] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X12,app_2E2(X0,X1,X11,X13)))
| ~ p(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(X0,X1,X11,X12)) ) )
& ! [X14: tyop_2Emin_2Efun(X0,X1),X15: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( p(c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(X0,X1,X14,X15))
| ? [X16: X1] :
( ! [X17: X0] : ( app_2E2(X0,X1,X14,X17) != X16 )
& p(app_2E2(X1,tyop_2Emin_2Ebool,X15,X16)) ) )
& ( ! [X16: X1] :
( ? [X17: X0] : ( X16 = app_2E2(X0,X1,X14,X17) )
| ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X15,X16)) )
| ~ p(c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(X0,X1,X14,X15)) ) )
& ! [X18: tyop_2Emin_2Efun(X0,X1),X19: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( p(c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(X0,X1,X18,X19))
| ? [X20: X1] :
( ! [X21: X0] : ( app_2E2(X0,X1,X18,X21) != X20 )
& ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X19,X20)) ) )
& ( ! [X20: X1] :
( ? [X21: X0] : ( X20 = app_2E2(X0,X1,X18,X21) )
| p(app_2E2(X1,tyop_2Emin_2Ebool,X19,X20)) )
| ~ p(c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(X0,X1,X18,X19)) ) ) ),
inference(flattening,[],[f127]) ).
tff(f129,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( p(c_2EquantHeuristics_2EGUESS__EXISTS_2E2(X0,X1,X2,X3))
| ? [X4: X1] :
( ! [X5: X0] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X3,app_2E2(X0,X1,X2,X5)))
& p(app_2E2(X1,tyop_2Emin_2Ebool,X3,X4)) ) )
& ( ! [X6: X1] :
( ? [X7: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,X3,app_2E2(X0,X1,X2,X7)))
| ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X3,X6)) )
| ~ p(c_2EquantHeuristics_2EGUESS__EXISTS_2E2(X0,X1,X2,X3)) )
& ( p(c_2EquantHeuristics_2EGUESS__FORALL_2E2(X0,X1,X2,X3))
| ? [X8: X1] :
( ! [X9: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,X3,app_2E2(X0,X1,X2,X9)))
& ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X3,X8)) ) )
& ( ! [X10: X1] :
( ? [X11: X0] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X3,app_2E2(X0,X1,X2,X11)))
| p(app_2E2(X1,tyop_2Emin_2Ebool,X3,X10)) )
| ~ p(c_2EquantHeuristics_2EGUESS__FORALL_2E2(X0,X1,X2,X3)) )
& ! [X12: tyop_2Emin_2Efun(X0,X1),X13: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( p(c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(X0,X1,X12,X13))
| ? [X14: X0] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X13,app_2E2(X0,X1,X12,X14))) )
& ( ! [X15: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,X13,app_2E2(X0,X1,X12,X15)))
| ~ p(c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(X0,X1,X12,X13)) ) )
& ! [X16: tyop_2Emin_2Efun(X0,X1),X17: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( p(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(X0,X1,X16,X17))
| ? [X18: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,X17,app_2E2(X0,X1,X16,X18))) )
& ( ! [X19: X0] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X17,app_2E2(X0,X1,X16,X19)))
| ~ p(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(X0,X1,X16,X17)) ) )
& ! [X20: tyop_2Emin_2Efun(X0,X1),X21: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( p(c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(X0,X1,X20,X21))
| ? [X22: X1] :
( ! [X23: X0] : ( app_2E2(X0,X1,X20,X23) != X22 )
& p(app_2E2(X1,tyop_2Emin_2Ebool,X21,X22)) ) )
& ( ! [X24: X1] :
( ? [X25: X0] : ( app_2E2(X0,X1,X20,X25) = X24 )
| ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X21,X24)) )
| ~ p(c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(X0,X1,X20,X21)) ) )
& ! [X26: tyop_2Emin_2Efun(X0,X1),X27: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( p(c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(X0,X1,X26,X27))
| ? [X28: X1] :
( ! [X29: X0] : ( app_2E2(X0,X1,X26,X29) != X28 )
& ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X27,X28)) ) )
& ( ! [X30: X1] :
( ? [X31: X0] : ( app_2E2(X0,X1,X26,X31) = X30 )
| p(app_2E2(X1,tyop_2Emin_2Ebool,X27,X30)) )
| ~ p(c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(X0,X1,X26,X27)) ) ) ),
inference(rectify,[],[f128]) ).
tff(f130,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( p(c_2EquantHeuristics_2EGUESS__EXISTS_2E2(X0,X1,X2,X3))
| ( ! [X5: X0] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X3,app_2E2(X0,X1,X2,X5)))
& p(app_2E2(X1,tyop_2Emin_2Ebool,X3,sK13(X0,X1,X2,X3))) ) )
& ( ! [X6: X1] :
( p(app_2E2(X1,tyop_2Emin_2Ebool,X3,app_2E2(X0,X1,X2,sK14(X0,X1,X2,X3))))
| ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X3,X6)) )
| ~ p(c_2EquantHeuristics_2EGUESS__EXISTS_2E2(X0,X1,X2,X3)) )
& ( p(c_2EquantHeuristics_2EGUESS__FORALL_2E2(X0,X1,X2,X3))
| ( ! [X9: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,X3,app_2E2(X0,X1,X2,X9)))
& ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X3,sK15(X0,X1,X2,X3))) ) )
& ( ! [X10: X1] :
( ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X3,app_2E2(X0,X1,X2,sK16(X0,X1,X2,X3))))
| p(app_2E2(X1,tyop_2Emin_2Ebool,X3,X10)) )
| ~ p(c_2EquantHeuristics_2EGUESS__FORALL_2E2(X0,X1,X2,X3)) )
& ! [X12: tyop_2Emin_2Efun(X0,X1),X13: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( p(c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(X0,X1,X12,X13))
| ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X13,app_2E2(X0,X1,X12,sK17(X0,X1,X12,X13)))) )
& ( ! [X15: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,X13,app_2E2(X0,X1,X12,X15)))
| ~ p(c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(X0,X1,X12,X13)) ) )
& ! [X16: tyop_2Emin_2Efun(X0,X1),X17: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( p(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(X0,X1,X16,X17))
| p(app_2E2(X1,tyop_2Emin_2Ebool,X17,app_2E2(X0,X1,X16,sK18(X0,X1,X16,X17)))) )
& ( ! [X19: X0] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X17,app_2E2(X0,X1,X16,X19)))
| ~ p(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(X0,X1,X16,X17)) ) )
& ! [X20: tyop_2Emin_2Efun(X0,X1),X21: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( p(c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(X0,X1,X20,X21))
| ( ! [X23: X0] : ( app_2E2(X0,X1,X20,X23) != sK19(X0,X1,X20,X21) )
& p(app_2E2(X1,tyop_2Emin_2Ebool,X21,sK19(X0,X1,X20,X21))) ) )
& ( ! [X24: X1] :
( ( app_2E2(X0,X1,X20,sK20(X0,X1,X20,X24)) = X24 )
| ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X21,X24)) )
| ~ p(c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(X0,X1,X20,X21)) ) )
& ! [X26: tyop_2Emin_2Efun(X0,X1),X27: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( p(c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(X0,X1,X26,X27))
| ( ! [X29: X0] : ( app_2E2(X0,X1,X26,X29) != sK21(X0,X1,X26,X27) )
& ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X27,sK21(X0,X1,X26,X27))) ) )
& ( ! [X30: X1] :
( ( app_2E2(X0,X1,X26,sK22(X0,X1,X26,X30)) = X30 )
| p(app_2E2(X1,tyop_2Emin_2Ebool,X27,X30)) )
| ~ p(c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(X0,X1,X26,X27)) ) ) ),
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))],[f129]) ).
tff(f171,plain,
( ~ p(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(sK24,sK23,sK25,sK27))
& p(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(sK24,sK23,sK25,sK26))
& ! [X5: sK23] :
( p(app_2E2(sK23,tyop_2Emin_2Ebool,sK26,X5))
| ~ p(app_2E2(sK23,tyop_2Emin_2Ebool,sK27,X5)) ) ),
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)],[f76]) ).
tff(f173,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| p(X1)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f93]) ).
tff(f213,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] : ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(X0,X1,X2,X3) = app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E0(X0,X1),X2),X3) ),
inference(cnf_transformation,[],[f26]) ).
tff(f222,plain,
! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(c_2Ebool_2EF_2E0) ),
inference(cnf_transformation,[],[f117]) ).
tff(f245,plain,
! [X0: tyop_2Emin_2Ebool] :
( p(X0)
| ( c_2Ebool_2EF_2E0 = X0 ) ),
inference(cnf_transformation,[],[f122]) ).
tff(f272,plain,
! [X1: $tType,X0: $tType,X19: X0,X16: tyop_2Emin_2Efun(X0,X1),X17: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X17,app_2E2(X0,X1,X16,X19)))
| ~ p(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(X0,X1,X16,X17)) ),
inference(cnf_transformation,[],[f130]) ).
tff(f273,plain,
! [X1: $tType,X0: $tType,X16: tyop_2Emin_2Efun(X0,X1),X17: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( p(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(X0,X1,X16,X17))
| p(app_2E2(X1,tyop_2Emin_2Ebool,X17,app_2E2(X0,X1,X16,sK18(X0,X1,X16,X17)))) ),
inference(cnf_transformation,[],[f130]) ).
tff(f373,plain,
! [X5: sK23] :
( ~ p(app_2E2(sK23,tyop_2Emin_2Ebool,sK27,X5))
| p(app_2E2(sK23,tyop_2Emin_2Ebool,sK26,X5)) ),
inference(cnf_transformation,[],[f171]) ).
tff(f374,plain,
p(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(sK24,sK23,sK25,sK26)),
inference(cnf_transformation,[],[f171]) ).
tff(f375,plain,
~ p(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(sK24,sK23,sK25,sK27)),
inference(cnf_transformation,[],[f171]) ).
tff(f389,plain,
! [X1: $tType,X0: $tType,X16: tyop_2Emin_2Efun(X0,X1),X17: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E0(X0,X1),X16),X17))
| p(app_2E2(X1,tyop_2Emin_2Ebool,X17,app_2E2(X0,X1,X16,sK18(X0,X1,X16,X17)))) ),
inference(definition_unfolding,[],[f273,f213]) ).
tff(f390,plain,
! [X1: $tType,X0: $tType,X19: X0,X16: tyop_2Emin_2Efun(X0,X1),X17: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ~ p(app_2E2(X1,tyop_2Emin_2Ebool,X17,app_2E2(X0,X1,X16,X19)))
| ~ p(app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E0(X0,X1),X16),X17)) ),
inference(definition_unfolding,[],[f272,f213]) ).
tff(f397,plain,
~ p(app_2E2(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(sK24,sK23),tyop_2Emin_2Efun(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E0(sK24,sK23),sK25),sK27)),
inference(definition_unfolding,[],[f375,f213]) ).
tff(f398,plain,
p(app_2E2(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(sK24,sK23),tyop_2Emin_2Efun(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E0(sK24,sK23),sK25),sK26)),
inference(definition_unfolding,[],[f374,f213]) ).
tff(f510,plain,
c_2Ebool_2EF_2E0 = app_2E2(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(sK24,sK23),tyop_2Emin_2Efun(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E0(sK24,sK23),sK25),sK27),
inference(resolution,[],[f245,f397]) ).
tff(f862,plain,
! [X0: tyop_2Emin_2Ebool] :
( p(X0)
| ( app_2E2(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(sK24,sK23),tyop_2Emin_2Efun(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E0(sK24,sK23),sK25),sK27) = X0 ) ),
inference(resolution,[],[f173,f397]) ).
tff(f897,plain,
! [X0: tyop_2Emin_2Ebool] :
( p(X0)
| ( c_2Ebool_2EF_2E0 = X0 ) ),
inference(forward_demodulation,[],[f862,f510]) ).
tff(f1973,plain,
! [X0: sK24] : ~ p(app_2E2(sK23,tyop_2Emin_2Ebool,sK26,app_2E2(sK24,sK23,sK25,X0))),
inference(resolution,[],[f390,f398]) ).
tff(f2073,plain,
p(app_2E2(sK23,tyop_2Emin_2Ebool,sK27,app_2E2(sK24,sK23,sK25,sK18(sK24,sK23,sK25,sK27)))),
inference(resolution,[],[f389,f397]) ).
tff(f2834,plain,
! [X0: sK24] : ( c_2Ebool_2EF_2E0 = app_2E2(sK23,tyop_2Emin_2Ebool,sK26,app_2E2(sK24,sK23,sK25,X0)) ),
inference(resolution,[],[f1973,f897]) ).
tff(f2892,plain,
p(app_2E2(sK23,tyop_2Emin_2Ebool,sK26,app_2E2(sK24,sK23,sK25,sK18(sK24,sK23,sK25,sK27)))),
inference(resolution,[],[f2073,f373]) ).
tff(f2895,plain,
~ p(c_2Ebool_2EF_2E0),
inference(resolution,[],[f2073,f222]) ).
tff(f2907,plain,
p(c_2Ebool_2EF_2E0),
inference(forward_demodulation,[],[f2892,f2834]) ).
tff(f3060,plain,
$false,
inference(resolution,[],[f2907,f2895]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP006_3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.39 % Computer : n008.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sun Sep 27 11:53:10 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.42 Running first-order model finding
% 0.14/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.77/0.59 % (1090818)Will run a generic schedule for satisfiability detection.
% 0.77/0.59 % (1090827)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3152518469:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.77/0.59 % (1090824)% WARNING: option uhcvi not known.
% 0.77/0.59 % (1090826)dis+10_1_sil=32000:sp=arity:random_seed=1027606627:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.77/0.59 % (1090823)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4262511054_2999 on theBenchmark for (2999ds/0Mi)
% 0.77/0.59 % (1090824)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2793018744:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.77/0.59 % (1090828)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1393679981:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.77/0.59 % (1090825)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1111373249:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.77/0.59 % (1090829)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1040838147:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.77/0.59 % Exception at run slice level
% 0.77/0.59 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.77/0.59 % (1090837)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=656459964:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.77/0.59 % Exception at run slice level
% 0.77/0.59 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.77/0.59 % (1090827)Instruction limit reached!
% 0.77/0.59 % (1090827)------------------------------
% 0.77/0.59 % (1090827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.59 % (1090827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.59 % (1090827)CaDiCaL version: 2.1.3
% 0.77/0.59 % (1090827)Termination reason: Instruction limit
% 0.77/0.59 % (1090827)Termination phase: Saturation
% 0.77/0.59 % (1090827)Time elapsed: 0.036 s
% 0.77/0.59 % (1090827)Peak memory usage: 12 MB
% 0.77/0.59 % (1090827)Instructions burned: 118 (million)
% 0.77/0.59 % (1090840)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2773135016:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.77/0.59 % (1090839)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2181352527:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.77/0.59 % (1090826)Instruction limit reached!
% 0.77/0.59 % (1090826)------------------------------
% 0.77/0.59 % (1090826)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.59 % (1090826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.59 % (1090826)CaDiCaL version: 2.1.3
% 0.77/0.59 % (1090826)Termination reason: Instruction limit
% 0.77/0.59 % (1090826)Termination phase: Saturation
% 0.77/0.59 % (1090826)Time elapsed: 0.062 s
% 0.77/0.59 % (1090826)Peak memory usage: 12 MB
% 0.77/0.59 % (1090826)Instructions burned: 103 (million)
% 0.77/0.59 % (1090828)Instruction limit reached!
% 0.77/0.59 % (1090828)------------------------------
% 0.77/0.59 % (1090828)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.59 % (1090828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.59 % (1090828)CaDiCaL version: 2.1.3
% 0.77/0.59 % (1090828)Termination reason: Instruction limit
% 0.77/0.59 % (1090828)Termination phase: Saturation
% 0.77/0.59 % (1090828)Time elapsed: 0.077 s
% 0.77/0.59 % (1090828)Peak memory usage: 13 MB
% 0.77/0.59 % (1090828)Instructions burned: 132 (million)
% 0.77/0.59 % (1090843)ott-21_1_sil=16000:fs=off:random_seed=777833123:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.77/0.59 % (1090829)Instruction limit reached!
% 0.77/0.59 % (1090829)------------------------------
% 0.77/0.59 % (1090829)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.59 % (1090829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.59 % (1090829)CaDiCaL version: 2.1.3
% 0.77/0.59 % (1090829)Termination reason: Instruction limit
% 0.77/0.59 % (1090829)Termination phase: Saturation
% 0.77/0.59 % (1090829)Time elapsed: 0.093 s
% 0.77/0.59 % (1090829)Peak memory usage: 13 MB
% 0.77/0.59 % (1090829)Instructions burned: 159 (million)
% 0.77/0.59 % (1090844)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2914536253:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.77/0.59 % (1090846)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=4174401324:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.77/0.59 % (1090843) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1090818-1090843"...
% 0.77/0.59 % Exception at run slice level
% 0.77/0.59 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.77/0.59 % (1090843)...printing done.
% 0.77/0.59 % (1090843)Refutation found. Thanks to Tanya!
% 0.77/0.59 % SZS status Theorem for theBenchmark
% 0.77/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 0.77/0.59 % (1090843)------------------------------
% 0.77/0.59 % (1090843)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.59 % (1090843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.59 % (1090843)CaDiCaL version: 2.1.3
% 0.77/0.59 % (1090843)Termination reason: Refutation
% 0.77/0.59 % (1090843)Time elapsed: 0.036 s
% 0.77/0.59 % (1090843)Peak memory usage: 12 MB
% 0.77/0.59 % (1090843)Instructions burned: 62 (million)
% 0.77/0.59 % (1090818)Success in time 0.154 s
% 0.77/0.59 % Vampire exiting
%------------------------------------------------------------------------------