%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP006_1 : 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 11:33:59 AM UTC 2026
% Result : Theorem 0.95s 0.59s
% Output : Refutation 0.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 14 unt; 0 typ; 1 def)
% Number of atoms : 86 ( 10 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 82 ( 25 ~; 13 |; 17 &)
% ( 17 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 2 prp; 0-3 aty)
% Number of functors : 71 ( 71 usr; 30 con; 0-4 aty)
% Number of variables : 83 ( 0 sgn 65 !; 18 ?; 83 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
u: $tType ).
tff(type_def_6,type,
d: $tType ).
tff(type_def_7,type,
du: $tType ).
tff(type_def_8,type,
mono_2Etyop_2Emin_2Ebool: $tType ).
tff(type_def_9,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: $tType ).
tff(type_def_10,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: $tType ).
tff(func_def_0,type,
tyop_2Emin_2Ebool: d ).
tff(func_def_1,type,
tyop_2Emin_2Efun: ( d * d ) > d ).
tff(func_def_2,type,
s: ( d * u ) > du ).
tff(func_def_3,type,
app_2E2: ( du * du ) > u ).
tff(func_def_4,type,
combin_i_2E0: u ).
tff(func_def_5,type,
combin_k_2E0: u ).
tff(func_def_6,type,
combin_s_2E0: u ).
tff(func_def_7,type,
c_2Ebool_2E_21_2E0: u ).
tff(func_def_8,type,
c_2Ebool_2E_21_2E1: du > u ).
tff(func_def_9,type,
c_2Ebool_2E_2F_5C_2E0: u ).
tff(func_def_10,type,
c_2Ebool_2E_2F_5C_2E2: ( du * du ) > u ).
tff(func_def_11,type,
c_2Emin_2E_3D_2E0: u ).
tff(func_def_12,type,
c_2Emin_2E_3D_2E2: ( du * du ) > u ).
tff(func_def_13,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
tff(func_def_14,type,
c_2Emin_2E_3D_3D_3E_2E2: ( du * du ) > u ).
tff(func_def_15,type,
c_2Ebool_2E_3F_2E0: u ).
tff(func_def_16,type,
c_2Ebool_2E_3F_2E1: du > u ).
tff(func_def_17,type,
c_2Ebool_2EF_2E0: u ).
tff(func_def_18,type,
c_2EquantHeuristics_2EGUESS__EXISTS_2E0: u ).
tff(func_def_19,type,
c_2EquantHeuristics_2EGUESS__EXISTS_2E2: ( du * du ) > u ).
tff(func_def_20,type,
c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E0: u ).
tff(func_def_21,type,
c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2: ( du * du ) > u ).
tff(func_def_22,type,
c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E0: u ).
tff(func_def_23,type,
c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2: ( du * du ) > u ).
tff(func_def_24,type,
c_2EquantHeuristics_2EGUESS__FORALL_2E0: u ).
tff(func_def_25,type,
c_2EquantHeuristics_2EGUESS__FORALL_2E2: ( du * du ) > u ).
tff(func_def_26,type,
c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E0: u ).
tff(func_def_27,type,
c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2: ( du * du ) > u ).
tff(func_def_28,type,
c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E0: u ).
tff(func_def_29,type,
c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2: ( du * du ) > u ).
tff(func_def_30,type,
c_2Ebool_2ET_2E0: u ).
tff(func_def_31,type,
c_2Ebool_2E_5C_2F_2E0: u ).
tff(func_def_32,type,
c_2Ebool_2E_5C_2F_2E2: ( du * du ) > u ).
tff(func_def_33,type,
c_2Ebool_2E_7E_2E0: u ).
tff(func_def_34,type,
c_2Ebool_2E_7E_2E1: du > u ).
tff(func_def_35,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_36,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_37,type,
mono_2Ec_2Ebool_2E_2F_5C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_38,type,
mono_2Ec_2Ebool_2E_2F_5C_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_39,type,
mono_2Ec_2Emin_2E_3D_3D_3E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_40,type,
mono_2Ec_2Emin_2E_3D_3D_3E_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_41,type,
mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(func_def_42,type,
mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(func_def_43,type,
mono_2Ec_2Ebool_2E_5C_2F_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_44,type,
mono_2Ec_2Ebool_2E_5C_2F_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_45,type,
mono_2Ec_2Ebool_2E_7E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_46,type,
mono_2Ec_2Ebool_2E_7E_2E1: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_47,type,
i_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > u ).
tff(func_def_48,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 > u ).
tff(func_def_49,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 > u ).
tff(func_def_50,type,
j_mono_2Etyop_2Emin_2Ebool: du > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_51,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_52,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_53,type,
sK0: ( d * d * u * u ) > u ).
tff(func_def_54,type,
sK1: ( d * u ) > u ).
tff(func_def_55,type,
sK2: ( d * u ) > u ).
tff(func_def_56,type,
sK3: ( d * d * u * u ) > u ).
tff(func_def_57,type,
sK4: ( d * d * u * u ) > u ).
tff(func_def_58,type,
sK5: ( d * d * u * u ) > u ).
tff(func_def_59,type,
sK6: ( d * d * u * u ) > u ).
tff(func_def_60,type,
sK7: ( d * d * u * u ) > u ).
tff(func_def_61,type,
sK8: ( d * d * u * u ) > u ).
tff(func_def_62,type,
sK9: ( d * d * u * u ) > u ).
tff(func_def_63,type,
sK10: ( d * d * u * u ) > u ).
tff(func_def_64,type,
sK11: ( d * d * u * u ) > u ).
tff(func_def_65,type,
sK12: ( d * d * u * u ) > u ).
tff(func_def_66,type,
sK19: d ).
tff(func_def_67,type,
sK20: d ).
tff(func_def_68,type,
sK21: u ).
tff(func_def_69,type,
sK22: u ).
tff(func_def_70,type,
sK23: u ).
tff(pred_def_1,type,
p: mono_2Etyop_2Emin_2Ebool > $o ).
tff(pred_def_2,type,
sP13: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_3,type,
sP14: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_4,type,
sP15: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_5,type,
sP16: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_6,type,
sP17: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_7,type,
sP18: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(f4,axiom,
~ p(mono_2Ec_2Ebool_2EF_2E0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).
tff(f42,axiom,
! [X0: mono_2Etyop_2Emin_2Ebool] :
( ( ( mono_2Ec_2Ebool_2ET_2E0 = X0 )
<=> p(X0) )
& ( ( X0 = mono_2Ec_2Ebool_2ET_2E0 )
<=> p(X0) )
& ( ( mono_2Ec_2Ebool_2EF_2E0 = X0 )
<=> ~ p(X0) )
& ( ( X0 = mono_2Ec_2Ebool_2EF_2E0 )
<=> ~ p(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
tff(f45,axiom,
! [X0: d,X1: d,X2: u,X3: u] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(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: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X4)))))
=> ? [X5: u] : p(j_mono_2Etyop_2Emin_2Ebool(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(j_mono_2Etyop_2Emin_2Ebool(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: u] :
( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X6)))))
=> ? [X7: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(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))))))) ) )
& ! [X8: u,X9: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(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: u] : p(j_mono_2Etyop_2Emin_2Ebool(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))))))) )
& ! [X11: u,X12: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(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: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(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))))))) )
& ! [X14: u,X15: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(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: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X15),s(X1,X16)))))
=> ? [X17: u] : ( s(X1,X16) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X14),s(X0,X17))) ) ) )
& ! [X18: u,X19: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(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: u] :
( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X19),s(X1,X20)))))
=> ? [X21: u] : ( s(X1,X20) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X18),s(X0,X21))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EquantHeuristics_2EGUESS__REWRITES) ).
tff(f57,conjecture,
! [X0: d,X1: d,X2: u,X3: u,X4: u] :
( ! [X5: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4),s(X0,X5)))))
=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3),s(X0,X5))))) )
=> ( p(j_mono_2Etyop_2Emin_2Ebool(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(j_mono_2Etyop_2Emin_2Ebool(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/sandbox/benchmark/theBenchmark.p',thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT) ).
tff(f58,negated_conjecture,
~ ! [X0: d,X1: d,X2: u,X3: u,X4: u] :
( ! [X5: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4),s(X0,X5)))))
=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3),s(X0,X5))))) )
=> ( p(j_mono_2Etyop_2Emin_2Ebool(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(j_mono_2Etyop_2Emin_2Ebool(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)],[f57]) ).
tff(f68,plain,
! [X0: d,X1: d,X2: u,X3: u] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(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: u] :
( ? [X5: u] : p(j_mono_2Etyop_2Emin_2Ebool(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(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X4))))) ) )
& ( p(j_mono_2Etyop_2Emin_2Ebool(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: u] :
( ? [X7: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(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(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X6))))) ) )
& ! [X8: u,X9: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(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: u] : p(j_mono_2Etyop_2Emin_2Ebool(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))))))) )
& ! [X11: u,X12: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(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: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(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))))))) )
& ! [X14: u,X15: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(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: u] :
( ? [X17: u] : ( s(X1,X16) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X14),s(X0,X17))) )
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X15),s(X1,X16))))) ) )
& ! [X18: u,X19: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(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: u] :
( ? [X21: u] : ( s(X1,X20) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X18),s(X0,X21))) )
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X19),s(X1,X20))))) ) ) ),
inference(ennf_transformation,[],[f45]) ).
tff(f82,plain,
? [X0: d,X1: d,X2: u,X3: u,X4: u] :
( ~ p(j_mono_2Etyop_2Emin_2Ebool(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)))))
& p(j_mono_2Etyop_2Emin_2Ebool(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)))))
& ! [X5: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3),s(X0,X5)))))
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4),s(X0,X5))))) ) ),
inference(ennf_transformation,[],[f58]) ).
tff(f83,plain,
? [X0: d,X1: d,X2: u,X3: u,X4: u] :
( ~ p(j_mono_2Etyop_2Emin_2Ebool(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)))))
& p(j_mono_2Etyop_2Emin_2Ebool(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)))))
& ! [X5: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3),s(X0,X5)))))
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4),s(X0,X5))))) ) ),
inference(flattening,[],[f82]) ).
tff(f88,plain,
~ p(mono_2Ec_2Ebool_2EF_2E0),
inference(cnf_transformation,[],[f4]) ).
tff(f157,plain,
! [X0: mono_2Etyop_2Emin_2Ebool] :
( p(X0)
| ( mono_2Ec_2Ebool_2EF_2E0 = X0 ) ),
inference(cnf_transformation,[],[f42]) ).
tff(f181,plain,
! [X0: d,X11: u,X1: d,X12: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(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,sK7(X0,X1,X11,X12))))))))
| p(j_mono_2Etyop_2Emin_2Ebool(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))))) ),
inference(cnf_transformation,[],[f68]) ).
tff(f182,plain,
! [X0: d,X11: u,X1: d,X12: u,X13: u] :
( ~ p(j_mono_2Etyop_2Emin_2Ebool(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)))))
| ~ p(j_mono_2Etyop_2Emin_2Ebool(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))))))) ),
inference(cnf_transformation,[],[f68]) ).
tff(f242,plain,
! [X5: u] :
( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK19,tyop_2Emin_2Ebool),sK23),s(sK19,X5)))))
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK19,tyop_2Emin_2Ebool),sK22),s(sK19,X5))))) ),
inference(cnf_transformation,[],[f83]) ).
tff(f243,plain,
p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK20,sK19),sK21),s(tyop_2Emin_2Efun(sK19,tyop_2Emin_2Ebool),sK22))))),
inference(cnf_transformation,[],[f83]) ).
tff(f244,plain,
~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK20,sK19),sK21),s(tyop_2Emin_2Efun(sK19,tyop_2Emin_2Ebool),sK23))))),
inference(cnf_transformation,[],[f83]) ).
tff(f354,definition,
( spl24_12
<=> p(mono_2Ec_2Ebool_2EF_2E0) ),
introduced(definition,[new_symbols(definition,[spl24_12])],[avatar_definition]) ).
tff(f356,plain,
( ~ p(mono_2Ec_2Ebool_2EF_2E0)
| spl24_12 ),
inference(avatar_component_clause,[],[f354]) ).
tff(f370,plain,
~ spl24_12,
inference(avatar_split_clause,[],[f88,f354]) ).
tff(f381,plain,
mono_2Ec_2Ebool_2EF_2E0 = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK20,sK19),sK21),s(tyop_2Emin_2Efun(sK19,tyop_2Emin_2Ebool),sK23)))),
inference(resolution,[],[f157,f244]) ).
tff(f1749,plain,
! [X0: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK19,tyop_2Emin_2Ebool),sK22),s(sK19,app_2E2(s(tyop_2Emin_2Efun(sK20,sK19),sK21),s(sK20,X0))))))),
inference(resolution,[],[f182,f243]) ).
tff(f1820,plain,
! [X0: d,X1: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK19,tyop_2Emin_2Ebool),sK22),s(sK19,app_2E2(s(tyop_2Emin_2Efun(X0,sK19),X1),s(X0,sK7(X0,sK19,X1,sK23))))))))
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,sK19),X1),s(tyop_2Emin_2Efun(sK19,tyop_2Emin_2Ebool),sK23))))) ),
inference(resolution,[],[f181,f242]) ).
tff(f2912,plain,
p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK20,sK19),sK21),s(tyop_2Emin_2Efun(sK19,tyop_2Emin_2Ebool),sK23))))),
inference(resolution,[],[f1820,f1749]) ).
tff(f2938,plain,
p(mono_2Ec_2Ebool_2EF_2E0),
inference(forward_demodulation,[],[f2912,f381]) ).
tff(f2939,plain,
( $false
| spl24_12 ),
inference(forward_subsumption_resolution,[],[f2938,f356]) ).
tff(f2940,plain,
spl24_12,
inference(avatar_contradiction_clause,[],[f2939]) ).
cnf(s22,plain,
~ spl24_12,
inference(sat_conversion,[],[f370]) ).
cnf(s206,plain,
spl24_12,
inference(sat_conversion,[],[f2940]) ).
cnf(s215,plain,
$false,
inference(rat,[],[s22,s206]) ).
tff(f2941,plain,
$false,
inference(avatar_sat_refutation,[],[s215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP006_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 11:53:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.95/0.59 % (1091229)Will run a generic schedule for satisfiability detection.
% 0.95/0.59 % (1091238)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=121219932:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.95/0.59 % (1091235)% WARNING: option uhcvi not known.
% 0.95/0.59 % (1091234)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2045436336_2999 on theBenchmark for (2999ds/0Mi)
% 0.95/0.59 % (1091235)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3129358132:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.95/0.59 % (1091237)dis+10_1_sil=32000:sp=arity:random_seed=844843303:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.95/0.59 % (1091236)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2164834298:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.95/0.59 % (1091239)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3631948161:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.95/0.59 % (1091240)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4208381761:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.95/0.59 % (1091238)Instruction limit reached!
% 0.95/0.59 % (1091238)------------------------------
% 0.95/0.59 % (1091238)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.59 % (1091238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.59 % (1091238)CaDiCaL version: 2.1.3
% 0.95/0.59 % (1091238)Termination reason: Instruction limit
% 0.95/0.59 % (1091238)Termination phase: Saturation
% 0.95/0.59 % (1091238)Time elapsed: 0.034 s
% 0.95/0.59 % (1091238)Peak memory usage: 12 MB
% 0.95/0.59 % (1091238)Instructions burned: 117 (million)
% 0.95/0.59 % (1091248)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3555090420:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.95/0.59 % (1091237)Instruction limit reached!
% 0.95/0.59 % (1091237)------------------------------
% 0.95/0.59 % (1091237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.59 % (1091237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.59 % (1091237)CaDiCaL version: 2.1.3
% 0.95/0.59 % (1091237)Termination reason: Instruction limit
% 0.95/0.59 % (1091237)Termination phase: Saturation
% 0.95/0.59 % (1091237)Time elapsed: 0.058 s
% 0.95/0.59 % (1091237)Peak memory usage: 12 MB
% 0.95/0.59 % (1091237)Instructions burned: 103 (million)
% 0.95/0.59 % TRYING [1]
% 0.95/0.59 % TRYING [2]
% 0.95/0.59 % Detected minimum model sizes of [1,1,1,1,1]
% 0.95/0.59 % Detected maximum model sizes of [max,max,2,max,max]
% 0.95/0.59 % TRYING [1,1,1,1,1]
% 0.95/0.59 % TRYING [1,1,2,1,1]
% 0.95/0.59 % TRYING [1,1,2,2,1]
% 0.95/0.59 % (1091239)Instruction limit reached!
% 0.95/0.59 % (1091239)------------------------------
% 0.95/0.59 % (1091239)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.59 % (1091239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.59 % (1091239)CaDiCaL version: 2.1.3
% 0.95/0.59 % (1091239)Termination reason: Instruction limit
% 0.95/0.59 % (1091239)Termination phase: Saturation
% 0.95/0.59 % (1091239)Time elapsed: 0.077 s
% 0.95/0.59 % (1091239)Peak memory usage: 13 MB
% 0.95/0.59 % (1091239)Instructions burned: 132 (million)
% 0.95/0.59 % (1091250)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3024065218:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 0.95/0.59 % TRYING [1,1,2,3,1]
% 0.95/0.59 % TRYING [3]
% 0.95/0.59 % TRYING [1,1,2,2,2]
% 0.95/0.59 % TRYING [1,1,2,3,2]
% 0.95/0.59 % TRYING [1,1,2,4,2]
% 0.95/0.59 % (1091240)Instruction limit reached!
% 0.95/0.59 % (1091240)------------------------------
% 0.95/0.59 % (1091240)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.59 % (1091240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.59 % (1091240)CaDiCaL version: 2.1.3
% 0.95/0.59 % (1091240)Termination reason: Instruction limit
% 0.95/0.59 % (1091240)Termination phase: Saturation
% 0.95/0.59 % (1091240)Time elapsed: 0.092 s
% 0.95/0.59 % (1091240)Peak memory usage: 13 MB
% 0.95/0.59 % (1091240)Instructions burned: 160 (million)
% 0.95/0.59 % TRYING [1,1,2,3,3]
% 0.95/0.59 % TRYING [1,1,2,4,3]
% 0.95/0.59 % (1091252)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=4027969129:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.95/0.59 % TRYING [1,2,2,4,3]
% 0.95/0.59 % TRYING [2,2,2,4,3]
% 0.95/0.59 % (1091253)ott-21_1_sil=16000:fs=off:random_seed=1854701553:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.95/0.59 % (1091235) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1091229-1091235"...
% 0.95/0.59 % (1091235)...printing done.
% 0.95/0.59 % (1091235)Refutation found. Thanks to Tanya!
% 0.95/0.59 % SZS status Theorem for theBenchmark
% 0.95/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 0.95/0.59 % (1091235)------------------------------
% 0.95/0.59 % (1091235)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.59 % (1091235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.59 % (1091235)CaDiCaL version: 2.1.3
% 0.95/0.59 % (1091235)Termination reason: Refutation
% 0.95/0.59 % (1091235)Time elapsed: 0.121 s
% 0.95/0.59 % (1091235)Peak memory usage: 14 MB
% 0.95/0.59 % (1091235)Instructions burned: 207 (million)
% 0.95/0.59 % (1091229)Success in time 0.173 s
% 0.95/0.59 % Vampire exiting
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