%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP021_3 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 11:28:43 AM UTC 2026
% Result : Theorem 2.39s 1.76s
% Output : Refutation 5.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 8
% Syntax : Number of formulae : 63 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 163 ( 31 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 161 ( 61 ~; 85 |; 11 &)
% ( 2 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 30 ( 30 usr; 11 con; 0-4 aty)
% Number of variables : 54 ( 45 !; 9 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
tyop_2Eextreal_2Eextreal: $tType ).
tff(type_def_6,type,
tyop_2Emin_2Ebool: $tType ).
tff(type_def_7,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $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_2ECOND_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0))) ).
tff(func_def_15,type,
c_2Ebool_2ECOND_2E3:
!>[X0: $tType] : ( ( tyop_2Emin_2Ebool * X0 * X0 ) > X0 ) ).
tff(func_def_16,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(func_def_17,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(func_def_18,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_19,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_20,type,
c_2Eextreal_2Eextreal__le_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)) ).
tff(func_def_21,type,
c_2Eextreal_2Eextreal__le_2E2: ( tyop_2Eextreal_2Eextreal * tyop_2Eextreal_2Eextreal ) > tyop_2Emin_2Ebool ).
tff(func_def_22,type,
c_2Eextreal_2Eextreal__max_2E0: tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal)) ).
tff(func_def_23,type,
c_2Eextreal_2Eextreal__max_2E2: ( tyop_2Eextreal_2Eextreal * tyop_2Eextreal_2Eextreal ) > tyop_2Eextreal_2Eextreal ).
tff(func_def_24,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(func_def_25,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(func_def_26,type,
sK12: tyop_2Eextreal_2Eextreal ).
tff(func_def_27,type,
sK13: tyop_2Eextreal_2Eextreal ).
tff(func_def_28,type,
sK14: tyop_2Eextreal_2Eextreal ).
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 * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_12,type,
sP10: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_13,type,
sP11: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(f4,axiom,
~ p(c_2Ebool_2EF_2E0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Enotfalse) ).
tff(f5,axiom,
! [X0: tyop_2Emin_2Ebool] :
( ( X0 = c_2Ebool_2ET_2E0 )
| ( X0 = c_2Ebool_2EF_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ebool__cases__ax) ).
tff(f27,axiom,
p(c_2Ebool_2ET_2E0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
tff(f37,axiom,
! [X0: $tType,X1: X0,X2: X0] :
( ( c_2Ebool_2ECOND_2E3(X0,c_2Ebool_2ET_2E0,X1,X2) = X1 )
& ( c_2Ebool_2ECOND_2E3(X0,c_2Ebool_2EF_2E0,X1,X2) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CLAUSES) ).
tff(f41,axiom,
! [X0: tyop_2Eextreal_2Eextreal,X1: tyop_2Eextreal_2Eextreal,X2: tyop_2Eextreal_2Eextreal] :
( ( p(c_2Eextreal_2Eextreal__le_2E2(X0,X1))
& p(c_2Eextreal_2Eextreal__le_2E2(X1,X2)) )
=> p(c_2Eextreal_2Eextreal__le_2E2(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__trans) ).
tff(f42,axiom,
! [X0: tyop_2Eextreal_2Eextreal,X1: tyop_2Eextreal_2Eextreal] :
( p(c_2Eextreal_2Eextreal__le_2E2(X0,X1))
| p(c_2Eextreal_2Eextreal__le_2E2(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__total) ).
tff(f43,axiom,
! [X0: tyop_2Eextreal_2Eextreal,X1: tyop_2Eextreal_2Eextreal] : ( c_2Eextreal_2Eextreal__max_2E2(X0,X1) = c_2Ebool_2ECOND_2E3(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__le_2E2(X0,X1),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextreal_2Eextreal__max__def) ).
tff(f54,conjecture,
! [X0: tyop_2Eextreal_2Eextreal,X1: tyop_2Eextreal_2Eextreal,X2: tyop_2Eextreal_2Eextreal] :
( p(c_2Eextreal_2Eextreal__le_2E2(c_2Eextreal_2Eextreal__max_2E2(X1,X2),X0))
<=> ( p(c_2Eextreal_2Eextreal__le_2E2(X1,X0))
& p(c_2Eextreal_2Eextreal__le_2E2(X2,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextreal_2Emax__le) ).
tff(f55,negated_conjecture,
~ ! [X0: tyop_2Eextreal_2Eextreal,X1: tyop_2Eextreal_2Eextreal,X2: tyop_2Eextreal_2Eextreal] :
( p(c_2Eextreal_2Eextreal__le_2E2(c_2Eextreal_2Eextreal__max_2E2(X1,X2),X0))
<=> ( p(c_2Eextreal_2Eextreal__le_2E2(X1,X0))
& p(c_2Eextreal_2Eextreal__le_2E2(X2,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f54]) ).
tff(f56,plain,
? [X0: tyop_2Eextreal_2Eextreal,X1: tyop_2Eextreal_2Eextreal,X2: tyop_2Eextreal_2Eextreal] :
( p(c_2Eextreal_2Eextreal__le_2E2(c_2Eextreal_2Eextreal__max_2E2(X1,X2),X0))
<~> ( p(c_2Eextreal_2Eextreal__le_2E2(X1,X0))
& p(c_2Eextreal_2Eextreal__le_2E2(X2,X0)) ) ),
inference(ennf_transformation,[],[f55]) ).
tff(f59,plain,
! [X0: tyop_2Eextreal_2Eextreal,X1: tyop_2Eextreal_2Eextreal,X2: tyop_2Eextreal_2Eextreal] :
( p(c_2Eextreal_2Eextreal__le_2E2(X0,X2))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(X0,X1))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(X1,X2)) ),
inference(ennf_transformation,[],[f41]) ).
tff(f60,plain,
! [X0: tyop_2Eextreal_2Eextreal,X1: tyop_2Eextreal_2Eextreal,X2: tyop_2Eextreal_2Eextreal] :
( p(c_2Eextreal_2Eextreal__le_2E2(X0,X2))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(X0,X1))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(X1,X2)) ),
inference(flattening,[],[f59]) ).
tff(f95,plain,
? [X0: tyop_2Eextreal_2Eextreal,X1: tyop_2Eextreal_2Eextreal,X2: tyop_2Eextreal_2Eextreal] :
( ( ~ p(c_2Eextreal_2Eextreal__le_2E2(X1,X0))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(X2,X0))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(c_2Eextreal_2Eextreal__max_2E2(X1,X2),X0)) )
& ( ( p(c_2Eextreal_2Eextreal__le_2E2(X1,X0))
& p(c_2Eextreal_2Eextreal__le_2E2(X2,X0)) )
| p(c_2Eextreal_2Eextreal__le_2E2(c_2Eextreal_2Eextreal__max_2E2(X1,X2),X0)) ) ),
inference(nnf_transformation,[],[f56]) ).
tff(f96,plain,
? [X0: tyop_2Eextreal_2Eextreal,X1: tyop_2Eextreal_2Eextreal,X2: tyop_2Eextreal_2Eextreal] :
( ( ~ p(c_2Eextreal_2Eextreal__le_2E2(X1,X0))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(X2,X0))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(c_2Eextreal_2Eextreal__max_2E2(X1,X2),X0)) )
& ( ( p(c_2Eextreal_2Eextreal__le_2E2(X1,X0))
& p(c_2Eextreal_2Eextreal__le_2E2(X2,X0)) )
| p(c_2Eextreal_2Eextreal__le_2E2(c_2Eextreal_2Eextreal__max_2E2(X1,X2),X0)) ) ),
inference(flattening,[],[f95]) ).
tff(f97,plain,
( ( ~ p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(sK14,sK12))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(c_2Eextreal_2Eextreal__max_2E2(sK13,sK14),sK12)) )
& ( ( p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12))
& p(c_2Eextreal_2Eextreal__le_2E2(sK14,sK12)) )
| p(c_2Eextreal_2Eextreal__le_2E2(c_2Eextreal_2Eextreal__max_2E2(sK13,sK14),sK12)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14]),skolemize(X0,sK12),skolemize(X1,sK13),skolemize(X2,sK14)],[f96]) ).
tff(f159,plain,
( p(c_2Eextreal_2Eextreal__le_2E2(sK14,sK12))
| p(c_2Eextreal_2Eextreal__le_2E2(c_2Eextreal_2Eextreal__max_2E2(sK13,sK14),sK12)) ),
inference(cnf_transformation,[],[f97]) ).
tff(f160,plain,
( p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12))
| p(c_2Eextreal_2Eextreal__le_2E2(c_2Eextreal_2Eextreal__max_2E2(sK13,sK14),sK12)) ),
inference(cnf_transformation,[],[f97]) ).
tff(f161,plain,
( ~ p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(sK14,sK12))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(c_2Eextreal_2Eextreal__max_2E2(sK13,sK14),sK12)) ),
inference(cnf_transformation,[],[f97]) ).
tff(f244,plain,
! [X0: tyop_2Eextreal_2Eextreal,X1: tyop_2Eextreal_2Eextreal] :
( p(c_2Eextreal_2Eextreal__le_2E2(X1,X0))
| p(c_2Eextreal_2Eextreal__le_2E2(X0,X1)) ),
inference(cnf_transformation,[],[f42]) ).
tff(f245,plain,
! [X2: tyop_2Eextreal_2Eextreal,X0: tyop_2Eextreal_2Eextreal,X1: tyop_2Eextreal_2Eextreal] :
( p(c_2Eextreal_2Eextreal__le_2E2(X0,X2))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(X0,X1))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(X1,X2)) ),
inference(cnf_transformation,[],[f60]) ).
tff(f246,plain,
! [X0: tyop_2Eextreal_2Eextreal,X1: tyop_2Eextreal_2Eextreal] : ( c_2Eextreal_2Eextreal__max_2E2(X0,X1) = c_2Ebool_2ECOND_2E3(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__le_2E2(X0,X1),X1,X0) ),
inference(cnf_transformation,[],[f43]) ).
tff(f278,plain,
! [X0: $tType,X2: X0,X1: X0] : ( c_2Ebool_2ECOND_2E3(X0,c_2Ebool_2EF_2E0,X1,X2) = X2 ),
inference(cnf_transformation,[],[f37]) ).
tff(f279,plain,
! [X0: $tType,X2: X0,X1: X0] : ( c_2Ebool_2ECOND_2E3(X0,c_2Ebool_2ET_2E0,X1,X2) = X1 ),
inference(cnf_transformation,[],[f37]) ).
tff(f304,plain,
~ p(c_2Ebool_2EF_2E0),
inference(cnf_transformation,[],[f4]) ).
tff(f334,plain,
p(c_2Ebool_2ET_2E0),
inference(cnf_transformation,[],[f27]) ).
tff(f335,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 = X0 )
| ( c_2Ebool_2EF_2E0 = X0 ) ),
inference(cnf_transformation,[],[f5]) ).
tff(f337,plain,
( ~ p(c_2Eextreal_2Eextreal__le_2E2(c_2Ebool_2ECOND_2E3(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__le_2E2(sK13,sK14),sK14,sK13),sK12))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(sK14,sK12))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12)) ),
inference(definition_unfolding,[],[f161,f246]) ).
tff(f338,plain,
( p(c_2Eextreal_2Eextreal__le_2E2(c_2Ebool_2ECOND_2E3(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__le_2E2(sK13,sK14),sK14,sK13),sK12))
| p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12)) ),
inference(definition_unfolding,[],[f160,f246]) ).
tff(f339,plain,
( p(c_2Eextreal_2Eextreal__le_2E2(c_2Ebool_2ECOND_2E3(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__le_2E2(sK13,sK14),sK14,sK13),sK12))
| p(c_2Eextreal_2Eextreal__le_2E2(sK14,sK12)) ),
inference(definition_unfolding,[],[f159,f246]) ).
tff(f358,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2EF_2E0 = X1 )
| ( X0 = X1 )
| ( c_2Ebool_2EF_2E0 = X0 ) ),
inference(superposition,[],[f335,f335]) ).
tff(f362,plain,
( ~ p(c_2Eextreal_2Eextreal__le_2E2(c_2Ebool_2ECOND_2E3(tyop_2Eextreal_2Eextreal,c_2Ebool_2ET_2E0,sK14,sK13),sK12))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(sK14,sK12))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12))
| ( c_2Ebool_2EF_2E0 = c_2Eextreal_2Eextreal__le_2E2(sK13,sK14) ) ),
inference(superposition,[],[f337,f335]) ).
tff(f363,plain,
( p(c_2Eextreal_2Eextreal__le_2E2(c_2Ebool_2ECOND_2E3(tyop_2Eextreal_2Eextreal,c_2Ebool_2ET_2E0,sK14,sK13),sK12))
| p(c_2Eextreal_2Eextreal__le_2E2(sK14,sK12))
| ( c_2Ebool_2EF_2E0 = c_2Eextreal_2Eextreal__le_2E2(sK13,sK14) ) ),
inference(superposition,[],[f339,f335]) ).
tff(f544,plain,
( ~ p(c_2Eextreal_2Eextreal__le_2E2(sK14,sK12))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(sK14,sK12))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12))
| ( c_2Ebool_2EF_2E0 = c_2Eextreal_2Eextreal__le_2E2(sK13,sK14) ) ),
inference(superposition,[],[f362,f279]) ).
tff(f546,plain,
( p(c_2Eextreal_2Eextreal__le_2E2(sK14,sK12))
| p(c_2Eextreal_2Eextreal__le_2E2(sK14,sK12))
| ( c_2Ebool_2EF_2E0 = c_2Eextreal_2Eextreal__le_2E2(sK13,sK14) ) ),
inference(superposition,[],[f363,f279]) ).
tff(f559,plain,
( ( c_2Ebool_2EF_2E0 = c_2Eextreal_2Eextreal__le_2E2(sK13,sK14) )
| p(c_2Eextreal_2Eextreal__le_2E2(sK14,sK12)) ),
inference(duplicate_literal_removal,[],[f546]) ).
tff(f560,plain,
( ~ p(c_2Eextreal_2Eextreal__le_2E2(sK14,sK12))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12))
| ( c_2Ebool_2EF_2E0 = c_2Eextreal_2Eextreal__le_2E2(sK13,sK14) ) ),
inference(duplicate_literal_removal,[],[f544]) ).
tff(f577,plain,
( p(c_2Eextreal_2Eextreal__le_2E2(c_2Ebool_2ECOND_2E3(tyop_2Eextreal_2Eextreal,c_2Ebool_2EF_2E0,sK14,sK13),sK12))
| p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12))
| p(c_2Eextreal_2Eextreal__le_2E2(sK14,sK12)) ),
inference(superposition,[],[f338,f559]) ).
tff(f579,plain,
( p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12))
| p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12))
| p(c_2Eextreal_2Eextreal__le_2E2(sK14,sK12)) ),
inference(forward_demodulation,[],[f577,f278]) ).
tff(f580,plain,
( p(c_2Eextreal_2Eextreal__le_2E2(sK14,sK12))
| p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12)) ),
inference(duplicate_literal_removal,[],[f579]) ).
tff(f584,plain,
( ( c_2Ebool_2EF_2E0 = c_2Eextreal_2Eextreal__le_2E2(sK13,sK14) )
| ~ p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12)) ),
inference(forward_subsumption_resolution,[],[f560,f559]) ).
tff(f590,plain,
( ~ p(c_2Eextreal_2Eextreal__le_2E2(c_2Ebool_2ECOND_2E3(tyop_2Eextreal_2Eextreal,c_2Ebool_2EF_2E0,sK14,sK13),sK12))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(sK14,sK12))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12)) ),
inference(superposition,[],[f337,f584]) ).
tff(f593,plain,
( ~ p(c_2Eextreal_2Eextreal__le_2E2(c_2Ebool_2ECOND_2E3(tyop_2Eextreal_2Eextreal,c_2Ebool_2EF_2E0,sK14,sK13),sK12))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(sK14,sK12))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12)) ),
inference(duplicate_literal_removal,[],[f590]) ).
tff(f596,plain,
( ~ p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(sK14,sK12))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12)) ),
inference(forward_demodulation,[],[f593,f278]) ).
tff(f597,plain,
( ~ p(c_2Eextreal_2Eextreal__le_2E2(sK14,sK12))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12)) ),
inference(duplicate_literal_removal,[],[f596]) ).
tff(f606,plain,
( ~ p(c_2Ebool_2ET_2E0)
| ~ p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12))
| ( c_2Ebool_2EF_2E0 = c_2Eextreal_2Eextreal__le_2E2(sK14,sK12) ) ),
inference(superposition,[],[f597,f335]) ).
tff(f607,plain,
( ( c_2Ebool_2EF_2E0 = c_2Eextreal_2Eextreal__le_2E2(sK14,sK12) )
| ~ p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12)) ),
inference(forward_subsumption_resolution,[],[f606,f334]) ).
tff(f631,plain,
( p(c_2Eextreal_2Eextreal__le_2E2(sK12,sK14))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12)) ),
inference(resolution,[],[f244,f597]) ).
tff(f1148,plain,
! [X0: tyop_2Emin_2Ebool] :
( p(c_2Eextreal_2Eextreal__le_2E2(c_2Ebool_2ECOND_2E3(tyop_2Eextreal_2Eextreal,c_2Ebool_2EF_2E0,sK14,sK13),sK12))
| p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12))
| ( c_2Eextreal_2Eextreal__le_2E2(sK13,sK14) = X0 )
| ( c_2Ebool_2EF_2E0 = X0 ) ),
inference(superposition,[],[f338,f358]) ).
tff(f1179,plain,
! [X0: tyop_2Emin_2Ebool] :
( p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12))
| p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12))
| ( c_2Eextreal_2Eextreal__le_2E2(sK13,sK14) = X0 )
| ( c_2Ebool_2EF_2E0 = X0 ) ),
inference(forward_demodulation,[],[f1148,f278]) ).
tff(f1180,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( c_2Eextreal_2Eextreal__le_2E2(sK13,sK14) = X0 )
| p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12))
| ( c_2Ebool_2EF_2E0 = X0 ) ),
inference(duplicate_literal_removal,[],[f1179]) ).
tff(f1254,plain,
( p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK14))
| p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12))
| p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12))
| ( c_2Ebool_2EF_2E0 = c_2Eextreal_2Eextreal__le_2E2(sK14,sK12) ) ),
inference(superposition,[],[f580,f1180]) ).
tff(f1260,plain,
( p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK14))
| p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12))
| ( c_2Ebool_2EF_2E0 = c_2Eextreal_2Eextreal__le_2E2(sK14,sK12) ) ),
inference(duplicate_literal_removal,[],[f1254]) ).
tff(f1283,plain,
( ( c_2Ebool_2EF_2E0 = c_2Eextreal_2Eextreal__le_2E2(sK14,sK12) )
| p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK14)) ),
inference(forward_subsumption_resolution,[],[f1260,f607]) ).
tff(f1301,plain,
( p(c_2Ebool_2EF_2E0)
| p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12))
| p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK14)) ),
inference(superposition,[],[f580,f1283]) ).
tff(f1304,plain,
( p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK14))
| p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12)) ),
inference(forward_subsumption_resolution,[],[f1301,f304]) ).
tff(f2139,plain,
! [X0: tyop_2Eextreal_2Eextreal] :
( p(c_2Ebool_2EF_2E0)
| ~ p(c_2Eextreal_2Eextreal__le_2E2(sK13,X0))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(X0,sK14))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12)) ),
inference(superposition,[],[f245,f584]) ).
tff(f2169,plain,
! [X0: tyop_2Eextreal_2Eextreal] :
( ~ p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(X0,sK14))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(sK13,X0)) ),
inference(forward_subsumption_resolution,[],[f2139,f304]) ).
tff(f2191,plain,
( ~ p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(sK12,sK14)) ),
inference(factoring,[],[f2169]) ).
tff(f2204,plain,
~ p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12)),
inference(forward_subsumption_resolution,[],[f2191,f631]) ).
tff(f2205,plain,
! [X0: tyop_2Eextreal_2Eextreal] :
( ~ p(c_2Eextreal_2Eextreal__le_2E2(sK13,X0))
| ~ p(c_2Eextreal_2Eextreal__le_2E2(X0,sK12)) ),
inference(resolution,[],[f2204,f245]) ).
tff(f2351,plain,
( ~ p(c_2Eextreal_2Eextreal__le_2E2(sK14,sK12))
| p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12)) ),
inference(resolution,[],[f2205,f1304]) ).
tff(f2387,plain,
p(c_2Eextreal_2Eextreal__le_2E2(sK13,sK12)),
inference(forward_subsumption_resolution,[],[f2351,f580]) ).
tff(f2397,plain,
$false,
inference(forward_subsumption_resolution,[],[f2387,f2204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP021_3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n016.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 12:12:01 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.46 Running first-order theorem proving
% 0.13/0.46 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.39/1.76 % (2526122)Detected formulas, will run a generic FOF schedule.
% 2.39/1.76 % (2526130)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4263799621:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.39/1.76 % (2526130)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.39/1.76 % (2526130)Instruction limit reached!
% 2.39/1.76 % (2526130)------------------------------
% 2.39/1.76 % (2526130)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.39/1.76 % (2526130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/1.76 % (2526130)CaDiCaL version: 2.1.3
% 2.39/1.76 % (2526130)Termination reason: Instruction limit
% 2.39/1.76 % (2526130)Termination phase: Saturation
% 2.39/1.76 % (2526130)Time elapsed: 0.040 s
% 2.39/1.76 % (2526130)Peak memory usage: 88 MB
% 2.39/1.76 % (2526130)Instructions burned: 109 (million)
% 2.39/1.76 % (2526128)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=453459236:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.39/1.76 % (2526132)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3874903576:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.39/1.76 % (2526131)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1132631782:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.39/1.76 % (2526129)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2250445639:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.39/1.76 % (2526129)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.39/1.76 % (2526127)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2776802610:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.39/1.76 % (2526133)dis-21_1_sil=8000:lcm=predicate:random_seed=1810095757:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.39/1.76 % (2526131)First to succeed.
% 2.39/1.76 % (2526131)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2526122"
% 2.39/1.76 % (2526133)Instruction limit reached!
% 2.39/1.76 % (2526133)------------------------------
% 2.39/1.76 % (2526133)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.39/1.76 % (2526133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/1.76 % (2526133)CaDiCaL version: 2.1.3
% 2.39/1.76 % (2526133)Termination reason: Instruction limit
% 2.39/1.76 % (2526133)Termination phase: Saturation
% 2.39/1.76 % (2526133)Time elapsed: 0.104 s
% 2.39/1.76 % (2526133)Peak memory usage: 89 MB
% 2.39/1.76 % (2526133)Instructions burned: 129 (million)
% 2.39/1.76 % (2526132)Instruction limit reached!
% 2.39/1.76 % (2526132)------------------------------
% 2.39/1.76 % (2526132)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.39/1.76 % (2526132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/1.76 % (2526132)CaDiCaL version: 2.1.3
% 2.39/1.76 % (2526132)Termination reason: Instruction limit
% 2.39/1.76 % (2526132)Termination phase: Saturation
% 2.39/1.76 % (2526132)Time elapsed: 0.131 s
% 2.39/1.76 % (2526132)Peak memory usage: 89 MB
% 2.39/1.76 % (2526132)Instructions burned: 139 (million)
% 2.39/1.76 % (2526136)lrs+10_1_sil=8000:sp=occurrence:random_seed=3563041638:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.39/1.76 % (2526144)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2778935809:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 2.39/1.76 % (2526136)Instruction limit reached!
% 2.39/1.76 % (2526136)------------------------------
% 2.39/1.76 % (2526136)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.39/1.76 % (2526136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/1.76 % (2526136)CaDiCaL version: 2.1.3
% 2.39/1.76 % (2526136)Termination reason: Instruction limit
% 2.39/1.76 % (2526136)Termination phase: Saturation
% 2.39/1.76 % (2526136)Time elapsed: 0.216 s
% 2.39/1.76 % (2526136)Peak memory usage: 90 MB
% 2.39/1.76 % (2526136)Instructions burned: 285 (million)
% 2.39/1.76 % (2526145)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2922835424:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 2.39/1.76 % (2526144)Instruction limit reached!
% 2.39/1.76 % (2526144)------------------------------
% 2.39/1.76 % (2526144)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.39/1.76 % (2526144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/1.76 % (2526144)CaDiCaL version: 2.1.3
% 2.39/1.76 % (2526144)Termination reason: Instruction limit
% 2.39/1.76 % (2526144)Termination phase: Saturation
% 2.39/1.76 % (2526144)Time elapsed: 0.070 s
% 2.39/1.76 % (2526144)Peak memory usage: 90 MB
% 2.39/1.76 % (2526144)Instructions burned: 158 (million)
% 2.39/1.76 % (2526131)Refutation found. Thanks to Tanya!
% 2.39/1.76 % SZS status Theorem for theBenchmark
% 2.39/1.76 % SZS output start Proof for theBenchmark
% See solution above
% 5.84/1.98 % (2526131)------------------------------
% 5.84/1.98 % (2526131)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.84/1.98 % (2526131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.84/1.98 % (2526131)CaDiCaL version: 2.1.3
% 5.84/1.98 % (2526131)Termination reason: Refutation
% 5.84/1.98 % (2526131)Time elapsed: 0.065 s
% 5.84/1.98 % (2526131)Peak memory usage: 88 MB
% 5.84/1.98 % (2526131)Instructions burned: 71 (million)
% 5.84/1.98 % (2526131)------------------------------
% 5.84/1.98 % (2526131)------------------------------
% 5.84/1.98 % (2526122)Success in time 0.716 s
% 5.84/1.98 % Vampire exiting
%------------------------------------------------------------------------------