%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SCT040-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:37:25 PM UTC 2026
% Result : Unsatisfiable 0.64s 0.63s
% Output : Refutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 50 ( 14 unt; 3 def)
% Number of atoms : 121 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 134 ( 63 ~; 68 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-4 aty)
% Number of variables : 27 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f709,axiom,
! [X0] :
( ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_1_1) ).
fof(f710,axiom,
! [X0] :
( c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_1_0) ).
fof(f736,axiom,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(X1,X0))
| c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
fof(f737,axiom,
! [X2,X0,X1] :
( ~ c_in(X1,X0,X2)
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
fof(f738,axiom,
c_in(v_Q____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f739,axiom,
c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f740,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X0,X1,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X0,X1,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_3) ).
fof(f742,axiom,
! [X2,X3,X0,X1] :
( c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X0,X1,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X0,X1,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1) ).
fof(f744,axiom,
! [X0] :
( ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_Q____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1_03) ).
fof(f745,axiom,
! [X0] :
( ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_Q____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_04) ).
fof(f746,axiom,
c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_Q____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_05) ).
fof(f747,negated_conjecture,
~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f856,plain,
! [X0] :
( c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_Q____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[],[f744,f710]) ).
fof(f862,definition,
( spl0_1
<=> c_in(v_Q____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f864,plain,
( ~ c_in(v_Q____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| spl0_1 ),
inference(avatar_component_clause,[],[f862]) ).
fof(f877,plain,
! [X0] :
( c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_a_H____,v_b_H____,v_P_H____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X0,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____(v_sko__CHAINED__1(v_a_H____,v_b_H____,v_P_H____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[],[f742,f709]) ).
fof(f887,plain,
! [X0] :
( c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_a_H____,v_b_H____,v_P_H____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X0,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____(v_sko__CHAINED__1(v_a_H____,v_b_H____,v_P_H____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(forward_subsumption_resolution,[],[f877,f747]) ).
fof(f889,plain,
! [X0] :
( c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_a_H____,v_b_H____,v_P_H____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X0,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____(v_sko__CHAINED__1(v_a_H____,v_b_H____,v_P_H____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(forward_subsumption_resolution,[],[f887,f739]) ).
fof(f893,plain,
( ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_Q____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_Q____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____(v_sko__CHAINED__1(v_a_H____,v_b_H____,v_P_H____,v_Q____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_a_H____,v_b_H____,v_P_H____,v_Q____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[],[f889,f745]) ).
fof(f1063,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P_H____)),
inference(resolution,[],[f737,f739]) ).
fof(f1064,plain,
hBOOL(hAPP(v_F(v_Q____),c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(resolution,[],[f737,f746]) ).
fof(f1066,plain,
! [X0] :
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| hBOOL(hAPP(hAPP(v_Q____,X0),c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(resolution,[],[f737,f856]) ).
fof(f1069,plain,
! [X0] :
( ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| hBOOL(hAPP(hAPP(X0,v_sko__CHAINED__1(v_a_H____,v_b_H____,v_P_H____,X0)),c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_in(X0,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____(v_sko__CHAINED__1(v_a_H____,v_b_H____,v_P_H____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[],[f737,f889]) ).
fof(f1090,plain,
! [X0] : c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,X0),
inference(resolution,[],[f1063,f736]) ).
fof(f1116,plain,
! [X0] : c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_Q____),X0),
inference(resolution,[],[f1064,f736]) ).
fof(f1119,plain,
( hBOOL(hAPP(hAPP(v_Q____,v_sko__CHAINED__1(v_a_H____,v_b_H____,v_P_H____,v_Q____)),c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_in(v_Q____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____(v_sko__CHAINED__1(v_a_H____,v_b_H____,v_P_H____,v_Q____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[],[f1116,f1069]) ).
fof(f1261,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f738,f864]) ).
fof(f1262,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f1261]) ).
fof(f1265,plain,
( ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_Q____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_Q____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_a_H____,v_b_H____,v_P_H____,v_Q____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(forward_subsumption_resolution,[],[f893,f710]) ).
fof(f1290,definition,
( spl0_5
<=> hBOOL(hAPP(hAPP(v_Q____,v_sko__CHAINED__1(v_a_H____,v_b_H____,v_P_H____,v_Q____)),c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f1292,plain,
( hBOOL(hAPP(hAPP(v_Q____,v_sko__CHAINED__1(v_a_H____,v_b_H____,v_P_H____,v_Q____)),c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f1290]) ).
fof(f1294,definition,
( spl0_6
<=> c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_a_H____,v_b_H____,v_P_H____,v_Q____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f1321,plain,
( hBOOL(hAPP(hAPP(v_Q____,v_sko__CHAINED__1(v_a_H____,v_b_H____,v_P_H____,v_Q____)),c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_in(v_Q____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
inference(forward_subsumption_resolution,[],[f1119,f1066]) ).
fof(f1385,plain,
( ~ c_in(v_Q____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_a_H____,v_b_H____,v_P_H____,v_Q____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(forward_subsumption_resolution,[],[f1265,f1116]) ).
fof(f1404,plain,
( ~ spl0_1
| spl0_5 ),
inference(avatar_split_clause,[],[f1321,f1290,f862]) ).
fof(f1409,plain,
( spl0_6
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f1385,f862,f1294]) ).
fof(f1417,plain,
( ! [X0] : c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_Q____,v_sko__CHAINED__1(v_a_H____,v_b_H____,v_P_H____,v_Q____)),X0)
| ~ spl0_5 ),
inference(resolution,[],[f1292,f736]) ).
fof(f1420,plain,
( ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_Q____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_a_H____,v_b_H____,v_P_H____,v_Q____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_Q____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ spl0_5 ),
inference(resolution,[],[f1417,f740]) ).
fof(f1423,plain,
( c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_a_H____,v_b_H____,v_P_H____,v_Q____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_Q____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f1420,f1116]) ).
fof(f1424,plain,
( ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_a_H____,v_b_H____,v_P_H____,v_Q____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_Q____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f1423,f747]) ).
fof(f1425,plain,
( ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_a_H____,v_b_H____,v_P_H____,v_Q____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_Q____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f1424,f1090]) ).
fof(f1426,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f1425,f1290,f1294,f862]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f1262]) ).
cnf(s40,plain,
( ~ spl0_1
| spl0_5 ),
inference(sat_conversion,[],[f1404]) ).
cnf(s45,plain,
( ~ spl0_1
| spl0_6 ),
inference(sat_conversion,[],[f1409]) ).
cnf(s49,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f1426]) ).
cnf(s53,plain,
spl0_6,
inference(rat,[],[s45,s2]) ).
cnf(s56,plain,
spl0_5,
inference(rat,[],[s40,s2]) ).
cnf(s66,plain,
$false,
inference(rat,[],[s49,s2,s53,s56]) ).
fof(f1427,plain,
$false,
inference(avatar_sat_refutation,[],[s66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT040-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n013.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 23:31:37 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 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
% 0.64/0.63 % (665601)Will run a generic schedule for satisfiability detection.
% 0.64/0.63 % (665612)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3827940731:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.64/0.63 % (665607)% WARNING: option uhcvi not known.
% 0.64/0.63 % (665606)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3776927029_2999 on theBenchmark for (2999ds/0Mi)
% 0.64/0.63 % (665607)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2455175556:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.64/0.63 % (665608)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2993057622:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.64/0.63 % (665609)dis+10_1_sil=32000:sp=arity:random_seed=408324426:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.64/0.63 % (665610)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=379875733:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.64/0.63 % (665611)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1647758941:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.64/0.63 % (665612)Instruction limit reached!
% 0.64/0.63 % (665612)------------------------------
% 0.64/0.63 % (665612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.63 % (665612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.63 % (665612)CaDiCaL version: 2.1.3
% 0.64/0.63 % (665612)Termination reason: Instruction limit
% 0.64/0.63 % (665612)Termination phase: Saturation
% 0.64/0.63 % (665612)Time elapsed: 0.057 s
% 0.64/0.63 % (665612)Peak memory usage: 14 MB
% 0.64/0.63 % (665612)Instructions burned: 160 (million)
% 0.64/0.63 % (665620)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=387734819:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 0.64/0.63 % (665609)Instruction limit reached!
% 0.64/0.63 % (665609)------------------------------
% 0.64/0.63 % (665609)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.63 % (665609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.63 % (665609)CaDiCaL version: 2.1.3
% 0.64/0.63 % (665609)Termination reason: Instruction limit
% 0.64/0.63 % (665609)Termination phase: Saturation
% 0.64/0.63 % (665609)Time elapsed: 0.066 s
% 0.64/0.63 % (665609)Peak memory usage: 12 MB
% 0.64/0.63 % (665609)Instructions burned: 103 (million)
% 0.64/0.63 % (665610)Instruction limit reached!
% 0.64/0.63 % (665610)------------------------------
% 0.64/0.63 % (665610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.63 % (665610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.63 % (665610)CaDiCaL version: 2.1.3
% 0.64/0.63 % (665610)Termination reason: Instruction limit
% 0.64/0.63 % (665610)Termination phase: Saturation
% 0.64/0.63 % (665610)Time elapsed: 0.073 s
% 0.64/0.63 % (665610)Peak memory usage: 13 MB
% 0.64/0.63 % (665610)Instructions burned: 117 (million)
% 0.64/0.63 % (665611)Instruction limit reached!
% 0.64/0.63 % (665611)------------------------------
% 0.64/0.63 % (665611)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.63 % (665611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.63 % (665611)CaDiCaL version: 2.1.3
% 0.64/0.63 % (665611)Termination reason: Instruction limit
% 0.64/0.63 % (665611)Termination phase: Saturation
% 0.64/0.63 % (665611)Time elapsed: 0.086 s
% 0.64/0.63 % (665611)Peak memory usage: 13 MB
% 0.64/0.63 % (665611)Instructions burned: 132 (million)
% 0.64/0.63 % (665622)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3343809166:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 0.64/0.63 % (665623)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=3497829732:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.64/0.63 % (665625)ott-21_1_sil=16000:fs=off:random_seed=415264367:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.64/0.63 % (665623) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-665601-665623"...
% 0.64/0.63 % (665623)...printing done.
% 0.64/0.63 % (665623)Refutation found. Thanks to Tanya!
% 0.64/0.63 % SZS status Unsatisfiable for theBenchmark
% 0.64/0.63 % SZS output start Proof for theBenchmark
% See solution above
% 0.64/0.63 % (665623)------------------------------
% 0.64/0.63 % (665623)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.63 % (665623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.63 % (665623)CaDiCaL version: 2.1.3
% 0.64/0.63 % (665623)Termination reason: Refutation
% 0.64/0.63 % (665623)Time elapsed: 0.042 s
% 0.64/0.63 % (665623)Peak memory usage: 14 MB
% 0.64/0.63 % (665623)Instructions burned: 74 (million)
% 0.64/0.63 % (665601)Success in time 0.201 s
% 0.64/0.64 % Vampire exiting
%------------------------------------------------------------------------------