%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SCT121+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 12:37:33 PM UTC 2026
% Result : Theorem 1.28s 0.65s
% Output : Refutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 17
% Syntax : Number of formulae : 91 ( 25 unt; 7 def)
% Number of atoms : 244 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 256 ( 103 ~; 120 |; 10 &)
% ( 14 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 8 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-4 aty)
% Number of variables : 94 ( 0 sgn 91 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : c_member(X1,X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__I) ).
fof(f3,axiom,
! [X0,X1] :
( c_Relation_Oirrefl(X1,X0)
<=> ! [X2] : ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X2),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_irrefl__def) ).
fof(f4,axiom,
! [X0,X1,X2] :
( c_Relation_Ototal__on(X2,X1,X0)
<=> ! [X3] :
( c_member(X2,X3,X1)
=> ! [X4] :
( c_member(X2,X4,X1)
=> ( X3 != X4
=> ( c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X3,X4),X0)
| c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X4,X3),X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__def) ).
fof(f5,axiom,
! [X0,X1] :
( c_Relation_Otrans(X1,X0)
<=> ! [X2,X3] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X0)
=> ! [X4] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X4),X0)
=> c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X4),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__def) ).
fof(f18,axiom,
! [X0,X1,X2] :
( c_member(X2,X1,X0)
<=> hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).
fof(f523,axiom,
! [X0] :
( ! [X1] :
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X0,X1))
& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X0,X1))
& c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(X0,X1)) )
=> ! [X2,X3] :
( X2 != X3
=> ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X3),hAPP(X0,v_i))
=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X3),v_F(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f524,axiom,
! [X0] :
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X0))
& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X0))
& c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f525,axiom,
c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),v_F(v_P)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
fof(f526,axiom,
( ! [X0] :
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X0))
& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X0))
& c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,X0)) )
=> ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
& c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),v_F(v_P)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
fof(f527,conjecture,
c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),hAPP(v_P,v_i)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
fof(f528,negated_conjecture,
~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),hAPP(v_P,v_i)),
inference(negated_conjecture,[status(cth)],[f527]) ).
fof(f531,plain,
~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),hAPP(v_P,v_i)),
inference(flattening,[],[f528]) ).
fof(f549,plain,
! [X0,X1,X2] :
( c_Relation_Ototal__on(X2,X1,X0)
<=> ! [X3] :
( ! [X4] :
( c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X3,X4),X0)
| c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X4,X3),X0)
| X3 = X4
| ~ c_member(X2,X4,X1) )
| ~ c_member(X2,X3,X1) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f550,plain,
! [X0,X1,X2] :
( c_Relation_Ototal__on(X2,X1,X0)
<=> ! [X3] :
( ! [X4] :
( c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X3,X4),X0)
| c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X4,X3),X0)
| X3 = X4
| ~ c_member(X2,X4,X1) )
| ~ c_member(X2,X3,X1) ) ),
inference(flattening,[],[f549]) ).
fof(f551,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,X0)
<=> ! [X2,X3] :
( ! [X4] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X4),X0)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X4),X0) )
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f979,plain,
! [X0] :
( ! [X2,X3] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X3),v_F(X0))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X3),hAPP(X0,v_i))
| X2 = X3 )
| ? [X1] :
( ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X0,X1))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X0,X1))
| ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(X0,X1)) ) ),
inference(ennf_transformation,[],[f523]) ).
fof(f980,plain,
! [X0] :
( ! [X2,X3] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X3),v_F(X0))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X3),hAPP(X0,v_i))
| X2 = X3 )
| ? [X1] :
( ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X0,X1))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X0,X1))
| ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(X0,X1)) ) ),
inference(flattening,[],[f979]) ).
fof(f981,plain,
( ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
& c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),v_F(v_P)) )
| ? [X0] :
( ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X0))
| ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,X0)) ) ),
inference(ennf_transformation,[],[f526]) ).
fof(f983,plain,
! [X0,X1] : c_member(X1,X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
inference(cnf_transformation,[],[f2]) ).
fof(f985,plain,
! [X2,X0,X1] :
( ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X2),X0)
| ~ c_Relation_Oirrefl(X1,X0) ),
inference(cnf_transformation,[],[f3]) ).
fof(f990,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_Relation_Ototal__on(X2,X1,X0)
| ~ c_member(X2,X4,X1)
| X3 = X4
| c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X4,X3),X0)
| c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X3,X4),X0)
| ~ c_member(X2,X3,X1) ),
inference(cnf_transformation,[],[f550]) ).
fof(f994,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X4),X0)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X0)
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X4),X0)
| ~ c_Relation_Otrans(X1,X0) ),
inference(cnf_transformation,[],[f551]) ).
fof(f1024,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| c_member(X2,X1,X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f1025,plain,
! [X2,X0,X1] :
( ~ c_member(X2,X1,X0)
| hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f1723,plain,
! [X2,X3,X0] :
( ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X0,sK85(X0)))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X0,sK85(X0)))
| ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(X0,sK85(X0)))
| X2 = X3
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X3),hAPP(X0,v_i))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X3),v_F(X0)) ),
inference(cnf_transformation,[],[f980]) ).
fof(f1724,plain,
! [X0] : c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,X0)),
inference(cnf_transformation,[],[f524]) ).
fof(f1725,plain,
! [X0] : c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X0)),
inference(cnf_transformation,[],[f524]) ).
fof(f1726,plain,
! [X0] : c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X0)),
inference(cnf_transformation,[],[f524]) ).
fof(f1727,plain,
c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),v_F(v_P)),
inference(cnf_transformation,[],[f525]) ).
fof(f1728,plain,
( ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,sK86))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sK86))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sK86))
| c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)) ),
inference(cnf_transformation,[],[f981]) ).
fof(f1729,plain,
( ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,sK86))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sK86))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sK86))
| c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)) ),
inference(cnf_transformation,[],[f981]) ).
fof(f1731,plain,
~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),hAPP(v_P,v_i)),
inference(cnf_transformation,[],[f531]) ).
fof(f1932,definition,
( spl87_1
<=> c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)) ),
introduced(definition,[new_symbols(definition,[spl87_1])],[avatar_definition]) ).
fof(f1934,plain,
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ spl87_1 ),
inference(avatar_component_clause,[],[f1932]) ).
fof(f1936,definition,
( spl87_2
<=> c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sK86)) ),
introduced(definition,[new_symbols(definition,[spl87_2])],[avatar_definition]) ).
fof(f1938,plain,
( ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sK86))
| spl87_2 ),
inference(avatar_component_clause,[],[f1936]) ).
fof(f1940,definition,
( spl87_3
<=> c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sK86)) ),
introduced(definition,[new_symbols(definition,[spl87_3])],[avatar_definition]) ).
fof(f1942,plain,
( ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sK86))
| spl87_3 ),
inference(avatar_component_clause,[],[f1940]) ).
fof(f1944,definition,
( spl87_4
<=> c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,sK86)) ),
introduced(definition,[new_symbols(definition,[spl87_4])],[avatar_definition]) ).
fof(f1946,plain,
( ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,sK86))
| spl87_4 ),
inference(avatar_component_clause,[],[f1944]) ).
fof(f1947,plain,
( spl87_1
| ~ spl87_2
| ~ spl87_3
| ~ spl87_4 ),
inference(avatar_split_clause,[],[f1728,f1944,f1940,f1936,f1932]) ).
fof(f1949,definition,
( spl87_5
<=> c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)) ),
introduced(definition,[new_symbols(definition,[spl87_5])],[avatar_definition]) ).
fof(f1951,plain,
( c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ spl87_5 ),
inference(avatar_component_clause,[],[f1949]) ).
fof(f1952,plain,
( spl87_5
| ~ spl87_2
| ~ spl87_3
| ~ spl87_4 ),
inference(avatar_split_clause,[],[f1729,f1944,f1940,f1936,f1949]) ).
fof(f1958,plain,
( $false
| spl87_2 ),
inference(forward_subsumption_resolution,[],[f1938,f1726]) ).
fof(f1959,plain,
spl87_2,
inference(avatar_contradiction_clause,[],[f1958]) ).
fof(f1960,plain,
( $false
| spl87_3 ),
inference(forward_subsumption_resolution,[],[f1942,f1725]) ).
fof(f1961,plain,
spl87_3,
inference(avatar_contradiction_clause,[],[f1960]) ).
fof(f1971,plain,
( $false
| spl87_4 ),
inference(forward_subsumption_resolution,[],[f1946,f1724]) ).
fof(f1972,plain,
spl87_4,
inference(avatar_contradiction_clause,[],[f1971]) ).
fof(f2191,plain,
! [X0] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_a),v_F(v_P))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_b),v_F(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)) ),
inference(resolution,[],[f994,f1727]) ).
fof(f2199,plain,
( ! [X0] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_a),v_F(v_P))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_b),v_F(v_P)) )
| ~ spl87_1 ),
inference(forward_subsumption_resolution,[],[f2191,f1934]) ).
fof(f2520,plain,
! [X2,X0,X1] :
( ~ c_member(tc_Arrow__Order__Mirabelle_Oalt,X0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)))
| X0 = X1
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(v_P,X2))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),hAPP(v_P,X2))
| ~ c_member(tc_Arrow__Order__Mirabelle_Oalt,X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool))) ),
inference(resolution,[],[f990,f1724]) ).
fof(f2523,plain,
! [X2,X0,X1] :
( ~ c_member(tc_Arrow__Order__Mirabelle_Oalt,X0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)))
| X0 = X1
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(v_P,X2))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),hAPP(v_P,X2)) ),
inference(forward_subsumption_resolution,[],[f2520,f983]) ).
fof(f2525,plain,
! [X2,X0,X1] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(v_P,X2))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),hAPP(v_P,X2))
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f2523,f983]) ).
fof(f2756,plain,
! [X0,X1] :
( ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sK85(v_P)))
| ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,sK85(v_P)))
| X0 = X1
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(v_P,v_i))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_F(v_P)) ),
inference(resolution,[],[f1723,f1726]) ).
fof(f2757,plain,
! [X0,X1] :
( ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,sK85(v_P)))
| X0 = X1
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(v_P,v_i))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_F(v_P)) ),
inference(forward_subsumption_resolution,[],[f2756,f1725]) ).
fof(f2758,plain,
! [X0,X1] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(v_P,v_i))
| X0 = X1
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_F(v_P)) ),
inference(forward_subsumption_resolution,[],[f2757,f1724]) ).
fof(f2845,plain,
hBOOL(hAPP(v_F(v_P),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b))),
inference(resolution,[],[f1025,f1727]) ).
fof(f2853,plain,
! [X0] : c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),v_F(v_P)),
inference(resolution,[],[f2845,f1024]) ).
fof(f3186,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),hAPP(v_P,v_i))
| v_a = v_b ),
inference(resolution,[],[f2525,f1731]) ).
fof(f3219,definition,
( spl87_7
<=> v_a = v_b ),
introduced(definition,[new_symbols(definition,[spl87_7])],[avatar_definition]) ).
fof(f3220,plain,
( v_a != v_b
| spl87_7 ),
inference(avatar_component_clause,[],[f3219]) ).
fof(f3221,plain,
( v_a = v_b
| ~ spl87_7 ),
inference(avatar_component_clause,[],[f3219]) ).
fof(f3223,definition,
( spl87_8
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),hAPP(v_P,v_i)) ),
introduced(definition,[new_symbols(definition,[spl87_8])],[avatar_definition]) ).
fof(f3225,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),hAPP(v_P,v_i))
| ~ spl87_8 ),
inference(avatar_component_clause,[],[f3223]) ).
fof(f3230,plain,
( spl87_7
| spl87_8 ),
inference(avatar_split_clause,[],[f3186,f3223,f3219]) ).
fof(f3235,plain,
( ! [X0] : c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_a),v_F(v_P))
| ~ spl87_7 ),
inference(superposition,[],[f2853,f3221]) ).
fof(f3239,plain,
( ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ spl87_7 ),
inference(resolution,[],[f3235,f985]) ).
fof(f3242,plain,
( $false
| ~ spl87_5
| ~ spl87_7 ),
inference(forward_subsumption_resolution,[],[f3239,f1951]) ).
fof(f3243,plain,
( ~ spl87_5
| ~ spl87_7 ),
inference(avatar_contradiction_clause,[],[f3242]) ).
fof(f3244,plain,
( v_a = v_b
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),v_F(v_P))
| ~ spl87_8 ),
inference(resolution,[],[f3225,f2758]) ).
fof(f3248,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),v_F(v_P))
| spl87_7
| ~ spl87_8 ),
inference(forward_subsumption_resolution,[],[f3244,f3220]) ).
fof(f3257,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_b),v_F(v_P))
| ~ spl87_1
| spl87_7
| ~ spl87_8 ),
inference(resolution,[],[f3248,f2199]) ).
fof(f3269,plain,
( ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ spl87_1
| spl87_7
| ~ spl87_8 ),
inference(resolution,[],[f3257,f985]) ).
fof(f3272,plain,
( $false
| ~ spl87_1
| ~ spl87_5
| spl87_7
| ~ spl87_8 ),
inference(forward_subsumption_resolution,[],[f3269,f1951]) ).
fof(f3273,plain,
( ~ spl87_1
| ~ spl87_5
| spl87_7
| ~ spl87_8 ),
inference(avatar_contradiction_clause,[],[f3272]) ).
cnf(s1,plain,
( spl87_1
| ~ spl87_2
| ~ spl87_3
| ~ spl87_4 ),
inference(sat_conversion,[],[f1947]) ).
cnf(s2,plain,
( ~ spl87_2
| ~ spl87_3
| ~ spl87_4
| spl87_5 ),
inference(sat_conversion,[],[f1952]) ).
cnf(s4,plain,
spl87_2,
inference(sat_conversion,[],[f1959]) ).
cnf(s5,plain,
spl87_3,
inference(sat_conversion,[],[f1961]) ).
cnf(s6,plain,
spl87_4,
inference(sat_conversion,[],[f1972]) ).
cnf(s8,plain,
( spl87_7
| spl87_8 ),
inference(sat_conversion,[],[f3230]) ).
cnf(s9,plain,
( ~ spl87_5
| ~ spl87_7 ),
inference(sat_conversion,[],[f3243]) ).
cnf(s10,plain,
( ~ spl87_1
| ~ spl87_5
| spl87_7
| ~ spl87_8 ),
inference(sat_conversion,[],[f3273]) ).
cnf(s12,plain,
spl87_5,
inference(rat,[],[s2,s6,s5,s4]) ).
cnf(s13,plain,
~ spl87_7,
inference(rat,[],[s9,s12]) ).
cnf(s14,plain,
spl87_8,
inference(rat,[],[s8,s13]) ).
cnf(s15,plain,
~ spl87_1,
inference(rat,[],[s10,s14,s12,s13]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s1,s6,s5,s4,s15]) ).
fof(f3274,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT121+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 23:48:09 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.28/0.65 % (2860089)Will run a generic schedule for satisfiability detection.
% 1.28/0.65 % (2860094)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2829174292_2999 on theBenchmark for (2999ds/0Mi)
% 1.28/0.65 % (2860095)% WARNING: option uhcvi not known.
% 1.28/0.65 % (2860095)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3714768265:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.28/0.65 % (2860096)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2346804718:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.28/0.65 % (2860097)dis+10_1_sil=32000:sp=arity:random_seed=1771980954:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.28/0.65 % (2860098)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2185236713:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.28/0.65 % (2860099)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3299208386:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.28/0.65 % (2860100)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2937667919:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.28/0.65 % (2860097)Instruction limit reached!
% 1.28/0.65 % (2860097)------------------------------
% 1.28/0.65 % (2860097)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.28/0.65 % (2860097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.28/0.65 % (2860097)CaDiCaL version: 2.1.3
% 1.28/0.65 % (2860097)Termination reason: Instruction limit
% 1.28/0.65 % (2860097)Termination phase: Saturation
% 1.28/0.65 % (2860097)Time elapsed: 0.062 s
% 1.28/0.65 % (2860097)Peak memory usage: 13 MB
% 1.28/0.65 % (2860097)Instructions burned: 104 (million)
% 1.28/0.65 % (2860098)Instruction limit reached!
% 1.28/0.65 % (2860098)------------------------------
% 1.28/0.65 % (2860098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.28/0.65 % (2860098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.28/0.65 % (2860098)CaDiCaL version: 2.1.3
% 1.28/0.65 % (2860098)Termination reason: Instruction limit
% 1.28/0.65 % (2860098)Termination phase: Saturation
% 1.28/0.65 % (2860098)Time elapsed: 0.067 s
% 1.28/0.65 % (2860098)Peak memory usage: 14 MB
% 1.28/0.65 % (2860098)Instructions burned: 121 (million)
% 1.28/0.65 % (2860099)Instruction limit reached!
% 1.28/0.65 % (2860099)------------------------------
% 1.28/0.65 % (2860099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.28/0.65 % (2860099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.28/0.65 % (2860099)CaDiCaL version: 2.1.3
% 1.28/0.65 % (2860099)Termination reason: Instruction limit
% 1.28/0.65 % (2860099)Termination phase: Saturation
% 1.28/0.65 % (2860099)Time elapsed: 0.079 s
% 1.28/0.65 % (2860099)Peak memory usage: 14 MB
% 1.28/0.65 % (2860099)Instructions burned: 131 (million)
% 1.28/0.65 % (2860108)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2607811687:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 1.28/0.65 % (2860109)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=123257119:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.28/0.65 % (2860110)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=1125236047:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.28/0.65 % (2860100)Instruction limit reached!
% 1.28/0.65 % (2860100)------------------------------
% 1.28/0.65 % (2860100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.28/0.65 % (2860100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.28/0.65 % (2860100)CaDiCaL version: 2.1.3
% 1.28/0.65 % (2860100)Termination reason: Instruction limit
% 1.28/0.65 % (2860100)Termination phase: Saturation
% 1.28/0.65 % (2860100)Time elapsed: 0.100 s
% 1.28/0.65 % (2860100)Peak memory usage: 14 MB
% 1.28/0.65 % (2860100)Instructions burned: 160 (million)
% 1.28/0.65 % TRYING [1]
% 1.28/0.65 % (2860114)ott-21_1_sil=16000:fs=off:random_seed=4169955762:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.28/0.65 % TRYING [2]
% 1.28/0.65 % (2860109)Instruction limit reached!
% 1.28/0.65 % (2860109)------------------------------
% 1.28/0.65 % (2860109)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.28/0.65 % (2860109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.28/0.65 % (2860109)CaDiCaL version: 2.1.3
% 1.28/0.65 % (2860109)Termination reason: Instruction limit
% 1.28/0.65 % (2860109)Termination phase: Saturation
% 1.28/0.65 % (2860109)Time elapsed: 0.070 s
% 1.28/0.65 % (2860109)Peak memory usage: 14 MB
% 1.28/0.65 % (2860109)Instructions burned: 132 (million)
% 1.28/0.65 % (2860110) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2860089-2860110"...
% 1.28/0.65 % (2860110)...printing done.
% 1.28/0.65 % (2860116)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3704865927:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 1.28/0.65 % (2860110)Refutation found. Thanks to Tanya!
% 1.28/0.65 % SZS status Theorem for theBenchmark
% 1.28/0.65 % SZS output start Proof for theBenchmark
% See solution above
% 1.28/0.65 % (2860110)------------------------------
% 1.28/0.65 % (2860110)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.28/0.65 % (2860110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.28/0.65 % (2860110)CaDiCaL version: 2.1.3
% 1.28/0.65 % (2860110)Termination reason: Refutation
% 1.28/0.65 % (2860110)Time elapsed: 0.078 s
% 1.28/0.65 % (2860110)Peak memory usage: 15 MB
% 1.28/0.65 % (2860110)Instructions burned: 135 (million)
% 1.28/0.65 % (2860089)Success in time 0.238 s
% 1.28/0.65 % Vampire exiting
%------------------------------------------------------------------------------