%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL106-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 09:37:59 AM UTC 2026
% Result : Unsatisfiable 3.71s 1.61s
% Output : Refutation 7.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 67 ( 14 unt; 5 def)
% Number of atoms : 160 ( 52 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 153 ( 60 ~; 88 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-4 aty)
% Number of variables : 39 ( 0 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya),v_xb,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
! [X0] :
( ~ c_in(c_Pair(v_xb,X0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(v_x,X0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X0,X1),X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| X2 = c_Comb_Ocomb_Oop_A_D_D(X0,X1)
| X0 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2)
| X0 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(X0,X1,X2)),v_sko__uTG(X0,X1,X2))
| X2 = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(X0,X1,X2),v_sko__uTH(X0,X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_OAp__parcontractE_0) ).
fof(f4,plain,
! [X2,X0,X1] :
( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X0,X1),X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| c_Comb_Ocomb_Oop_A_D_D(X0,X1) = X2
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2) = X0
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(X0,X1,X2)),v_sko__uTG(X0,X1,X2)) = X0
| c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(X0,X1,X2),v_sko__uTH(X0,X1,X2)) = X2 ),
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X0,X1),X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| c_in(c_Pair(X0,v_sko__uTI(X0,X1,X2),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| X2 = c_Comb_Ocomb_Oop_A_D_D(X0,X1)
| X0 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2)
| X0 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(X0,X1,X2)),v_sko__uTG(X0,X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_OAp__parcontractE_2) ).
fof(f6,plain,
! [X2,X0,X1] :
( c_in(c_Pair(X0,v_sko__uTI(X0,X1,X2),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X0,X1),X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| c_Comb_Ocomb_Oop_A_D_D(X0,X1) = X2
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2) = X0
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(X0,X1,X2)),v_sko__uTG(X0,X1,X2)) = X0 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X0,X1] : c_Comb_Ocomb_OK != c_Comb_Ocomb_Oop_A_D_D(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Ocomb_Odistinct__3__iff1_0) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( c_Comb_Ocomb_Oop_A_D_D(X0,X1) != c_Comb_Ocomb_Oop_A_D_D(X2,X3)
| X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Ocomb_Oinject__iff1_0) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( c_Comb_Ocomb_Oop_A_D_D(X0,X1) != c_Comb_Ocomb_Oop_A_D_D(X2,X3)
| X1 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Ocomb_Oinject__iff1_1) ).
fof(f10,axiom,
! [X0,X1] :
( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0),X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| X1 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_OK1__parcontractD__dest_0) ).
fof(f11,plain,
! [X0,X1] :
( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0),X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(X0,X1)) = X1 ),
inference(reorient_equations,[],[f10]) ).
fof(f12,axiom,
! [X0,X1] :
( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0),X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| c_in(c_Pair(X0,v_sko__uTE(X0,X1),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_OK1__parcontractD__dest_1) ).
fof(f13,axiom,
! [X0] : c_in(c_Pair(X0,X0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Oparcontract_Ointros__1_0) ).
fof(f14,axiom,
! [X0,X1] : c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0),X1),X0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Oparcontract_Ointros__2_0) ).
fof(f18,plain,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya) = v_xb
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)),v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb))
| v_xb = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb),v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)) ),
inference(resolution,[],[f1,f4]) ).
fof(f20,definition,
( spl0_1
<=> v_xb = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb),v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f22,plain,
( v_xb = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb),v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f24,definition,
( spl0_2
<=> c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)),v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f25,plain,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) != c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)),v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb))
| spl0_2 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f26,plain,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)),v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f28,definition,
( spl0_3
<=> c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f29,plain,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) != c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb)
| spl0_3 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f30,plain,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f32,definition,
( spl0_4
<=> c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya) = v_xb ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f33,plain,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya) != v_xb
| spl0_4 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f34,plain,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya) = v_xb
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f35,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f18,f32,f28,f24,f20]) ).
fof(f39,plain,
( ! [X0,X1] :
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) != c_Comb_Ocomb_Oop_A_D_D(X0,X1)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)) = X0 )
| ~ spl0_2 ),
inference(superposition,[],[f8,f26]) ).
fof(f56,plain,
( c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb))
| ~ spl0_2 ),
inference(equality_resolution,[],[f39]) ).
fof(f57,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f56,f7]) ).
fof(f58,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f57]) ).
fof(f67,plain,
( ! [X0,X1] :
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) != c_Comb_Ocomb_Oop_A_D_D(X0,X1)
| v_xb = X1 )
| ~ spl0_3 ),
inference(superposition,[],[f9,f30]) ).
fof(f72,plain,
( v_x = v_xb
| ~ spl0_3 ),
inference(equality_resolution,[],[f67]) ).
fof(f76,plain,
( ! [X0] :
( ~ c_in(c_Pair(v_x,X0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(v_x,X0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) )
| ~ spl0_3 ),
inference(superposition,[],[f2,f72]) ).
fof(f77,plain,
( ! [X0] : ~ c_in(c_Pair(v_x,X0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ spl0_3 ),
inference(duplicate_literal_removal,[],[f76]) ).
fof(f81,plain,
( $false
| ~ spl0_3 ),
inference(resolution,[],[f77,f13]) ).
fof(f82,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f81]) ).
fof(f84,plain,
( c_in(c_Pair(v_xb,v_x,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ spl0_4 ),
inference(superposition,[],[f14,f34]) ).
fof(f93,plain,
( ~ c_in(c_Pair(v_x,v_x,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ spl0_4 ),
inference(resolution,[],[f84,f2]) ).
fof(f94,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f93,f13]) ).
fof(f95,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f94]) ).
fof(f189,definition,
( spl0_12
<=> c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f190,plain,
( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| spl0_12 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f191,plain,
( c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f214,plain,
( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya),v_xb,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya) = v_xb
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)),v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb))
| spl0_12 ),
inference(resolution,[],[f190,f6]) ).
fof(f215,plain,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya) = v_xb
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)),v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb))
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f214,f1]) ).
fof(f216,plain,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)),v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb))
| spl0_4
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f215,f33]) ).
fof(f217,plain,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)),v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb))
| spl0_3
| spl0_4
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f216,f29]) ).
fof(f218,plain,
( $false
| spl0_2
| spl0_3
| spl0_4
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f217,f25]) ).
fof(f219,plain,
( spl0_2
| spl0_3
| spl0_4
| spl0_12 ),
inference(avatar_contradiction_clause,[],[f218]) ).
fof(f283,plain,
( c_in(c_Pair(v_x,v_sko__uTE(v_x,v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ spl0_12 ),
inference(resolution,[],[f191,f12]) ).
fof(f284,plain,
( v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(v_x,v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)))
| ~ spl0_12 ),
inference(resolution,[],[f191,f11]) ).
fof(f299,plain,
( ! [X0] : c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb),X0),v_sko__uTE(v_x,v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ spl0_12 ),
inference(superposition,[],[f14,f284]) ).
fof(f335,plain,
( c_in(c_Pair(v_xb,v_sko__uTE(v_x,v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ spl0_1
| ~ spl0_12 ),
inference(superposition,[],[f299,f22]) ).
fof(f337,plain,
( ~ c_in(c_Pair(v_x,v_sko__uTE(v_x,v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ spl0_1
| ~ spl0_12 ),
inference(resolution,[],[f335,f2]) ).
fof(f338,plain,
( $false
| ~ spl0_1
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f337,f283]) ).
fof(f339,plain,
( ~ spl0_1
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f338]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f35]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f58]) ).
cnf(s3,plain,
~ spl0_3,
inference(sat_conversion,[],[f82]) ).
cnf(s4,plain,
~ spl0_4,
inference(sat_conversion,[],[f95]) ).
cnf(s11,plain,
( spl0_2
| spl0_3
| spl0_4
| spl0_12 ),
inference(sat_conversion,[],[f219]) ).
cnf(s18,plain,
( ~ spl0_1
| ~ spl0_12 ),
inference(sat_conversion,[],[f339]) ).
cnf(s19,plain,
spl0_12,
inference(rat,[],[s11,s3,s4,s2]) ).
cnf(s20,plain,
~ spl0_1,
inference(rat,[],[s18,s19]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s1,s4,s3,s2,s20]) ).
fof(f340,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL106-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n019.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 21:39:49 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.71/1.61 % (302696)Input is clausal, will run a generic CNF schedule.
% 3.71/1.61 % (302703)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2980556678:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.71/1.61 % (302704)lrs+10_1_sil=8000:sp=occurrence:random_seed=4116098546:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.71/1.61 % (302702)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3460772460:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.71/1.61 % (302707)dis-21_1_sil=8000:lcm=predicate:random_seed=2588602106:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.71/1.61 % (302706)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4247956118:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.71/1.61 % (302705)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3651542170:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.71/1.61 % (302701)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=2721243435:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.71/1.61 % (302705)Refutation not found, incomplete strategy
% 3.71/1.61 % (302705)------------------------------
% 3.71/1.61 % (302705)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.61 % (302705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.61 % (302705)CaDiCaL version: 2.1.3
% 3.71/1.61 % (302705)Termination reason: Refutation not found, incomplete strategy
% 3.71/1.61 % (302705)Time elapsed: 0.001 s
% 3.71/1.61 % (302705)Peak memory usage: 87 MB
% 3.71/1.61 % (302705)Instructions burned: 1 (million)
% 3.71/1.61 % (302707)Refutation not found, incomplete strategy
% 3.71/1.61 % (302707)------------------------------
% 3.71/1.61 % (302707)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.61 % (302707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.61 % (302707)CaDiCaL version: 2.1.3
% 3.71/1.61 % (302707)Termination reason: Refutation not found, incomplete strategy
% 3.71/1.61 % (302707)Time elapsed: 0.009 s
% 3.71/1.61 % (302707)Peak memory usage: 88 MB
% 3.71/1.61 % (302707)Instructions burned: 14 (million)
% 3.71/1.61 % (302704)Instruction limit reached!
% 3.71/1.61 % (302704)------------------------------
% 3.71/1.61 % (302704)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.61 % (302704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.61 % (302704)CaDiCaL version: 2.1.3
% 3.71/1.61 % (302704)Termination reason: Instruction limit
% 3.71/1.61 % (302704)Termination phase: Saturation
% 3.71/1.61 % (302704)Time elapsed: 0.063 s
% 3.71/1.61 % (302704)Peak memory usage: 88 MB
% 3.71/1.61 % (302704)Instructions burned: 108 (million)
% 3.71/1.61 % (302706)Instruction limit reached!
% 3.71/1.61 % (302706)------------------------------
% 3.71/1.61 % (302706)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.61 % (302706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.61 % (302706)CaDiCaL version: 2.1.3
% 3.71/1.61 % (302706)Termination reason: Instruction limit
% 3.71/1.61 % (302706)Termination phase: Saturation
% 3.71/1.61 % (302706)Time elapsed: 0.110 s
% 3.71/1.61 % (302706)Peak memory usage: 89 MB
% 3.71/1.61 % (302706)Instructions burned: 180 (million)
% 3.71/1.61 % (302715)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=831128132:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.71/1.61 % (302715)Refutation not found, incomplete strategy
% 3.71/1.61 % (302715)------------------------------
% 3.71/1.61 % (302715)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.61 % (302715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.61 % (302715)CaDiCaL version: 2.1.3
% 3.71/1.61 % (302715)Termination reason: Refutation not found, incomplete strategy
% 3.71/1.61 % (302715)Time elapsed: 0.002 s
% 3.71/1.61 % (302715)Peak memory usage: 87 MB
% 3.71/1.61 % (302715)Instructions burned: 1 (million)
% 3.71/1.61 % (302705)------------------------------
% 3.71/1.61 % (302705)------------------------------
% 3.71/1.61 % (302716)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3509951491:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.71/1.61 % (302707)------------------------------
% 3.71/1.61 % (302707)------------------------------
% 3.71/1.61 % (302719)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=275789418:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 3.71/1.61 % (302716)Instruction limit reached!
% 3.71/1.61 % (302716)------------------------------
% 3.71/1.61 % (302716)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.61 % (302716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.61 % (302716)CaDiCaL version: 2.1.3
% 3.71/1.61 % (302716)Termination reason: Instruction limit
% 3.71/1.61 % (302716)Termination phase: Saturation
% 3.71/1.61 % (302716)Time elapsed: 0.103 s
% 3.71/1.61 % (302716)Peak memory usage: 90 MB
% 3.71/1.61 % (302716)Instructions burned: 190 (million)
% 3.71/1.61 % (302720)lrs+10_64_to=lpo:sil=8000:random_seed=3848422752:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 3.71/1.61 % (302719)Instruction limit reached!
% 3.71/1.61 % (302719)------------------------------
% 3.71/1.61 % (302719)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.61 % (302719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.61 % (302719)CaDiCaL version: 2.1.3
% 3.71/1.61 % (302719)Termination reason: Instruction limit
% 3.71/1.61 % (302719)Termination phase: Saturation
% 3.71/1.61 % (302719)Time elapsed: 0.062 s
% 3.71/1.61 % (302719)Peak memory usage: 89 MB
% 3.71/1.61 % (302719)Instructions burned: 219 (million)
% 3.71/1.61 % (302715)------------------------------
% 3.71/1.61 % (302715)------------------------------
% 3.71/1.61 % (302720)Instruction limit reached!
% 3.71/1.61 % (302720)------------------------------
% 3.71/1.61 % (302720)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.61 % (302720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.61 % (302720)CaDiCaL version: 2.1.3
% 3.71/1.61 % (302720)Termination reason: Instruction limit
% 3.71/1.61 % (302720)Termination phase: Saturation
% 3.71/1.61 % (302720)Time elapsed: 0.074 s
% 3.71/1.61 % (302720)Peak memory usage: 88 MB
% 3.71/1.61 % (302720)Instructions burned: 126 (million)
% 3.71/1.61 % (302724)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2710101928:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 3.71/1.61 % (302722)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3423957892:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 3.71/1.61 % (302724)Instruction limit reached!
% 3.71/1.61 % (302724)------------------------------
% 3.71/1.61 % (302724)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.61 % (302724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.61 % (302724)CaDiCaL version: 2.1.3
% 3.71/1.61 % (302724)Termination reason: Instruction limit
% 3.71/1.61 % (302724)Termination phase: Saturation
% 3.71/1.61 % (302724)Time elapsed: 0.056 s
% 3.71/1.61 % (302724)Peak memory usage: 90 MB
% 3.71/1.61 % (302724)Instructions burned: 159 (million)
% 3.71/1.61 % (302725)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3245902255:i=3394:sd=4:ss=included:sgt=64_2994 on theBenchmark for (2994ds/3394Mi)
% 3.71/1.61 % (302726)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=2176608499:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 3.71/1.61 % (302722)Instruction limit reached!
% 3.71/1.61 % (302722)------------------------------
% 3.71/1.61 % (302722)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.61 % (302722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.61 % (302722)CaDiCaL version: 2.1.3
% 3.71/1.61 % (302722)Termination reason: Instruction limit
% 3.71/1.61 % (302722)Termination phase: Saturation
% 3.71/1.61 % (302722)Time elapsed: 0.117 s
% 3.71/1.61 % (302722)Peak memory usage: 89 MB
% 3.71/1.61 % (302722)Instructions burned: 194 (million)
% 3.71/1.61 % (302729)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=3780505208:i=107_2993 on theBenchmark for (2993ds/107Mi)
% 3.71/1.61 % (302729)First to succeed.
% 3.71/1.61 % (302729)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-302696"
% 3.71/1.61 % (302726)Instruction limit reached!
% 3.71/1.61 % (302726)------------------------------
% 3.71/1.61 % (302726)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.61 % (302726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.61 % (302726)CaDiCaL version: 2.1.3
% 3.71/1.61 % (302726)Termination reason: Instruction limit
% 3.71/1.61 % (302726)Termination phase: Saturation
% 3.71/1.61 % (302726)Time elapsed: 0.057 s
% 3.71/1.61 % (302726)Peak memory usage: 88 MB
% 3.71/1.61 % (302726)Instructions burned: 108 (million)
% 3.71/1.61 % (302732)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=2286212215:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2992 on theBenchmark for (2992ds/242Mi)
% 3.71/1.61 % (302729)Refutation found. Thanks to Tanya!
% 3.71/1.61 % SZS status Unsatisfiable for theBenchmark
% 3.71/1.61 % SZS output start Proof for theBenchmark
% See solution above
% 7.26/1.79 % (302729)------------------------------
% 7.26/1.79 % (302729)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.26/1.79 % (302729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.26/1.79 % (302729)CaDiCaL version: 2.1.3
% 7.26/1.79 % (302729)Termination reason: Refutation
% 7.26/1.79 % (302729)Time elapsed: 0.008 s
% 7.26/1.79 % (302729)Peak memory usage: 89 MB
% 7.26/1.79 % (302729)Instructions burned: 21 (million)
% 7.26/1.79 % (302729)------------------------------
% 7.26/1.79 % (302729)------------------------------
% 7.26/1.79 % (302696)Success in time 0.947 s
% 7.26/1.79 % Vampire exiting
%------------------------------------------------------------------------------