%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL106-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 09:38:29 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.34s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of formulae : 75 ( 18 unt; 8 def)
% Number of atoms : 174 ( 53 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 165 ( 66 ~; 91 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-4 aty)
% Number of variables : 42 ( 0 sgn 42 !; 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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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(X0,v_sko__uTE(X0,X1),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(c_Comb_Ocomb_OK,X0),X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_Comb_Oparcontract_Ointros__2_0) ).
fof(f167,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,[],[f4,f1]) ).
fof(f176,definition,
( spl0_4
<=> 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_4])],[avatar_definition]) ).
fof(f178,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_4 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f180,definition,
( spl0_5
<=> 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_5])],[avatar_definition]) ).
fof(f182,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_5 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f184,definition,
( spl0_6
<=> 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_6])],[avatar_definition]) ).
fof(f186,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_6 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f188,definition,
( spl0_7
<=> 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_7])],[avatar_definition]) ).
fof(f190,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_7 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f191,plain,
( spl0_4
| spl0_5
| spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f167,f188,f184,f180,f176]) ).
fof(f195,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_5 ),
inference(superposition,[],[f8,f182]) ).
fof(f235,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_5 ),
inference(equality_resolution,[],[f195]) ).
fof(f238,plain,
( c_Comb_Ocomb_OK != c_Comb_Ocomb_OK
| ~ spl0_5 ),
inference(superposition,[],[f7,f235]) ).
fof(f250,plain,
( $false
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f238]) ).
fof(f251,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[],[f250]) ).
fof(f315,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_6 ),
inference(superposition,[],[f9,f186]) ).
fof(f340,plain,
( v_x = v_xb
| ~ spl0_6 ),
inference(equality_resolution,[],[f315]) ).
fof(f341,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_6 ),
inference(superposition,[],[f2,f340]) ).
fof(f385,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_6 ),
inference(duplicate_literal_removal,[],[f341]) ).
fof(f386,plain,
( $false
| ~ spl0_6 ),
inference(resolution,[],[f385,f13]) ).
fof(f388,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f386]) ).
fof(f392,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_7 ),
inference(superposition,[],[f14,f190]) ).
fof(f415,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_7 ),
inference(resolution,[],[f2,f392]) ).
fof(f419,plain,
( $false
| ~ spl0_7 ),
inference(resolution,[],[f415,f13]) ).
fof(f420,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[],[f419]) ).
fof(f449,plain,
! [X2,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),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(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0),X1) = X2
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0) = 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,X0),X1,X2)),v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0),X1,X2))
| v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0),X1,X2) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(X0,v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X0),X1,X2))) ),
inference(resolution,[],[f6,f11]) ).
fof(f864,definition,
( spl0_40
<=> 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)) ),
introduced(definition,[new_symbols(definition,[spl0_40])],[avatar_definition]) ).
fof(f866,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))
| spl0_40 ),
inference(avatar_component_clause,[],[f864]) ).
fof(f868,plain,
( $false
| spl0_40 ),
inference(resolution,[],[f866,f1]) ).
fof(f870,plain,
spl0_40,
inference(avatar_contradiction_clause,[],[f868]) ).
fof(f876,definition,
( spl0_42
<=> 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_42])],[avatar_definition]) ).
fof(f878,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_42 ),
inference(avatar_component_clause,[],[f876]) ).
fof(f883,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_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))) ),
inference(resolution,[],[f449,f1]) ).
fof(f894,definition,
( spl0_43
<=> 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))) ),
introduced(definition,[new_symbols(definition,[spl0_43])],[avatar_definition]) ).
fof(f896,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_43 ),
inference(avatar_component_clause,[],[f894]) ).
fof(f897,plain,
( spl0_43
| spl0_5
| spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f883,f188,f184,f180,f894]) ).
fof(f899,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_43 ),
inference(superposition,[],[f14,f896]) ).
fof(f975,definition,
( spl0_50
<=> 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)) ),
introduced(definition,[new_symbols(definition,[spl0_50])],[avatar_definition]) ).
fof(f976,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_50 ),
inference(avatar_component_clause,[],[f975]) ).
fof(f1048,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_42 ),
inference(resolution,[],[f878,f6]) ).
fof(f1049,plain,
( spl0_5
| spl0_6
| spl0_7
| ~ spl0_40
| spl0_42 ),
inference(avatar_split_clause,[],[f1048,f876,f864,f188,f184,f180]) ).
fof(f1238,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_4
| ~ spl0_43 ),
inference(superposition,[],[f899,f178]) ).
fof(f1239,plain,
( spl0_50
| ~ spl0_4
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f1238,f894,f176,f975]) ).
fof(f1244,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_50 ),
inference(resolution,[],[f976,f2]) ).
fof(f1248,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_50 ),
inference(resolution,[],[f1244,f12]) ).
fof(f1249,plain,
( ~ spl0_42
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f1248,f975,f876]) ).
cnf(s4,plain,
( spl0_4
| spl0_5
| spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f191]) ).
cnf(s6,plain,
~ spl0_5,
inference(sat_conversion,[],[f251]) ).
cnf(s13,plain,
~ spl0_6,
inference(sat_conversion,[],[f388]) ).
cnf(s15,plain,
~ spl0_7,
inference(sat_conversion,[],[f420]) ).
cnf(s33,plain,
spl0_40,
inference(sat_conversion,[],[f870]) ).
cnf(s35,plain,
( spl0_5
| spl0_6
| spl0_7
| spl0_43 ),
inference(sat_conversion,[],[f897]) ).
cnf(s59,plain,
( spl0_5
| spl0_6
| spl0_7
| ~ spl0_40
| spl0_42 ),
inference(sat_conversion,[],[f1049]) ).
cnf(s65,plain,
( ~ spl0_4
| ~ spl0_43
| spl0_50 ),
inference(sat_conversion,[],[f1239]) ).
cnf(s66,plain,
( ~ spl0_42
| ~ spl0_50 ),
inference(sat_conversion,[],[f1249]) ).
cnf(s69,plain,
spl0_42,
inference(rat,[],[s59,s13,s33,s15,s6]) ).
cnf(s70,plain,
spl0_43,
inference(rat,[],[s35,s13,s15,s6]) ).
cnf(s71,plain,
~ spl0_50,
inference(rat,[],[s66,s69]) ).
cnf(s72,plain,
~ spl0_4,
inference(rat,[],[s65,s71,s70]) ).
cnf(s74,plain,
$false,
inference(rat,[],[s4,s15,s13,s6,s72]) ).
fof(f1250,plain,
$false,
inference(avatar_sat_refutation,[],[s74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL106-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n026.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 21:42:27 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.19/0.34 % (103585)Will run a generic schedule for satisfiability detection.
% 0.19/0.34 % (103592)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1553234202:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.34 % (103591)% WARNING: option uhcvi not known.
% 0.19/0.34 % (103590)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=321401124_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.34 % (103595)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=805367695:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.34 % (103591)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2790387575:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.34 % (103593)dis+10_1_sil=32000:sp=arity:random_seed=1981127947:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.34 % (103594)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=472830954:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.34 % (103596)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1152846752:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.34 % TRYING [1]
% 0.19/0.34 % TRYING [2]
% 0.19/0.34 % TRYING [3]
% 0.19/0.34 % TRYING [4]
% 0.19/0.34 % TRYING [5]
% 0.19/0.34 % (103596) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-103585-103596"...
% 0.19/0.34 % (103596)...printing done.
% 0.19/0.34 % (103593)Instruction limit reached!
% 0.19/0.34 % (103593)------------------------------
% 0.19/0.34 % (103593)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.34 % (103593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.34 % (103593)CaDiCaL version: 2.1.3
% 0.19/0.34 % (103593)Termination reason: Instruction limit
% 0.19/0.34 % (103593)Termination phase: Saturation
% 0.19/0.34 % (103593)Time elapsed: 0.061 s
% 0.19/0.34 % (103593)Peak memory usage: 12 MB
% 0.19/0.34 % (103593)Instructions burned: 106 (million)
% 0.19/0.34 % (103595) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-103585-103595"...
% 0.19/0.34 % (103596)Refutation found. Thanks to Tanya!
% 0.19/0.34 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.34 % (103596)------------------------------
% 0.19/0.34 % (103596)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.34 % (103596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.34 % (103596)CaDiCaL version: 2.1.3
% 0.19/0.34 % (103596)Termination reason: Refutation
% 0.19/0.34 % (103596)Time elapsed: 0.059 s
% 0.19/0.34 % (103596)Peak memory usage: 13 MB
% 0.19/0.34 % (103596)Instructions burned: 95 (million)
% 0.19/0.34 % (103585)Success in time 0.103 s
% 0.19/0.34 % Vampire exiting
%------------------------------------------------------------------------------