%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL094-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 09:37:56 AM UTC 2026
% Result : Unsatisfiable 5.52s 1.55s
% Output : Refutation 6.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 31
% Syntax : Number of formulae : 140 ( 22 unt; 12 def)
% Number of atoms : 312 ( 39 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 335 ( 163 ~; 160 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 13 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 63 ( 0 sgn 63 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
combK != combS,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_s) ).
fof(f3,axiom,
! [X0,X1] : combS != comb_app(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_app) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( comb_app(X0,X1) != comb_app(X2,X3)
| X0 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app_app1) ).
fof(f7,axiom,
! [X0,X1] :
( ~ member(comb_app(X0,X1),comb)
| member(X0,comb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_E1) ).
fof(f8,axiom,
! [X0,X1] :
( ~ member(comb_app(X0,X1),comb)
| member(X1,comb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_E2) ).
fof(f10,axiom,
member(combS,comb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',comb_intros2) ).
fof(f11,axiom,
! [X0,X1] :
( member(comb_app(X0,X1),comb)
| ~ member(X1,comb)
| ~ member(X0,comb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',comb_intros3) ).
fof(f37,axiom,
! [X0] :
( member(pair(X0,X0),parcontract)
| ~ member(X0,comb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',parcontract_intros1) ).
fof(f45,axiom,
! [X0] :
( ~ member(pair(combS,X0),parcontract)
| X0 = combS ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_parcontractE2) ).
fof(f46,plain,
! [X0] :
( ~ member(pair(combS,X0),parcontract)
| combS = X0 ),
inference(reorient_equations,[],[f45]) ).
fof(f47,axiom,
! [X2,X0,X1] :
( ~ member(pair(comb_app(X0,X1),X2),parcontract)
| ap_parcontractE_c1(X0,X1,X2)
| ap_parcontractE_c2(X0,X1,X2)
| ap_parcontractE_c3(X0,X1,X2)
| ap_parcontractE_c4(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE1) ).
fof(f48,axiom,
! [X2,X0,X1] :
( ~ ap_parcontractE_c1(X0,X1,X2)
| member(comb_app(X0,X1),comb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE2) ).
fof(f49,axiom,
! [X2,X0,X1] :
( ~ ap_parcontractE_c1(X0,X1,X2)
| X2 = comb_app(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE3) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ ap_parcontractE_c1(X0,X1,X2)
| comb_app(X0,X1) = X2 ),
inference(reorient_equations,[],[f49]) ).
fof(f53,axiom,
! [X2,X0,X1] :
( ~ ap_parcontractE_c2(X0,X1,X2)
| X0 = comb_app(combK,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE6) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ ap_parcontractE_c2(X0,X1,X2)
| comb_app(combK,X2) = X0 ),
inference(reorient_equations,[],[f53]) ).
fof(f60,axiom,
! [X2,X0,X1] :
( ~ ap_parcontractE_c3(X0,X1,X2)
| X0 = comb_app(comb_app(combS,ap_parcontractE_sk1p(X0,X1,X2)),ap_parcontractE_sk1q(X0,X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE11) ).
fof(f61,plain,
! [X2,X0,X1] :
( ~ ap_parcontractE_c3(X0,X1,X2)
| comb_app(comb_app(combS,ap_parcontractE_sk1p(X0,X1,X2)),ap_parcontractE_sk1q(X0,X1,X2)) = X0 ),
inference(reorient_equations,[],[f60]) ).
fof(f62,axiom,
! [X2,X0,X1] :
( ~ ap_parcontractE_c4(X0,X1,X2)
| member(pair(X0,ap_parcontractE_sk2q(X0,X1,X2)),parcontract) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE12) ).
fof(f63,axiom,
! [X2,X0,X1] :
( ~ ap_parcontractE_c4(X0,X1,X2)
| member(pair(X1,ap_parcontractE_sk2s(X0,X1,X2)),parcontract) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE13) ).
fof(f64,axiom,
! [X2,X0,X1] :
( ~ ap_parcontractE_c4(X0,X1,X2)
| X2 = comb_app(ap_parcontractE_sk2q(X0,X1,X2),ap_parcontractE_sk2s(X0,X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE14) ).
fof(f65,plain,
! [X2,X0,X1] :
( ~ ap_parcontractE_c4(X0,X1,X2)
| comb_app(ap_parcontractE_sk2q(X0,X1,X2),ap_parcontractE_sk2s(X0,X1,X2)) = X2 ),
inference(reorient_equations,[],[f64]) ).
fof(f66,axiom,
member(pair(comb_app(comb_app(combS,p),q),r),parcontract),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_parcontractD_h1) ).
fof(f67,negated_conjecture,
! [X0,X1] :
( r != comb_app(comb_app(combS,X0),X1)
| ~ member(pair(p,X0),parcontract)
| ~ member(pair(q,X1),parcontract) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_parcontractD_c1) ).
fof(f68,plain,
! [X0,X1] :
( comb_app(comb_app(combS,X0),X1) != r
| ~ member(pair(p,X0),parcontract)
| ~ member(pair(q,X1),parcontract) ),
inference(reorient_equations,[],[f67]) ).
fof(f72,definition,
( spl0_1
<=> member(combS,comb) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f74,plain,
( member(combS,comb)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f87,plain,
spl0_1,
inference(avatar_split_clause,[],[f10,f72]) ).
fof(f96,plain,
( ap_parcontractE_c1(comb_app(combS,p),q,r)
| ap_parcontractE_c2(comb_app(combS,p),q,r)
| ap_parcontractE_c3(comb_app(combS,p),q,r)
| ap_parcontractE_c4(comb_app(combS,p),q,r) ),
inference(resolution,[],[f47,f66]) ).
fof(f101,definition,
( spl0_5
<=> ap_parcontractE_c4(comb_app(combS,p),q,r) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f103,plain,
( ap_parcontractE_c4(comb_app(combS,p),q,r)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f105,definition,
( spl0_6
<=> ap_parcontractE_c3(comb_app(combS,p),q,r) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f107,plain,
( ap_parcontractE_c3(comb_app(combS,p),q,r)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f109,definition,
( spl0_7
<=> ap_parcontractE_c2(comb_app(combS,p),q,r) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f111,plain,
( ap_parcontractE_c2(comb_app(combS,p),q,r)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f113,definition,
( spl0_8
<=> ap_parcontractE_c1(comb_app(combS,p),q,r) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f115,plain,
( ap_parcontractE_c1(comb_app(combS,p),q,r)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f116,plain,
( spl0_5
| spl0_6
| spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f96,f113,f109,f105,f101]) ).
fof(f119,plain,
( member(pair(comb_app(combS,p),ap_parcontractE_sk2q(comb_app(combS,p),q,r)),parcontract)
| ~ spl0_5 ),
inference(resolution,[],[f103,f62]) ).
fof(f120,plain,
( ap_parcontractE_c1(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| ap_parcontractE_c2(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| ap_parcontractE_c3(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| ap_parcontractE_c4(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| ~ spl0_5 ),
inference(resolution,[],[f119,f47]) ).
fof(f122,definition,
( spl0_9
<=> ap_parcontractE_c4(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r)) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f124,plain,
( ap_parcontractE_c4(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f126,definition,
( spl0_10
<=> ap_parcontractE_c3(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r)) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f128,plain,
( ap_parcontractE_c3(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f130,definition,
( spl0_11
<=> ap_parcontractE_c2(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r)) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f132,plain,
( ap_parcontractE_c2(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f134,definition,
( spl0_12
<=> ap_parcontractE_c1(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r)) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f136,plain,
( ap_parcontractE_c1(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f137,plain,
( spl0_9
| spl0_10
| spl0_11
| spl0_12
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f120,f101,f134,f130,f126,f122]) ).
fof(f211,plain,
( r = comb_app(ap_parcontractE_sk2q(comb_app(combS,p),q,r),ap_parcontractE_sk2s(comb_app(combS,p),q,r))
| ~ spl0_5 ),
inference(resolution,[],[f103,f65]) ).
fof(f212,plain,
( member(pair(q,ap_parcontractE_sk2s(comb_app(combS,p),q,r)),parcontract)
| ~ spl0_5 ),
inference(resolution,[],[f103,f63]) ).
fof(f214,plain,
( ap_parcontractE_sk2q(comb_app(combS,p),q,r) = comb_app(ap_parcontractE_sk2q(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r)),ap_parcontractE_sk2s(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r)))
| ~ spl0_9 ),
inference(resolution,[],[f124,f65]) ).
fof(f215,plain,
( member(pair(p,ap_parcontractE_sk2s(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))),parcontract)
| ~ spl0_9 ),
inference(resolution,[],[f124,f63]) ).
fof(f216,plain,
( member(pair(combS,ap_parcontractE_sk2q(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))),parcontract)
| ~ spl0_9 ),
inference(resolution,[],[f124,f62]) ).
fof(f220,plain,
( combS = ap_parcontractE_sk2q(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| ~ spl0_9 ),
inference(resolution,[],[f216,f46]) ).
fof(f221,plain,
( ap_parcontractE_sk2q(comb_app(combS,p),q,r) = comb_app(combS,ap_parcontractE_sk2s(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r)))
| ~ spl0_9 ),
inference(backward_demodulation,[],[f214,f220]) ).
fof(f260,plain,
( ! [X0] :
( r != comb_app(ap_parcontractE_sk2q(comb_app(combS,p),q,r),X0)
| ~ member(pair(p,ap_parcontractE_sk2s(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))),parcontract)
| ~ member(pair(q,X0),parcontract) )
| ~ spl0_9 ),
inference(superposition,[],[f68,f221]) ).
fof(f296,plain,
( ! [X0] :
( r != comb_app(ap_parcontractE_sk2q(comb_app(combS,p),q,r),X0)
| ~ member(pair(q,X0),parcontract) )
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f260,f215]) ).
fof(f315,plain,
( r != r
| ~ member(pair(q,ap_parcontractE_sk2s(comb_app(combS,p),q,r)),parcontract)
| ~ spl0_5
| ~ spl0_9 ),
inference(superposition,[],[f296,f211]) ).
fof(f316,plain,
( ~ member(pair(q,ap_parcontractE_sk2s(comb_app(combS,p),q,r)),parcontract)
| ~ spl0_5
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f315]) ).
fof(f317,plain,
( $false
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f316,f212]) ).
fof(f318,plain,
( ~ spl0_5
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f317]) ).
fof(f319,plain,
( comb_app(combS,p) = comb_app(combK,r)
| ~ spl0_7 ),
inference(resolution,[],[f111,f54]) ).
fof(f329,plain,
( ! [X0,X1] :
( comb_app(X0,X1) != comb_app(combS,p)
| combK = X0 )
| ~ spl0_7 ),
inference(superposition,[],[f4,f319]) ).
fof(f352,plain,
( combK = combS
| ~ spl0_7 ),
inference(equality_resolution,[],[f329]) ).
fof(f353,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f352,f1]) ).
fof(f354,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[],[f353]) ).
fof(f356,plain,
( comb_app(comb_app(combS,p),q) = r
| ~ spl0_8 ),
inference(resolution,[],[f115,f50]) ).
fof(f357,plain,
( member(comb_app(comb_app(combS,p),q),comb)
| ~ spl0_8 ),
inference(resolution,[],[f115,f48]) ).
fof(f359,plain,
( ! [X0,X1] :
( comb_app(comb_app(combS,X0),X1) != comb_app(comb_app(combS,p),q)
| ~ member(pair(p,X0),parcontract)
| ~ member(pair(q,X1),parcontract) )
| ~ spl0_8 ),
inference(backward_demodulation,[],[f68,f356]) ).
fof(f396,plain,
( ~ member(pair(p,p),parcontract)
| ~ member(pair(q,q),parcontract)
| ~ spl0_8 ),
inference(equality_resolution,[],[f359]) ).
fof(f398,definition,
( spl0_31
<=> member(pair(q,q),parcontract) ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
fof(f400,plain,
( ~ member(pair(q,q),parcontract)
| spl0_31 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f402,definition,
( spl0_32
<=> member(pair(p,p),parcontract) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f404,plain,
( ~ member(pair(p,p),parcontract)
| spl0_32 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f405,plain,
( ~ spl0_31
| ~ spl0_32
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f396,f113,f402,f398]) ).
fof(f406,plain,
( ~ member(q,comb)
| spl0_31 ),
inference(resolution,[],[f400,f37]) ).
fof(f413,plain,
( member(q,comb)
| ~ spl0_8 ),
inference(resolution,[],[f357,f8]) ).
fof(f414,plain,
( member(comb_app(combS,p),comb)
| ~ spl0_8 ),
inference(resolution,[],[f357,f7]) ).
fof(f415,plain,
( $false
| ~ spl0_8
| spl0_31 ),
inference(forward_subsumption_resolution,[],[f413,f406]) ).
fof(f416,plain,
( ~ spl0_8
| spl0_31 ),
inference(avatar_contradiction_clause,[],[f415]) ).
fof(f417,plain,
( ~ member(p,comb)
| spl0_32 ),
inference(resolution,[],[f404,f37]) ).
fof(f418,plain,
( member(p,comb)
| ~ spl0_8 ),
inference(resolution,[],[f414,f8]) ).
fof(f420,plain,
( $false
| ~ spl0_8
| spl0_32 ),
inference(forward_subsumption_resolution,[],[f418,f417]) ).
fof(f421,plain,
( ~ spl0_8
| spl0_32 ),
inference(avatar_contradiction_clause,[],[f420]) ).
fof(f422,plain,
( r = comb_app(ap_parcontractE_sk2q(comb_app(combS,p),q,r),ap_parcontractE_sk2s(comb_app(combS,p),q,r))
| ~ spl0_5 ),
inference(resolution,[],[f103,f65]) ).
fof(f423,plain,
( member(pair(q,ap_parcontractE_sk2s(comb_app(combS,p),q,r)),parcontract)
| ~ spl0_5 ),
inference(resolution,[],[f103,f63]) ).
fof(f427,plain,
( member(comb_app(combS,p),comb)
| ~ spl0_12 ),
inference(resolution,[],[f136,f48]) ).
fof(f440,plain,
( combS = comb_app(comb_app(combS,ap_parcontractE_sk1p(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))),ap_parcontractE_sk1q(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r)))
| ~ spl0_10 ),
inference(resolution,[],[f128,f61]) ).
fof(f444,plain,
( $false
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f440,f3]) ).
fof(f445,plain,
~ spl0_10,
inference(avatar_contradiction_clause,[],[f444]) ).
fof(f446,plain,
( combS = comb_app(combK,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| ~ spl0_11 ),
inference(resolution,[],[f132,f54]) ).
fof(f451,plain,
( $false
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f446,f3]) ).
fof(f452,plain,
~ spl0_11,
inference(avatar_contradiction_clause,[],[f451]) ).
fof(f453,plain,
( member(p,comb)
| ~ spl0_12 ),
inference(resolution,[],[f427,f8]) ).
fof(f458,plain,
( comb_app(combS,p) = ap_parcontractE_sk2q(comb_app(combS,p),q,r)
| ~ spl0_12 ),
inference(resolution,[],[f136,f50]) ).
fof(f468,plain,
( r = comb_app(comb_app(combS,p),ap_parcontractE_sk2s(comb_app(combS,p),q,r))
| ~ spl0_5
| ~ spl0_12 ),
inference(backward_demodulation,[],[f422,f458]) ).
fof(f487,plain,
( r != r
| ~ member(pair(p,p),parcontract)
| ~ member(pair(q,ap_parcontractE_sk2s(comb_app(combS,p),q,r)),parcontract)
| ~ spl0_5
| ~ spl0_12 ),
inference(superposition,[],[f68,f468]) ).
fof(f506,plain,
( ~ member(pair(p,p),parcontract)
| ~ member(pair(q,ap_parcontractE_sk2s(comb_app(combS,p),q,r)),parcontract)
| ~ spl0_5
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f487]) ).
fof(f507,plain,
( ~ member(pair(p,p),parcontract)
| ~ spl0_5
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f506,f423]) ).
fof(f508,plain,
( ~ spl0_32
| ~ spl0_5
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f507,f134,f101,f402]) ).
fof(f519,plain,
( comb_app(combS,p) = comb_app(comb_app(combS,ap_parcontractE_sk1p(comb_app(combS,p),q,r)),ap_parcontractE_sk1q(comb_app(combS,p),q,r))
| ~ spl0_6 ),
inference(resolution,[],[f107,f61]) ).
fof(f641,plain,
( ! [X0,X1] :
( comb_app(X0,X1) != comb_app(combS,p)
| comb_app(combS,ap_parcontractE_sk1p(comb_app(combS,p),q,r)) = X0 )
| ~ spl0_6 ),
inference(superposition,[],[f4,f519]) ).
fof(f681,definition,
( spl0_48
<=> member(comb_app(combS,p),comb) ),
introduced(definition,[new_symbols(definition,[spl0_48])],[avatar_definition]) ).
fof(f682,plain,
( member(comb_app(combS,p),comb)
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f681]) ).
fof(f683,plain,
( ~ member(comb_app(combS,p),comb)
| spl0_48 ),
inference(avatar_component_clause,[],[f681]) ).
fof(f715,plain,
( ~ member(p,comb)
| ~ member(combS,comb)
| spl0_48 ),
inference(resolution,[],[f683,f11]) ).
fof(f716,plain,
( ~ member(p,comb)
| ~ spl0_1
| spl0_48 ),
inference(forward_subsumption_resolution,[],[f715,f74]) ).
fof(f721,plain,
( member(p,comb)
| ~ spl0_48 ),
inference(resolution,[],[f682,f8]) ).
fof(f1533,plain,
( combS = comb_app(combS,ap_parcontractE_sk1p(comb_app(combS,p),q,r))
| ~ spl0_6 ),
inference(equality_resolution,[],[f641]) ).
fof(f1534,plain,
( $false
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f1533,f3]) ).
fof(f1535,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f1534]) ).
fof(f1536,plain,
( $false
| spl0_32
| ~ spl0_48 ),
inference(forward_subsumption_resolution,[],[f417,f721]) ).
fof(f1537,plain,
( spl0_32
| ~ spl0_48 ),
inference(avatar_contradiction_clause,[],[f1536]) ).
fof(f1542,plain,
( $false
| ~ spl0_1
| ~ spl0_12
| spl0_48 ),
inference(forward_subsumption_resolution,[],[f453,f716]) ).
fof(f1543,plain,
( ~ spl0_1
| ~ spl0_12
| spl0_48 ),
inference(avatar_contradiction_clause,[],[f1542]) ).
cnf(s3,plain,
spl0_1,
inference(sat_conversion,[],[f87]) ).
cnf(s5,plain,
( spl0_5
| spl0_6
| spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f116]) ).
cnf(s6,plain,
( ~ spl0_5
| spl0_9
| spl0_10
| spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f137]) ).
cnf(s24,plain,
( ~ spl0_5
| ~ spl0_9 ),
inference(sat_conversion,[],[f318]) ).
cnf(s26,plain,
~ spl0_7,
inference(sat_conversion,[],[f354]) ).
cnf(s27,plain,
( ~ spl0_8
| ~ spl0_31
| ~ spl0_32 ),
inference(sat_conversion,[],[f405]) ).
cnf(s30,plain,
( ~ spl0_8
| spl0_31 ),
inference(sat_conversion,[],[f416]) ).
cnf(s31,plain,
( ~ spl0_8
| spl0_32 ),
inference(sat_conversion,[],[f421]) ).
cnf(s33,plain,
~ spl0_10,
inference(sat_conversion,[],[f445]) ).
cnf(s35,plain,
~ spl0_11,
inference(sat_conversion,[],[f452]) ).
cnf(s38,plain,
( ~ spl0_5
| ~ spl0_12
| ~ spl0_32 ),
inference(sat_conversion,[],[f508]) ).
cnf(s83,plain,
~ spl0_6,
inference(sat_conversion,[],[f1535]) ).
cnf(s85,plain,
( spl0_32
| ~ spl0_48 ),
inference(sat_conversion,[],[f1537]) ).
cnf(s88,plain,
( ~ spl0_1
| ~ spl0_12
| spl0_48 ),
inference(sat_conversion,[],[f1543]) ).
cnf(s89,plain,
( ~ spl0_5
| spl0_9
| spl0_12 ),
inference(rat,[],[s6,s35,s33]) ).
cnf(s90,plain,
( spl0_5
| spl0_8 ),
inference(rat,[],[s5,s26,s83]) ).
cnf(s91,plain,
~ spl0_8,
inference(rat,[],[s27,s30,s31]) ).
cnf(s92,plain,
spl0_5,
inference(rat,[],[s90,s91]) ).
cnf(s93,plain,
~ spl0_9,
inference(rat,[],[s24,s92]) ).
cnf(s94,plain,
spl0_12,
inference(rat,[],[s89,s92,s93]) ).
cnf(s95,plain,
spl0_48,
inference(rat,[],[s88,s3,s94]) ).
cnf(s96,plain,
~ spl0_32,
inference(rat,[],[s38,s92,s94]) ).
cnf(s98,plain,
$false,
inference(rat,[],[s85,s95,s96]) ).
fof(f1544,plain,
$false,
inference(avatar_sat_refutation,[],[s98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL094-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n003.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 21:37:43 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.52/1.55 % (2054817)Input is clausal, will run a generic CNF schedule.
% 5.52/1.55 % (2054828)dis-21_1_sil=8000:lcm=predicate:random_seed=3452375117: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)
% 5.52/1.55 % (2054827)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1002200291:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.52/1.55 % (2054826)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=187814296:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.52/1.55 % (2054823)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1366536679:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.52/1.55 % (2054825)lrs+10_1_sil=8000:sp=occurrence:random_seed=1251433508:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.52/1.55 % (2054822)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=3181981571:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.52/1.55 % (2054824)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2582910241:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.52/1.55 % (2054825)Refutation not found, incomplete strategy
% 5.52/1.55 % (2054825)------------------------------
% 5.52/1.55 % (2054825)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.52/1.55 % (2054825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.55 % (2054825)CaDiCaL version: 2.1.3
% 5.52/1.55 % (2054825)Termination reason: Refutation not found, incomplete strategy
% 5.52/1.55 % (2054825)Time elapsed: 0.002 s
% 5.52/1.55 % (2054825)Peak memory usage: 87 MB
% 5.52/1.55 % (2054825)Instructions burned: 1 (million)
% 5.52/1.55 % (2054826)Refutation not found, incomplete strategy
% 5.52/1.55 % (2054826)------------------------------
% 5.52/1.55 % (2054826)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.52/1.55 % (2054826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.55 % (2054826)CaDiCaL version: 2.1.3
% 5.52/1.55 % (2054826)Termination reason: Refutation not found, incomplete strategy
% 5.52/1.55 % (2054826)Time elapsed: 0.002 s
% 5.52/1.55 % (2054826)Peak memory usage: 88 MB
% 5.52/1.55 % (2054826)Instructions burned: 2 (million)
% 5.52/1.55 % (2054828)Instruction limit reached!
% 5.52/1.55 % (2054828)------------------------------
% 5.52/1.55 % (2054828)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.52/1.55 % (2054828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.55 % (2054828)CaDiCaL version: 2.1.3
% 5.52/1.55 % (2054828)Termination reason: Instruction limit
% 5.52/1.55 % (2054828)Termination phase: Saturation
% 5.52/1.55 % (2054828)Time elapsed: 0.039 s
% 5.52/1.55 % (2054828)Peak memory usage: 89 MB
% 5.52/1.55 % (2054828)Instructions burned: 119 (million)
% 5.52/1.55 % (2054827)Instruction limit reached!
% 5.52/1.55 % (2054827)------------------------------
% 5.52/1.55 % (2054827)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.52/1.55 % (2054827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.55 % (2054827)CaDiCaL version: 2.1.3
% 5.52/1.55 % (2054827)Termination reason: Instruction limit
% 5.52/1.55 % (2054827)Termination phase: Saturation
% 5.52/1.55 % (2054827)Time elapsed: 0.097 s
% 5.52/1.55 % (2054827)Peak memory usage: 90 MB
% 5.52/1.55 % (2054827)Instructions burned: 182 (million)
% 5.52/1.55 % (2054836)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=2491138336:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 5.52/1.55 % (2054836)Refutation not found, incomplete strategy
% 5.52/1.55 % (2054836)------------------------------
% 5.52/1.55 % (2054836)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.52/1.55 % (2054836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.55 % (2054836)CaDiCaL version: 2.1.3
% 5.52/1.55 % (2054836)Termination reason: Refutation not found, incomplete strategy
% 5.52/1.55 % (2054836)Time elapsed: 0.015 s
% 5.52/1.55 % (2054836)Peak memory usage: 89 MB
% 5.52/1.55 % (2054836)Instructions burned: 21 (million)
% 5.52/1.55 % (2054837)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1180375896: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)
% 5.52/1.55 % (2054826)------------------------------
% 5.52/1.55 % (2054826)------------------------------
% 5.52/1.55 % (2054825)------------------------------
% 5.52/1.55 % (2054825)------------------------------
% 5.52/1.55 % (2054837)Instruction limit reached!
% 5.52/1.55 % (2054837)------------------------------
% 5.52/1.55 % (2054837)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.52/1.55 % (2054837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.55 % (2054837)CaDiCaL version: 2.1.3
% 5.52/1.55 % (2054837)Termination reason: Instruction limit
% 5.52/1.55 % (2054837)Termination phase: Saturation
% 5.52/1.55 % (2054837)Time elapsed: 0.051 s
% 5.52/1.55 % (2054837)Peak memory usage: 90 MB
% 5.52/1.55 % (2054837)Instructions burned: 191 (million)
% 5.52/1.55 % (2054842)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3014952860:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 5.52/1.55 % (2054841)lrs+10_64_to=lpo:sil=8000:random_seed=302334745:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 5.52/1.55 % (2054840)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=713234501:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 5.52/1.55 % (2054840)Refutation not found, incomplete strategy
% 5.52/1.55 % (2054840)------------------------------
% 5.52/1.55 % (2054840)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.52/1.55 % (2054840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.55 % (2054840)CaDiCaL version: 2.1.3
% 5.52/1.55 % (2054840)Termination reason: Refutation not found, incomplete strategy
% 5.52/1.55 % (2054840)Time elapsed: 0.011 s
% 5.52/1.55 % (2054840)Peak memory usage: 88 MB
% 5.52/1.55 % (2054840)Instructions burned: 16 (million)
% 5.52/1.55 % (2054836)------------------------------
% 5.52/1.55 % (2054836)------------------------------
% 5.52/1.55 % (2054841)First to succeed.
% 5.52/1.55 % (2054841)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2054817"
% 5.52/1.55 % (2054842)Instruction limit reached!
% 5.52/1.55 % (2054842)------------------------------
% 5.52/1.55 % (2054842)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.52/1.55 % (2054842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.55 % (2054842)CaDiCaL version: 2.1.3
% 5.52/1.55 % (2054842)Termination reason: Instruction limit
% 5.52/1.55 % (2054842)Termination phase: Saturation
% 5.52/1.55 % (2054842)Time elapsed: 0.064 s
% 5.52/1.55 % (2054842)Peak memory usage: 90 MB
% 5.52/1.55 % (2054842)Instructions burned: 195 (million)
% 5.52/1.55 % (2054847)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=4047626478:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 5.52/1.55 % (2054846)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2063155025:i=157:gtg=all_2993 on theBenchmark for (2993ds/157Mi)
% 5.52/1.55 % (2054840)------------------------------
% 5.52/1.55 % (2054840)------------------------------
% 5.52/1.55 % (2054846)Instruction limit reached!
% 5.52/1.55 % (2054846)------------------------------
% 5.52/1.55 % (2054846)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.52/1.55 % (2054846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.55 % (2054846)CaDiCaL version: 2.1.3
% 5.52/1.55 % (2054846)Termination reason: Instruction limit
% 5.52/1.55 % (2054846)Termination phase: Saturation
% 5.52/1.55 % (2054846)Time elapsed: 0.102 s
% 5.52/1.55 % (2054846)Peak memory usage: 91 MB
% 5.52/1.55 % (2054846)Instructions burned: 158 (million)
% 5.52/1.55 % (2054841)Refutation found. Thanks to Tanya!
% 5.52/1.55 % SZS status Unsatisfiable for theBenchmark
% 5.52/1.55 % SZS output start Proof for theBenchmark
% See solution above
% 6.90/1.75 % (2054841)------------------------------
% 6.90/1.75 % (2054841)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.90/1.75 % (2054841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/1.75 % (2054841)CaDiCaL version: 2.1.3
% 6.90/1.75 % (2054841)Termination reason: Refutation
% 6.90/1.75 % (2054841)Time elapsed: 0.061 s
% 6.90/1.75 % (2054841)Peak memory usage: 90 MB
% 6.90/1.75 % (2054841)Instructions burned: 102 (million)
% 6.90/1.75 % (2054841)------------------------------
% 6.90/1.75 % (2054841)------------------------------
% 6.90/1.75 % (2054817)Success in time 0.889 s
% 6.90/1.75 % Vampire exiting
%------------------------------------------------------------------------------