%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL095-2 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 4.34s 1.38s
% Output : Refutation 5.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 36
% Syntax : Number of formulae : 148 ( 34 unt; 16 def)
% Number of atoms : 316 ( 48 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 323 ( 155 ~; 157 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 12 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-3 aty)
% Number of variables : 84 ( 0 sgn 84 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f158,axiom,
! [X0,X1] : combK != comb_app(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_app) ).
fof(f160,axiom,
! [X2,X3,X0,X1] :
( comb_app(X0,X1) != comb_app(X2,X3)
| X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app_app1) ).
fof(f161,axiom,
! [X2,X3,X0,X1] :
( comb_app(X0,X1) != comb_app(X2,X3)
| X1 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app_app2) ).
fof(f163,axiom,
! [X0,X1] :
( ~ member(comb_app(X0,X1),comb)
| member(X0,comb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_E1) ).
fof(f164,axiom,
! [X0,X1] :
( ~ member(comb_app(X0,X1),comb)
| member(X1,comb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_E2) ).
fof(f193,axiom,
! [X0] :
( member(pair(X0,X0),parcontract)
| ~ member(X0,comb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',parcontract_intros1) ).
fof(f194,axiom,
! [X0,X1] :
( member(pair(comb_app(comb_app(combK,X0),X1),X0),parcontract)
| ~ member(X1,comb)
| ~ member(X0,comb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',parcontract_intros2) ).
fof(f203,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/sandbox2/benchmark/theBenchmark.p',ap_parcontractE1) ).
fof(f205,axiom,
! [X2,X0,X1] :
( ~ ap_parcontractE_c1(X0,X1,X2)
| X2 = comb_app(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE3) ).
fof(f206,plain,
! [X2,X0,X1] :
( ~ ap_parcontractE_c1(X0,X1,X2)
| comb_app(X0,X1) = X2 ),
inference(reorient_equations,[],[f205]) ).
fof(f209,axiom,
! [X2,X0,X1] :
( ~ ap_parcontractE_c2(X0,X1,X2)
| X0 = comb_app(combK,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE6) ).
fof(f210,plain,
! [X2,X0,X1] :
( ~ ap_parcontractE_c2(X0,X1,X2)
| comb_app(combK,X2) = X0 ),
inference(reorient_equations,[],[f209]) ).
fof(f216,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/sandbox2/benchmark/theBenchmark.p',ap_parcontractE11) ).
fof(f217,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,[],[f216]) ).
fof(f218,axiom,
! [X2,X0,X1] :
( member(pair(X0,ap_parcontractE_sk2q(X0,X1,X2)),parcontract)
| ~ ap_parcontractE_c4(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE12) ).
fof(f220,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/sandbox2/benchmark/theBenchmark.p',ap_parcontractE14) ).
fof(f221,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,[],[f220]) ).
fof(f222,axiom,
! [X0,X1] :
( ~ member(pair(comb_app(combK,X0),X1),parcontract)
| X1 = comb_app(combK,k1_parcontractD_sk1(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k1_parcontractD_1) ).
fof(f223,plain,
! [X0,X1] :
( ~ member(pair(comb_app(combK,X0),X1),parcontract)
| comb_app(combK,k1_parcontractD_sk1(X0,X1)) = X1 ),
inference(reorient_equations,[],[f222]) ).
fof(f224,axiom,
! [X0,X1] :
( ~ member(pair(comb_app(combK,X0),X1),parcontract)
| member(pair(X0,k1_parcontractD_sk1(X0,X1)),parcontract) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k1_parcontractD_2) ).
fof(f238,axiom,
! [X0,X1] :
( ~ member(pair(X0,X1),parcontract)
| member(X1,comb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',parcontract_combD2) ).
fof(f239,axiom,
member(p,comb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_parcontract_2h1) ).
fof(f240,axiom,
member(q,comb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_parcontract_2h2) ).
fof(f241,negated_conjecture,
member(pair(comb_app(comb_app(combK,p),q),yp),parcontract),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_parcontract_2c1) ).
fof(f242,negated_conjecture,
! [X0] :
( ~ member(pair(p,X0),parcontract)
| ~ member(pair(yp,X0),parcontract) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_parcontract_2c2) ).
fof(f256,definition,
sF0 = comb_app(combK,p),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f257,plain,
comb_app(combK,p) = sF0,
inference(reorient_equations,[],[f256]) ).
fof(f258,definition,
sF1 = comb_app(sF0,q),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f259,plain,
comb_app(sF0,q) = sF1,
inference(reorient_equations,[],[f258]) ).
fof(f260,definition,
sF2 = pair(sF1,yp),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f261,plain,
pair(sF1,yp) = sF2,
inference(reorient_equations,[],[f260]) ).
fof(f262,plain,
member(sF2,parcontract),
inference(definition_folding,[],[f241,f261,f259,f257]) ).
fof(f263,definition,
! [X0] : sF3(X0) = pair(p,X0),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f264,plain,
! [X0] : pair(p,X0) = sF3(X0),
inference(reorient_equations,[],[f263]) ).
fof(f265,definition,
! [X0] : sF4(X0) = pair(yp,X0),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f266,plain,
! [X0] : pair(yp,X0) = sF4(X0),
inference(reorient_equations,[],[f265]) ).
fof(f267,plain,
! [X0] :
( ~ member(sF4(X0),parcontract)
| ~ member(sF3(X0),parcontract) ),
inference(definition_folding,[],[f242,f266,f264]) ).
fof(f286,plain,
( member(sF4(yp),parcontract)
| ~ member(yp,comb) ),
inference(superposition,[],[f193,f266]) ).
fof(f287,plain,
( member(sF3(p),parcontract)
| ~ member(p,comb) ),
inference(superposition,[],[f193,f264]) ).
fof(f288,plain,
member(sF3(p),parcontract),
inference(forward_subsumption_resolution,[],[f287,f239]) ).
fof(f290,definition,
( spl5_5
<=> member(yp,comb) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
fof(f291,plain,
( member(yp,comb)
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f292,plain,
( ~ member(yp,comb)
| spl5_5 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f294,definition,
( spl5_6
<=> member(sF4(yp),parcontract) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
fof(f296,plain,
( member(sF4(yp),parcontract)
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f297,plain,
( ~ spl5_5
| spl5_6 ),
inference(avatar_split_clause,[],[f286,f294,f290]) ).
fof(f300,plain,
! [X0] :
( ~ member(pair(sF1,X0),parcontract)
| ap_parcontractE_c1(sF0,q,X0)
| ap_parcontractE_c2(sF0,q,X0)
| ap_parcontractE_c3(sF0,q,X0)
| ap_parcontractE_c4(sF0,q,X0) ),
inference(superposition,[],[f203,f259]) ).
fof(f325,plain,
! [X0] :
( member(pair(comb_app(sF0,X0),p),parcontract)
| ~ member(X0,comb)
| ~ member(p,comb) ),
inference(superposition,[],[f194,f257]) ).
fof(f326,plain,
! [X0] :
( member(pair(comb_app(sF0,X0),p),parcontract)
| ~ member(X0,comb) ),
inference(forward_subsumption_resolution,[],[f325,f239]) ).
fof(f343,plain,
( ~ member(sF2,parcontract)
| member(yp,comb) ),
inference(superposition,[],[f238,f261]) ).
fof(f344,plain,
member(yp,comb),
inference(forward_subsumption_resolution,[],[f343,f262]) ).
fof(f345,plain,
( $false
| spl5_5 ),
inference(forward_subsumption_resolution,[],[f344,f292]) ).
fof(f346,plain,
spl5_5,
inference(avatar_contradiction_clause,[],[f345]) ).
fof(f347,plain,
( ~ member(sF3(yp),parcontract)
| ~ spl5_6 ),
inference(resolution,[],[f296,f267]) ).
fof(f350,plain,
( member(pair(sF1,p),parcontract)
| ~ member(q,comb) ),
inference(superposition,[],[f326,f259]) ).
fof(f351,plain,
member(pair(sF1,p),parcontract),
inference(forward_subsumption_resolution,[],[f350,f240]) ).
fof(f378,plain,
( ~ member(sF2,parcontract)
| ap_parcontractE_c1(sF0,q,yp)
| ap_parcontractE_c2(sF0,q,yp)
| ap_parcontractE_c3(sF0,q,yp)
| ap_parcontractE_c4(sF0,q,yp) ),
inference(superposition,[],[f300,f261]) ).
fof(f379,plain,
( ap_parcontractE_c1(sF0,q,yp)
| ap_parcontractE_c2(sF0,q,yp)
| ap_parcontractE_c3(sF0,q,yp)
| ap_parcontractE_c4(sF0,q,yp) ),
inference(forward_subsumption_resolution,[],[f378,f262]) ).
fof(f399,definition,
( spl5_17
<=> ap_parcontractE_c4(sF0,q,yp) ),
introduced(definition,[new_symbols(definition,[spl5_17])],[avatar_definition]) ).
fof(f401,plain,
( ap_parcontractE_c4(sF0,q,yp)
| ~ spl5_17 ),
inference(avatar_component_clause,[],[f399]) ).
fof(f403,definition,
( spl5_18
<=> ap_parcontractE_c3(sF0,q,yp) ),
introduced(definition,[new_symbols(definition,[spl5_18])],[avatar_definition]) ).
fof(f405,plain,
( ap_parcontractE_c3(sF0,q,yp)
| ~ spl5_18 ),
inference(avatar_component_clause,[],[f403]) ).
fof(f407,definition,
( spl5_19
<=> ap_parcontractE_c2(sF0,q,yp) ),
introduced(definition,[new_symbols(definition,[spl5_19])],[avatar_definition]) ).
fof(f409,plain,
( ap_parcontractE_c2(sF0,q,yp)
| ~ spl5_19 ),
inference(avatar_component_clause,[],[f407]) ).
fof(f411,definition,
( spl5_20
<=> ap_parcontractE_c1(sF0,q,yp) ),
introduced(definition,[new_symbols(definition,[spl5_20])],[avatar_definition]) ).
fof(f413,plain,
( ap_parcontractE_c1(sF0,q,yp)
| ~ spl5_20 ),
inference(avatar_component_clause,[],[f411]) ).
fof(f414,plain,
( spl5_17
| spl5_18
| spl5_19
| spl5_20 ),
inference(avatar_split_clause,[],[f379,f411,f407,f403,f399]) ).
fof(f434,plain,
! [X2,X0,X1] :
( member(pair(X0,k1_parcontractD_sk1(X0,ap_parcontractE_sk2q(comb_app(combK,X0),X1,X2))),parcontract)
| ~ ap_parcontractE_c4(comb_app(combK,X0),X1,X2) ),
inference(resolution,[],[f224,f218]) ).
fof(f478,plain,
! [X0,X1] :
( comb_app(X0,X1) != sF0
| p = X1 ),
inference(superposition,[],[f161,f257]) ).
fof(f483,plain,
! [X0,X1] :
( comb_app(X0,X1) != sF0
| combK = X0 ),
inference(superposition,[],[f160,f257]) ).
fof(f491,plain,
! [X0,X1] :
( member(pair(p,k1_parcontractD_sk1(p,ap_parcontractE_sk2q(sF0,X0,X1))),parcontract)
| ~ ap_parcontractE_c4(sF0,X0,X1) ),
inference(superposition,[],[f434,f257]) ).
fof(f495,plain,
! [X0,X1] :
( member(sF3(k1_parcontractD_sk1(p,ap_parcontractE_sk2q(sF0,X0,X1))),parcontract)
| ~ ap_parcontractE_c4(sF0,X0,X1) ),
inference(forward_demodulation,[],[f491,f264]) ).
fof(f497,plain,
( yp = comb_app(ap_parcontractE_sk2q(sF0,q,yp),ap_parcontractE_sk2s(sF0,q,yp))
| ~ spl5_17 ),
inference(resolution,[],[f221,f401]) ).
fof(f504,plain,
( ~ member(yp,comb)
| member(ap_parcontractE_sk2q(sF0,q,yp),comb)
| ~ spl5_17 ),
inference(superposition,[],[f163,f497]) ).
fof(f505,plain,
( ~ member(yp,comb)
| member(ap_parcontractE_sk2s(sF0,q,yp),comb)
| ~ spl5_17 ),
inference(superposition,[],[f164,f497]) ).
fof(f513,definition,
( spl5_25
<=> member(ap_parcontractE_sk2q(sF0,q,yp),comb) ),
introduced(definition,[new_symbols(definition,[spl5_25])],[avatar_definition]) ).
fof(f514,plain,
( member(ap_parcontractE_sk2q(sF0,q,yp),comb)
| ~ spl5_25 ),
inference(avatar_component_clause,[],[f513]) ).
fof(f517,definition,
( spl5_26
<=> member(ap_parcontractE_sk2s(sF0,q,yp),comb) ),
introduced(definition,[new_symbols(definition,[spl5_26])],[avatar_definition]) ).
fof(f518,plain,
( member(ap_parcontractE_sk2s(sF0,q,yp),comb)
| ~ spl5_26 ),
inference(avatar_component_clause,[],[f517]) ).
fof(f537,plain,
( member(ap_parcontractE_sk2s(sF0,q,yp),comb)
| ~ spl5_5
| ~ spl5_17 ),
inference(forward_subsumption_resolution,[],[f505,f291]) ).
fof(f538,plain,
( member(ap_parcontractE_sk2q(sF0,q,yp),comb)
| ~ spl5_5
| ~ spl5_17 ),
inference(forward_subsumption_resolution,[],[f504,f291]) ).
fof(f539,plain,
( spl5_26
| ~ spl5_5
| ~ spl5_17 ),
inference(avatar_split_clause,[],[f537,f399,f290,f517]) ).
fof(f540,plain,
( spl5_25
| ~ spl5_5
| ~ spl5_17 ),
inference(avatar_split_clause,[],[f538,f399,f290,f513]) ).
fof(f647,plain,
( sF0 = comb_app(combK,yp)
| ~ spl5_19 ),
inference(resolution,[],[f409,f210]) ).
fof(f736,plain,
! [X2,X0,X1] :
( ~ ap_parcontractE_c4(comb_app(combK,X0),X1,X2)
| ap_parcontractE_sk2q(comb_app(combK,X0),X1,X2) = comb_app(combK,k1_parcontractD_sk1(X0,ap_parcontractE_sk2q(comb_app(combK,X0),X1,X2))) ),
inference(resolution,[],[f223,f218]) ).
fof(f742,plain,
! [X0,X1] :
( ~ ap_parcontractE_c4(sF0,X0,X1)
| ap_parcontractE_sk2q(sF0,X0,X1) = comb_app(combK,k1_parcontractD_sk1(p,ap_parcontractE_sk2q(sF0,X0,X1))) ),
inference(superposition,[],[f736,f257]) ).
fof(f831,definition,
( spl5_61
<=> yp = sF1 ),
introduced(definition,[new_symbols(definition,[spl5_61])],[avatar_definition]) ).
fof(f832,plain,
( yp != sF1
| spl5_61 ),
inference(avatar_component_clause,[],[f831]) ).
fof(f833,plain,
( yp = sF1
| ~ spl5_61 ),
inference(avatar_component_clause,[],[f831]) ).
fof(f839,plain,
( ! [X0] : sF4(X0) = pair(sF1,X0)
| ~ spl5_61 ),
inference(superposition,[],[f266,f833]) ).
fof(f870,plain,
( member(sF4(p),parcontract)
| ~ spl5_61 ),
inference(superposition,[],[f351,f839]) ).
fof(f898,plain,
( ~ member(sF3(p),parcontract)
| ~ spl5_61 ),
inference(resolution,[],[f870,f267]) ).
fof(f899,plain,
( $false
| ~ spl5_61 ),
inference(forward_subsumption_resolution,[],[f898,f288]) ).
fof(f900,plain,
~ spl5_61,
inference(avatar_contradiction_clause,[],[f899]) ).
fof(f903,plain,
( sF0 != sF0
| p = yp
| ~ spl5_19 ),
inference(superposition,[],[f478,f647]) ).
fof(f907,plain,
( p = yp
| ~ spl5_19 ),
inference(trivial_inequality_removal,[],[f903]) ).
fof(f916,plain,
( ~ member(sF3(p),parcontract)
| ~ spl5_6
| ~ spl5_19 ),
inference(superposition,[],[f347,f907]) ).
fof(f925,plain,
( $false
| ~ spl5_6
| ~ spl5_19 ),
inference(forward_subsumption_resolution,[],[f916,f288]) ).
fof(f926,plain,
( ~ spl5_6
| ~ spl5_19 ),
inference(avatar_contradiction_clause,[],[f925]) ).
fof(f930,plain,
( yp = comb_app(sF0,q)
| ~ spl5_20 ),
inference(resolution,[],[f413,f206]) ).
fof(f933,plain,
( yp = sF1
| ~ spl5_20 ),
inference(forward_demodulation,[],[f930,f259]) ).
fof(f934,plain,
( $false
| ~ spl5_20
| spl5_61 ),
inference(forward_subsumption_resolution,[],[f933,f832]) ).
fof(f935,plain,
( ~ spl5_20
| spl5_61 ),
inference(avatar_contradiction_clause,[],[f934]) ).
fof(f936,plain,
( ap_parcontractE_sk2q(sF0,q,yp) = comb_app(combK,k1_parcontractD_sk1(p,ap_parcontractE_sk2q(sF0,q,yp)))
| ~ spl5_17 ),
inference(resolution,[],[f401,f742]) ).
fof(f974,plain,
( ! [X0] :
( member(pair(comb_app(ap_parcontractE_sk2q(sF0,q,yp),X0),k1_parcontractD_sk1(p,ap_parcontractE_sk2q(sF0,q,yp))),parcontract)
| ~ member(X0,comb)
| ~ member(k1_parcontractD_sk1(p,ap_parcontractE_sk2q(sF0,q,yp)),comb) )
| ~ spl5_17 ),
inference(superposition,[],[f194,f936]) ).
fof(f981,plain,
( ~ member(ap_parcontractE_sk2q(sF0,q,yp),comb)
| member(k1_parcontractD_sk1(p,ap_parcontractE_sk2q(sF0,q,yp)),comb)
| ~ spl5_17 ),
inference(superposition,[],[f164,f936]) ).
fof(f1003,plain,
( member(k1_parcontractD_sk1(p,ap_parcontractE_sk2q(sF0,q,yp)),comb)
| ~ spl5_17
| ~ spl5_25 ),
inference(forward_subsumption_resolution,[],[f981,f514]) ).
fof(f1006,definition,
( spl5_68
<=> member(k1_parcontractD_sk1(p,ap_parcontractE_sk2q(sF0,q,yp)),comb) ),
introduced(definition,[new_symbols(definition,[spl5_68])],[avatar_definition]) ).
fof(f1010,definition,
( spl5_69
<=> ! [X0] :
( member(pair(comb_app(ap_parcontractE_sk2q(sF0,q,yp),X0),k1_parcontractD_sk1(p,ap_parcontractE_sk2q(sF0,q,yp))),parcontract)
| ~ member(X0,comb) ) ),
introduced(definition,[new_symbols(definition,[spl5_69])],[avatar_definition]) ).
fof(f1011,plain,
( ! [X0] :
( member(pair(comb_app(ap_parcontractE_sk2q(sF0,q,yp),X0),k1_parcontractD_sk1(p,ap_parcontractE_sk2q(sF0,q,yp))),parcontract)
| ~ member(X0,comb) )
| ~ spl5_69 ),
inference(avatar_component_clause,[],[f1010]) ).
fof(f1012,plain,
( ~ spl5_68
| spl5_69
| ~ spl5_17 ),
inference(avatar_split_clause,[],[f974,f399,f1010,f1006]) ).
fof(f1029,plain,
( spl5_68
| ~ spl5_17
| ~ spl5_25 ),
inference(avatar_split_clause,[],[f1003,f513,f399,f1006]) ).
fof(f1030,plain,
( sF0 = comb_app(comb_app(combS,ap_parcontractE_sk1p(sF0,q,yp)),ap_parcontractE_sk1q(sF0,q,yp))
| ~ spl5_18 ),
inference(resolution,[],[f405,f217]) ).
fof(f1047,plain,
( sF0 != sF0
| combK = comb_app(combS,ap_parcontractE_sk1p(sF0,q,yp))
| ~ spl5_18 ),
inference(superposition,[],[f483,f1030]) ).
fof(f1048,plain,
( combK = comb_app(combS,ap_parcontractE_sk1p(sF0,q,yp))
| ~ spl5_18 ),
inference(trivial_inequality_removal,[],[f1047]) ).
fof(f1050,plain,
( $false
| ~ spl5_18 ),
inference(forward_subsumption_resolution,[],[f1048,f158]) ).
fof(f1051,plain,
~ spl5_18,
inference(avatar_contradiction_clause,[],[f1050]) ).
fof(f1063,plain,
( yp = comb_app(ap_parcontractE_sk2q(sF0,q,yp),ap_parcontractE_sk2s(sF0,q,yp))
| ~ spl5_17 ),
inference(resolution,[],[f401,f221]) ).
fof(f1083,plain,
( member(pair(yp,k1_parcontractD_sk1(p,ap_parcontractE_sk2q(sF0,q,yp))),parcontract)
| ~ member(ap_parcontractE_sk2s(sF0,q,yp),comb)
| ~ spl5_17
| ~ spl5_69 ),
inference(superposition,[],[f1011,f1063]) ).
fof(f1084,plain,
( member(pair(yp,k1_parcontractD_sk1(p,ap_parcontractE_sk2q(sF0,q,yp))),parcontract)
| ~ spl5_17
| ~ spl5_26
| ~ spl5_69 ),
inference(forward_subsumption_resolution,[],[f1083,f518]) ).
fof(f1085,plain,
( member(sF4(k1_parcontractD_sk1(p,ap_parcontractE_sk2q(sF0,q,yp))),parcontract)
| ~ spl5_17
| ~ spl5_26
| ~ spl5_69 ),
inference(forward_demodulation,[],[f1084,f266]) ).
fof(f1086,plain,
( ~ member(sF3(k1_parcontractD_sk1(p,ap_parcontractE_sk2q(sF0,q,yp))),parcontract)
| ~ spl5_17
| ~ spl5_26
| ~ spl5_69 ),
inference(resolution,[],[f1085,f267]) ).
fof(f1087,plain,
( ~ ap_parcontractE_c4(sF0,q,yp)
| ~ spl5_17
| ~ spl5_26
| ~ spl5_69 ),
inference(resolution,[],[f1086,f495]) ).
fof(f1089,plain,
( $false
| ~ spl5_17
| ~ spl5_26
| ~ spl5_69 ),
inference(forward_subsumption_resolution,[],[f1087,f401]) ).
fof(f1090,plain,
( ~ spl5_17
| ~ spl5_26
| ~ spl5_69 ),
inference(avatar_contradiction_clause,[],[f1089]) ).
cnf(s5,plain,
( ~ spl5_5
| spl5_6 ),
inference(sat_conversion,[],[f297]) ).
cnf(s9,plain,
spl5_5,
inference(sat_conversion,[],[f346]) ).
cnf(s12,plain,
( spl5_17
| spl5_18
| spl5_19
| spl5_20 ),
inference(sat_conversion,[],[f414]) ).
cnf(s18,plain,
( ~ spl5_5
| ~ spl5_17
| spl5_26 ),
inference(sat_conversion,[],[f539]) ).
cnf(s19,plain,
( ~ spl5_5
| ~ spl5_17
| spl5_25 ),
inference(sat_conversion,[],[f540]) ).
cnf(s52,plain,
~ spl5_61,
inference(sat_conversion,[],[f900]) ).
cnf(s53,plain,
( ~ spl5_6
| ~ spl5_19 ),
inference(sat_conversion,[],[f926]) ).
cnf(s54,plain,
( ~ spl5_20
| spl5_61 ),
inference(sat_conversion,[],[f935]) ).
cnf(s59,plain,
( ~ spl5_17
| ~ spl5_68
| spl5_69 ),
inference(sat_conversion,[],[f1012]) ).
cnf(s64,plain,
( ~ spl5_17
| ~ spl5_25
| spl5_68 ),
inference(sat_conversion,[],[f1029]) ).
cnf(s65,plain,
~ spl5_18,
inference(sat_conversion,[],[f1051]) ).
cnf(s66,plain,
( ~ spl5_17
| ~ spl5_26
| ~ spl5_69 ),
inference(sat_conversion,[],[f1090]) ).
cnf(s67,plain,
~ spl5_20,
inference(rat,[],[s54,s52]) ).
cnf(s69,plain,
( spl5_17
| spl5_19 ),
inference(rat,[],[s12,s67,s65]) ).
cnf(s70,plain,
spl5_6,
inference(rat,[],[s5,s9]) ).
cnf(s71,plain,
~ spl5_19,
inference(rat,[],[s53,s70]) ).
cnf(s72,plain,
spl5_17,
inference(rat,[],[s69,s71]) ).
cnf(s74,plain,
spl5_25,
inference(rat,[],[s19,s9,s72]) ).
cnf(s75,plain,
spl5_26,
inference(rat,[],[s18,s9,s72]) ).
cnf(s77,plain,
spl5_68,
inference(rat,[],[s64,s72,s74]) ).
cnf(s82,plain,
~ spl5_69,
inference(rat,[],[s66,s72,s75]) ).
cnf(s83,plain,
$false,
inference(rat,[],[s59,s72,s82,s77]) ).
fof(f1091,plain,
$false,
inference(avatar_sat_refutation,[],[s83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL095-2 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n001.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
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 21:40:34 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 4.34/1.38 % (781604)Input is clausal, will run a generic CNF schedule.
% 4.34/1.38 % (781737)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=254379534:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.34/1.38 % (781739)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3616286430:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.34/1.38 % (781745)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3568179386:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.34/1.38 % (781743)lrs+10_1_sil=8000:sp=occurrence:random_seed=2217189044:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.34/1.38 % (781749)dis-21_1_sil=8000:lcm=predicate:random_seed=487761093: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)
% 4.34/1.38 % (781741)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=16019027:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.34/1.38 % (781747)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2251977804:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.34/1.38 % (781743)Instruction limit reached!
% 4.34/1.38 % (781743)------------------------------
% 4.34/1.38 % (781743)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.34/1.38 % (781743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.34/1.38 % (781743)CaDiCaL version: 2.1.3
% 4.34/1.38 % (781743)Termination reason: Instruction limit
% 4.34/1.38 % (781743)Termination phase: Saturation
% 4.34/1.38 % (781743)Time elapsed: 0.062 s
% 4.34/1.38 % (781743)Peak memory usage: 88 MB
% 4.34/1.38 % (781743)Instructions burned: 108 (million)
% 4.34/1.38 % (781745)Instruction limit reached!
% 4.34/1.38 % (781745)------------------------------
% 4.34/1.38 % (781745)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.34/1.38 % (781745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.34/1.38 % (781745)CaDiCaL version: 2.1.3
% 4.34/1.38 % (781745)Termination reason: Instruction limit
% 4.34/1.38 % (781745)Termination phase: Saturation
% 4.34/1.38 % (781745)Time elapsed: 0.071 s
% 4.34/1.38 % (781745)Peak memory usage: 88 MB
% 4.34/1.38 % (781745)Instructions burned: 115 (million)
% 4.34/1.38 % (781749)Instruction limit reached!
% 4.34/1.38 % (781749)------------------------------
% 4.34/1.38 % (781749)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.34/1.38 % (781749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.34/1.38 % (781749)CaDiCaL version: 2.1.3
% 4.34/1.38 % (781749)Termination reason: Instruction limit
% 4.34/1.38 % (781749)Termination phase: Saturation
% 4.34/1.38 % (781749)Time elapsed: 0.072 s
% 4.34/1.38 % (781749)Peak memory usage: 89 MB
% 4.34/1.38 % (781749)Instructions burned: 117 (million)
% 4.34/1.38 % (781747)Instruction limit reached!
% 4.34/1.38 % (781747)------------------------------
% 4.34/1.38 % (781747)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.34/1.38 % (781747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.34/1.38 % (781747)CaDiCaL version: 2.1.3
% 4.34/1.38 % (781747)Termination reason: Instruction limit
% 4.34/1.38 % (781747)Termination phase: Saturation
% 4.34/1.38 % (781747)Time elapsed: 0.118 s
% 4.34/1.38 % (781747)Peak memory usage: 89 MB
% 4.34/1.38 % (781747)Instructions burned: 180 (million)
% 4.34/1.38 % (781775)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=2202190904:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.34/1.38 % (781777)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2440754827:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 4.34/1.38 % (781776)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1618323285: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)
% 4.34/1.38 % (781777)Refutation not found, incomplete strategy
% 4.34/1.38 % (781777)------------------------------
% 4.34/1.38 % (781777)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.34/1.38 % (781777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.34/1.38 % (781777)CaDiCaL version: 2.1.3
% 4.34/1.38 % (781777)Termination reason: Refutation not found, incomplete strategy
% 4.34/1.38 % (781777)Time elapsed: 0.021 s
% 4.34/1.38 % (781777)Peak memory usage: 88 MB
% 4.34/1.38 % (781777)Instructions burned: 31 (million)
% 4.34/1.38 % (781778)lrs+10_64_to=lpo:sil=8000:random_seed=3164146734:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 4.34/1.38 % (781775)Instruction limit reached!
% 4.34/1.38 % (781775)------------------------------
% 4.34/1.38 % (781775)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.34/1.38 % (781775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.34/1.38 % (781775)CaDiCaL version: 2.1.3
% 4.34/1.38 % (781775)Termination reason: Instruction limit
% 4.34/1.38 % (781775)Termination phase: Saturation
% 4.34/1.38 % (781775)Time elapsed: 0.084 s
% 4.34/1.38 % (781775)Peak memory usage: 90 MB
% 4.34/1.38 % (781775)Instructions burned: 144 (million)
% 4.34/1.38 % (781776)Instruction limit reached!
% 4.34/1.38 % (781776)------------------------------
% 4.34/1.38 % (781776)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.34/1.38 % (781776)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.34/1.38 % (781776)CaDiCaL version: 2.1.3
% 4.34/1.38 % (781776)Termination reason: Instruction limit
% 4.34/1.38 % (781776)Termination phase: Saturation
% 4.34/1.38 % (781776)Time elapsed: 0.092 s
% 4.34/1.38 % (781776)Peak memory usage: 90 MB
% 4.34/1.38 % (781776)Instructions burned: 191 (million)
% 4.34/1.38 % (781778)Instruction limit reached!
% 4.34/1.38 % (781778)------------------------------
% 4.34/1.38 % (781778)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.34/1.38 % (781778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.34/1.38 % (781778)CaDiCaL version: 2.1.3
% 4.34/1.38 % (781778)Termination reason: Instruction limit
% 4.34/1.38 % (781778)Termination phase: Saturation
% 4.34/1.38 % (781778)Time elapsed: 0.077 s
% 4.34/1.38 % (781778)Peak memory usage: 90 MB
% 4.34/1.38 % (781778)Instructions burned: 128 (million)
% 4.34/1.38 % (781783)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2919507225:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 4.34/1.38 % (781737)First to succeed.
% 4.34/1.38 % (781737)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-781604"
% 4.34/1.38 % (781784)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=1563771345:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 4.34/1.38 % (781777)------------------------------
% 4.34/1.38 % (781777)------------------------------
% 4.34/1.38 % (781785)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=888581360:i=3394:sd=4:ss=included:sgt=64_2995 on theBenchmark for (2995ds/3394Mi)
% 4.34/1.38 % (781783)Instruction limit reached!
% 4.34/1.38 % (781783)------------------------------
% 4.34/1.38 % (781783)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.34/1.38 % (781783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.34/1.38 % (781783)CaDiCaL version: 2.1.3
% 4.34/1.38 % (781783)Termination reason: Instruction limit
% 4.34/1.38 % (781783)Termination phase: Saturation
% 4.34/1.38 % (781783)Time elapsed: 0.106 s
% 4.34/1.38 % (781783)Peak memory usage: 89 MB
% 4.34/1.38 % (781783)Instructions burned: 194 (million)
% 4.34/1.38 % (781784)Instruction limit reached!
% 4.34/1.38 % (781784)------------------------------
% 4.34/1.38 % (781784)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.34/1.38 % (781784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.34/1.38 % (781784)CaDiCaL version: 2.1.3
% 4.34/1.38 % (781784)Termination reason: Instruction limit
% 4.34/1.38 % (781784)Termination phase: Saturation
% 4.34/1.38 % (781784)Time elapsed: 0.099 s
% 4.34/1.38 % (781784)Peak memory usage: 91 MB
% 4.34/1.38 % (781784)Instructions burned: 158 (million)
% 4.34/1.38 % (781737)Refutation found. Thanks to Tanya!
% 4.34/1.38 % SZS status Unsatisfiable for theBenchmark
% 4.34/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 5.64/1.57 % (781737)------------------------------
% 5.64/1.57 % (781737)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.57 % (781737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.57 % (781737)CaDiCaL version: 2.1.3
% 5.64/1.57 % (781737)Termination reason: Refutation
% 5.64/1.57 % (781737)Time elapsed: 0.446 s
% 5.64/1.57 % (781737)Peak memory usage: 132 MB
% 5.64/1.57 % (781737)Instructions burned: 1119 (million)
% 5.64/1.57 % (781737)------------------------------
% 5.64/1.57 % (781737)------------------------------
% 5.64/1.57 % (781604)Success in time 0.711 s
% 5.64/1.57 % Vampire exiting
%------------------------------------------------------------------------------