%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL090-2 : 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 : n015.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 09:37:54 AM UTC 2026
% Result : Unsatisfiable 3.80s 1.23s
% Output : Refutation 3.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 49 ( 16 unt; 3 def)
% Number of atoms : 99 ( 18 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 91 ( 41 ~; 47 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 4 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 54 ( 0 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f157,axiom,
combK != combS,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_s) ).
fof(f159,axiom,
! [X0,X1] : combS != comb_app(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_app) ).
fof(f160,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(f171,axiom,
! [X2,X0,X1] :
( ~ member(pair(comb_app(X0,X1),X2),contract)
| ap_contractE_c1(X0,X1,X2)
| ap_contractE_c2(X0,X1,X2)
| ap_contractE_c3(X0,X1,X2)
| ap_contractE_c4(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE1) ).
fof(f174,axiom,
! [X2,X0,X1] :
( ~ ap_contractE_c1(X0,X1,X2)
| X0 = comb_app(combK,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE4) ).
fof(f175,plain,
! [X2,X0,X1] :
( ~ ap_contractE_c1(X0,X1,X2)
| comb_app(combK,X2) = X0 ),
inference(reorient_equations,[],[f174]) ).
fof(f181,axiom,
! [X2,X0,X1] :
( ~ ap_contractE_c2(X0,X1,X2)
| X0 = comb_app(comb_app(combS,ap_contractE_sk1p(X0,X1,X2)),ap_contractE_sk1q(X0,X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE9) ).
fof(f182,plain,
! [X2,X0,X1] :
( ~ ap_contractE_c2(X0,X1,X2)
| comb_app(comb_app(combS,ap_contractE_sk1p(X0,X1,X2)),ap_contractE_sk1q(X0,X1,X2)) = X0 ),
inference(reorient_equations,[],[f181]) ).
fof(f183,axiom,
! [X2,X0,X1] :
( member(pair(X0,ap_contractE_sk2q(X0,X1,X2)),contract)
| ~ ap_contractE_c3(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE10) ).
fof(f187,axiom,
! [X2,X0,X1] :
( member(pair(X1,ap_contractE_sk3q(X0,X1,X2)),contract)
| ~ ap_contractE_c4(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE13) ).
fof(f191,axiom,
! [X0] : ~ member(pair(combK,X0),contract),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_contractE) ).
fof(f192,axiom,
! [X0] : ~ member(pair(combS,X0),contract),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_contractE) ).
fof(f193,negated_conjecture,
member(pair(comb_app(comb_app(combS,combK),combK),r),contract),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_contract_E) ).
fof(f203,plain,
! [X0,X1] : ~ ap_contractE_c3(combS,X0,X1),
inference(resolution,[],[f183,f192]) ).
fof(f204,plain,
! [X0,X1] : ~ ap_contractE_c4(X0,combK,X1),
inference(resolution,[],[f187,f191]) ).
fof(f206,plain,
( ap_contractE_c1(comb_app(combS,combK),combK,r)
| ap_contractE_c2(comb_app(combS,combK),combK,r)
| ap_contractE_c3(comb_app(combS,combK),combK,r)
| ap_contractE_c4(comb_app(combS,combK),combK,r) ),
inference(resolution,[],[f171,f193]) ).
fof(f208,plain,
! [X2,X3,X0,X1] :
( ap_contractE_c4(X0,X1,ap_contractE_sk2q(comb_app(X0,X1),X2,X3))
| ap_contractE_c2(X0,X1,ap_contractE_sk2q(comb_app(X0,X1),X2,X3))
| ap_contractE_c3(X0,X1,ap_contractE_sk2q(comb_app(X0,X1),X2,X3))
| ap_contractE_c1(X0,X1,ap_contractE_sk2q(comb_app(X0,X1),X2,X3))
| ~ ap_contractE_c3(comb_app(X0,X1),X2,X3) ),
inference(resolution,[],[f171,f183]) ).
fof(f210,plain,
( ap_contractE_c1(comb_app(combS,combK),combK,r)
| ap_contractE_c2(comb_app(combS,combK),combK,r)
| ap_contractE_c3(comb_app(combS,combK),combK,r) ),
inference(forward_subsumption_resolution,[],[f206,f204]) ).
fof(f212,definition,
( spl0_1
<=> ap_contractE_c3(comb_app(combS,combK),combK,r) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f214,plain,
( ap_contractE_c3(comb_app(combS,combK),combK,r)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f216,definition,
( spl0_2
<=> ap_contractE_c2(comb_app(combS,combK),combK,r) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f218,plain,
( ap_contractE_c2(comb_app(combS,combK),combK,r)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f220,definition,
( spl0_3
<=> ap_contractE_c1(comb_app(combS,combK),combK,r) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f222,plain,
( ap_contractE_c1(comb_app(combS,combK),combK,r)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f223,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f210,f220,f216,f212]) ).
fof(f274,plain,
! [X2,X0,X1] :
( ap_contractE_c3(X0,combK,ap_contractE_sk2q(comb_app(X0,combK),X1,X2))
| ap_contractE_c2(X0,combK,ap_contractE_sk2q(comb_app(X0,combK),X1,X2))
| ap_contractE_c1(X0,combK,ap_contractE_sk2q(comb_app(X0,combK),X1,X2))
| ~ ap_contractE_c3(comb_app(X0,combK),X1,X2) ),
inference(resolution,[],[f208,f204]) ).
fof(f362,plain,
( comb_app(combS,combK) = comb_app(combK,r)
| ~ spl0_3 ),
inference(resolution,[],[f222,f175]) ).
fof(f376,plain,
( ! [X0,X1] :
( comb_app(X0,X1) != comb_app(combK,r)
| combS = X0 )
| ~ spl0_3 ),
inference(superposition,[],[f160,f362]) ).
fof(f428,plain,
! [X0,X1] :
( ap_contractE_c2(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),X0,X1))
| ap_contractE_c1(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),X0,X1))
| ~ ap_contractE_c3(comb_app(combS,combK),X0,X1) ),
inference(resolution,[],[f274,f203]) ).
fof(f461,plain,
( combK = combS
| ~ spl0_3 ),
inference(equality_resolution,[],[f376]) ).
fof(f462,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f461,f157]) ).
fof(f463,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f462]) ).
fof(f755,plain,
! [X0,X1] :
( ap_contractE_c1(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),X0,X1))
| ~ ap_contractE_c3(comb_app(combS,combK),X0,X1)
| combS = comb_app(comb_app(combS,ap_contractE_sk1p(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),X0,X1))),ap_contractE_sk1q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),X0,X1))) ),
inference(resolution,[],[f428,f182]) ).
fof(f758,plain,
! [X0,X1] :
( ap_contractE_c1(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),X0,X1))
| ~ ap_contractE_c3(comb_app(combS,combK),X0,X1) ),
inference(forward_subsumption_resolution,[],[f755,f159]) ).
fof(f1070,plain,
! [X0,X1] :
( ~ ap_contractE_c3(comb_app(combS,combK),X0,X1)
| combS = comb_app(combK,ap_contractE_sk2q(comb_app(combS,combK),X0,X1)) ),
inference(resolution,[],[f758,f175]) ).
fof(f1073,plain,
! [X0,X1] : ~ ap_contractE_c3(comb_app(combS,combK),X0,X1),
inference(forward_subsumption_resolution,[],[f1070,f159]) ).
fof(f1080,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f1073,f214]) ).
fof(f1089,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f1080]) ).
fof(f1094,plain,
( comb_app(combS,combK) = comb_app(comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)),ap_contractE_sk1q(comb_app(combS,combK),combK,r))
| ~ spl0_2 ),
inference(resolution,[],[f218,f182]) ).
fof(f1224,plain,
( ! [X0,X1] :
( comb_app(X0,X1) != comb_app(combS,combK)
| comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)) = X0 )
| ~ spl0_2 ),
inference(superposition,[],[f160,f1094]) ).
fof(f1310,plain,
( combS = comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r))
| ~ spl0_2 ),
inference(equality_resolution,[],[f1224]) ).
fof(f1311,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f1310,f159]) ).
fof(f1312,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f1311]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f223]) ).
cnf(s18,plain,
~ spl0_3,
inference(sat_conversion,[],[f463]) ).
cnf(s43,plain,
~ spl0_1,
inference(sat_conversion,[],[f1089]) ).
cnf(s49,plain,
~ spl0_2,
inference(sat_conversion,[],[f1312]) ).
cnf(s50,plain,
$false,
inference(rat,[],[s1,s18,s49,s43]) ).
fof(f1313,plain,
$false,
inference(avatar_sat_refutation,[],[s50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL090-2 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n015.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 21:38:32 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 3.01/1.13 % (3062566)Input is clausal, will run a generic CNF schedule.
% 3.01/1.13 % (3062573)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3185010954:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.01/1.13 % (3062576)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3376440738:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.01/1.13 % (3062577)dis-21_1_sil=8000:lcm=predicate:random_seed=1445134822: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)
% 3.01/1.13 % (3062575)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1948714500:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.01/1.13 % (3062572)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1209090599:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.01/1.13 % (3062574)lrs+10_1_sil=8000:sp=occurrence:random_seed=1428176709:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.01/1.13 % (3062571)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=3818132389:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.01/1.13 % (3062575)Refutation not found, incomplete strategy
% 3.01/1.13 % (3062575)------------------------------
% 3.01/1.13 % (3062575)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.01/1.13 % (3062575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/1.13 % (3062575)CaDiCaL version: 2.1.3
% 3.01/1.13 % (3062575)Termination reason: Refutation not found, incomplete strategy
% 3.01/1.13 % (3062575)Time elapsed: 0.002 s
% 3.01/1.13 % (3062575)Peak memory usage: 88 MB
% 3.01/1.13 % (3062575)Instructions burned: 2 (million)
% 3.01/1.13 % (3062574)First to succeed.
% 3.01/1.13 % (3062574)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3062566"
% 3.01/1.13 % (3062577)Instruction limit reached!
% 3.01/1.13 % (3062577)------------------------------
% 3.01/1.13 % (3062577)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.01/1.13 % (3062577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/1.13 % (3062577)CaDiCaL version: 2.1.3
% 3.01/1.13 % (3062577)Termination reason: Instruction limit
% 3.01/1.13 % (3062577)Termination phase: Saturation
% 3.01/1.13 % (3062577)Time elapsed: 0.079 s
% 3.01/1.13 % (3062577)Peak memory usage: 89 MB
% 3.01/1.13 % (3062577)Instructions burned: 117 (million)
% 3.01/1.13 % (3062576)Instruction limit reached!
% 3.01/1.13 % (3062576)------------------------------
% 3.01/1.13 % (3062576)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.01/1.13 % (3062576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/1.13 % (3062576)CaDiCaL version: 2.1.3
% 3.01/1.13 % (3062576)Termination reason: Instruction limit
% 3.01/1.13 % (3062576)Termination phase: Saturation
% 3.01/1.13 % (3062576)Time elapsed: 0.117 s
% 3.01/1.13 % (3062576)Peak memory usage: 90 MB
% 3.01/1.13 % (3062576)Instructions burned: 180 (million)
% 3.01/1.13 % (3062585)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=4254420733:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.01/1.13 % (3062585)Refutation not found, incomplete strategy
% 3.01/1.13 % (3062585)------------------------------
% 3.01/1.13 % (3062585)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.01/1.13 % (3062585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/1.13 % (3062585)CaDiCaL version: 2.1.3
% 3.01/1.13 % (3062585)Termination reason: Refutation not found, incomplete strategy
% 3.01/1.13 % (3062585)Time elapsed: 0.002 s
% 3.01/1.13 % (3062585)Peak memory usage: 88 MB
% 3.01/1.13 % (3062585)Instructions burned: 2 (million)
% 3.01/1.13 % (3062575)------------------------------
% 3.01/1.13 % (3062575)------------------------------
% 3.01/1.13 % (3062586)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=698762491: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)
% 3.01/1.13 % (3062586)Refutation not found, incomplete strategy
% 3.01/1.13 % (3062586)------------------------------
% 3.01/1.13 % (3062586)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.23 % (3062586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.23 % (3062586)CaDiCaL version: 2.1.3
% 3.80/1.23 % (3062586)Termination reason: Refutation not found, incomplete strategy
% 3.80/1.23 % (3062586)Time elapsed: 0.003 s
% 3.80/1.23 % (3062586)Peak memory usage: 88 MB
% 3.80/1.23 % (3062586)Instructions burned: 3 (million)
% 3.80/1.23 % (3062574)Refutation found. Thanks to Tanya!
% 3.80/1.23 % SZS status Unsatisfiable for theBenchmark
% 3.80/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 3.80/1.23 % (3062574)------------------------------
% 3.80/1.23 % (3062574)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.23 % (3062574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.23 % (3062574)CaDiCaL version: 2.1.3
% 3.80/1.23 % (3062574)Termination reason: Refutation
% 3.80/1.23 % (3062574)Time elapsed: 0.050 s
% 3.80/1.23 % (3062574)Peak memory usage: 90 MB
% 3.80/1.23 % (3062574)Instructions burned: 80 (million)
% 3.80/1.23 % (3062574)------------------------------
% 3.80/1.23 % (3062574)------------------------------
% 3.80/1.23 % (3062566)Success in time 0.46 s
% 3.80/1.23 % Vampire exiting
%------------------------------------------------------------------------------