%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL090-3 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 09:38:26 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 19
% Syntax : Number of formulae : 71 ( 22 unt; 8 def)
% Number of atoms : 140 ( 18 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 128 ( 59 ~; 61 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 9 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 33 ( 0 sgn 33 !; 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,
! [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(f10,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(f11,plain,
! [X2,X0,X1] :
( ~ ap_contractE_c1(X0,X1,X2)
| comb_app(combK,X2) = X0 ),
inference(reorient_equations,[],[f10]) ).
fof(f17,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(f18,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,[],[f17]) ).
fof(f19,axiom,
! [X2,X0,X1] :
( ~ ap_contractE_c3(X0,X1,X2)
| member(pair(X0,ap_contractE_sk2q(X0,X1,X2)),contract) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE10) ).
fof(f23,axiom,
! [X2,X0,X1] :
( ~ ap_contractE_c4(X0,X1,X2)
| member(pair(X1,ap_contractE_sk3q(X0,X1,X2)),contract) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE13) ).
fof(f27,axiom,
! [X0] : ~ member(pair(combK,X0),contract),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_contractE) ).
fof(f28,axiom,
! [X0] : ~ member(pair(combS,X0),contract),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_contractE) ).
fof(f29,negated_conjecture,
member(pair(comb_app(comb_app(combS,combK),combK),r),contract),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_contract_E) ).
fof(f34,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,[],[f7,f29]) ).
fof(f36,definition,
( spl0_1
<=> ap_contractE_c4(comb_app(combS,combK),combK,r) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f38,plain,
( ap_contractE_c4(comb_app(combS,combK),combK,r)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f40,definition,
( spl0_2
<=> ap_contractE_c3(comb_app(combS,combK),combK,r) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f42,plain,
( ap_contractE_c3(comb_app(combS,combK),combK,r)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f44,definition,
( spl0_3
<=> ap_contractE_c2(comb_app(combS,combK),combK,r) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f46,plain,
( ap_contractE_c2(comb_app(combS,combK),combK,r)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f48,definition,
( spl0_4
<=> ap_contractE_c1(comb_app(combS,combK),combK,r) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f50,plain,
( ap_contractE_c1(comb_app(combS,combK),combK,r)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f51,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f34,f48,f44,f40,f36]) ).
fof(f53,plain,
( member(pair(comb_app(combS,combK),ap_contractE_sk2q(comb_app(combS,combK),combK,r)),contract)
| ~ spl0_2 ),
inference(resolution,[],[f42,f19]) ).
fof(f62,plain,
( ap_contractE_c1(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c2(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c3(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c4(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ~ spl0_2 ),
inference(resolution,[],[f53,f7]) ).
fof(f64,definition,
( spl0_5
<=> ap_contractE_c4(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f66,plain,
( ap_contractE_c4(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f68,definition,
( spl0_6
<=> ap_contractE_c3(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f70,plain,
( ap_contractE_c3(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f72,definition,
( spl0_7
<=> ap_contractE_c2(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f74,plain,
( ap_contractE_c2(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f76,definition,
( spl0_8
<=> ap_contractE_c1(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f78,plain,
( ap_contractE_c1(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f79,plain,
( spl0_5
| spl0_6
| spl0_7
| spl0_8
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f62,f40,f76,f72,f68,f64]) ).
fof(f81,plain,
( member(pair(combK,ap_contractE_sk3q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),contract)
| ~ spl0_5 ),
inference(resolution,[],[f66,f23]) ).
fof(f83,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f81,f27]) ).
fof(f84,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[],[f83]) ).
fof(f86,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_3 ),
inference(resolution,[],[f46,f18]) ).
fof(f100,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_3 ),
inference(superposition,[],[f4,f86]) ).
fof(f118,plain,
( combS = comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r))
| ~ spl0_3 ),
inference(equality_resolution,[],[f100]) ).
fof(f119,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f118,f3]) ).
fof(f120,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f119]) ).
fof(f121,plain,
( comb_app(combS,combK) = comb_app(combK,r)
| ~ spl0_4 ),
inference(resolution,[],[f50,f11]) ).
fof(f127,plain,
( ! [X0,X1] :
( comb_app(X0,X1) != comb_app(combS,combK)
| combK = X0 )
| ~ spl0_4 ),
inference(superposition,[],[f4,f121]) ).
fof(f131,plain,
( combK = combS
| ~ spl0_4 ),
inference(equality_resolution,[],[f127]) ).
fof(f132,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f131,f1]) ).
fof(f133,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f132]) ).
fof(f146,plain,
( member(pair(combS,ap_contractE_sk2q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),contract)
| ~ spl0_6 ),
inference(resolution,[],[f70,f19]) ).
fof(f148,plain,
( $false
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f146,f28]) ).
fof(f149,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f148]) ).
fof(f151,plain,
( combS = comb_app(comb_app(combS,ap_contractE_sk1p(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),ap_contractE_sk1q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)))
| ~ spl0_7 ),
inference(resolution,[],[f74,f18]) ).
fof(f155,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f151,f3]) ).
fof(f156,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[],[f155]) ).
fof(f157,plain,
( combS = comb_app(combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ~ spl0_8 ),
inference(resolution,[],[f78,f11]) ).
fof(f160,plain,
( $false
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f157,f3]) ).
fof(f161,plain,
~ spl0_8,
inference(avatar_contradiction_clause,[],[f160]) ).
fof(f163,plain,
( member(pair(combK,ap_contractE_sk3q(comb_app(combS,combK),combK,r)),contract)
| ~ spl0_1 ),
inference(resolution,[],[f38,f23]) ).
fof(f165,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f163,f27]) ).
fof(f166,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f165]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f51]) ).
cnf(s2,plain,
( ~ spl0_2
| spl0_5
| spl0_6
| spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f79]) ).
cnf(s3,plain,
~ spl0_5,
inference(sat_conversion,[],[f84]) ).
cnf(s5,plain,
~ spl0_3,
inference(sat_conversion,[],[f120]) ).
cnf(s6,plain,
~ spl0_4,
inference(sat_conversion,[],[f133]) ).
cnf(s7,plain,
~ spl0_6,
inference(sat_conversion,[],[f149]) ).
cnf(s8,plain,
~ spl0_7,
inference(sat_conversion,[],[f156]) ).
cnf(s9,plain,
~ spl0_8,
inference(sat_conversion,[],[f161]) ).
cnf(s10,plain,
~ spl0_1,
inference(sat_conversion,[],[f166]) ).
cnf(s11,plain,
~ spl0_2,
inference(rat,[],[s2,s9,s8,s7,s3]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s6,s5,s11,s10]) ).
fof(f167,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL090-3 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n009.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 21:35:30 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
% 0.19/0.28 % (3516005)Will run a generic schedule for satisfiability detection.
% 0.19/0.28 % (3516010)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=863983312_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.28 % TRYING [1]
% 0.19/0.28 % TRYING [2]
% 0.19/0.28 % TRYING [3]
% 0.19/0.28 % (3516011)% WARNING: option uhcvi not known.
% 0.19/0.28 % TRYING [4]
% 0.19/0.28 % (3516011)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2790877674:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.28 % (3516012)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2549857235:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.28 % (3516013)dis+10_1_sil=32000:sp=arity:random_seed=675722573:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.28 % (3516014)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1114911600:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.28 % (3516015)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1194429615:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.28 % (3516016)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2022623538:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.28 % TRYING [5]
% 0.19/0.28 % (3516015) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3516005-3516015"...
% 0.19/0.28 % (3516011) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3516005-3516011"...
% 0.19/0.28 % (3516016) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3516005-3516016"...
% 0.19/0.28 % (3516015)...printing done.
% 0.19/0.28 % (3516011)...printing done.
% 0.19/0.28 % (3516015)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.28 % (3516015)------------------------------
% 0.19/0.28 % (3516015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (3516015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (3516015)CaDiCaL version: 2.1.3
% 0.19/0.28 % (3516015)Termination reason: Refutation
% 0.19/0.28 % (3516015)Time elapsed: 0.006 s
% 0.19/0.28 % (3516015)Peak memory usage: 12 MB
% 0.19/0.28 % (3516015)Instructions burned: 7 (million)
% 0.19/0.28 % (3516005)Success in time 0.047 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------