%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL074-3 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 09:38:23 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.26s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of formulae : 51 ( 23 unt; 2 def)
% Number of atoms : 82 ( 45 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 56 ( 25 ~; 29 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0,X1] : apply(apply(k,X0),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_definition) ).
fof(f3,axiom,
! [X0,X1] : apply(projection2,pair(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',projection2) ).
fof(f5,axiom,
! [X2,X0,X1] : apply(pair(X0,X1),X2) = pair(apply(X0,X2),apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pairwise_application) ).
fof(f7,axiom,
! [X0] : apply(eq,pair(X0,X0)) = projection1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality) ).
fof(f8,plain,
! [X0] : projection1 = apply(eq,pair(X0,X0)),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0,X1] :
( X0 = X1
| apply(eq,pair(X0,X1)) = projection2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality1) ).
fof(f10,plain,
! [X0,X1] :
( projection2 = apply(eq,pair(X0,X1))
| X0 = X1 ),
inference(reorient_equations,[],[f9]) ).
fof(f12,axiom,
projection1 != projection2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',different_projections) ).
fof(f13,axiom,
apply(k,projection1) = k_projection1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_projection1) ).
fof(f14,axiom,
apply(k,projection2) = k_projection2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_projection2) ).
fof(f15,axiom,
s = apply(eq,pair(apply(k,s),apply(k,projection2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',self_referential) ).
fof(f39,plain,
! [X0] : projection1 = apply(k_projection1,X0),
inference(superposition,[],[f1,f13]) ).
fof(f45,plain,
! [X0] : projection2 = apply(k_projection2,X0),
inference(superposition,[],[f1,f14]) ).
fof(f122,plain,
( projection2 = s
| apply(k,projection2) = apply(k,s) ),
inference(superposition,[],[f15,f10]) ).
fof(f127,plain,
( k_projection2 = apply(k,s)
| projection2 = s ),
inference(forward_demodulation,[],[f122,f14]) ).
fof(f129,definition,
( spl0_1
<=> projection2 = s ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f131,plain,
( projection2 = s
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f133,definition,
( spl0_2
<=> k_projection2 = apply(k,s) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f134,plain,
( k_projection2 != apply(k,s)
| spl0_2 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f135,plain,
( k_projection2 = apply(k,s)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f137,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f127,f133,f129]) ).
fof(f167,plain,
! [X0,X1] : apply(pair(eq,X0),pair(X1,X1)) = pair(projection1,apply(X0,pair(X1,X1))),
inference(superposition,[],[f5,f8]) ).
fof(f170,plain,
! [X0,X1] : apply(pair(k_projection1,X0),X1) = pair(projection1,apply(X0,X1)),
inference(superposition,[],[f5,f39]) ).
fof(f203,plain,
! [X0,X1] : apply(pair(eq,X0),pair(X1,X1)) = apply(pair(k_projection1,X0),pair(X1,X1)),
inference(forward_demodulation,[],[f167,f170]) ).
fof(f223,plain,
! [X0] : apply(pair(k_projection1,eq),pair(X0,X0)) = pair(projection1,projection1),
inference(superposition,[],[f170,f8]) ).
fof(f225,plain,
apply(pair(k_projection1,eq),pair(apply(k,s),apply(k,projection2))) = pair(projection1,s),
inference(superposition,[],[f170,f15]) ).
fof(f232,plain,
pair(projection1,s) = apply(pair(k_projection1,eq),pair(apply(k,s),k_projection2)),
inference(forward_demodulation,[],[f225,f14]) ).
fof(f233,plain,
! [X0] : pair(projection1,projection1) = apply(pair(eq,eq),pair(X0,X0)),
inference(forward_demodulation,[],[f223,f203]) ).
fof(f243,plain,
( pair(projection1,s) = apply(pair(k_projection1,eq),pair(k_projection2,k_projection2))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f232,f135]) ).
fof(f244,plain,
( pair(projection1,s) = apply(pair(eq,eq),pair(k_projection2,k_projection2))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f243,f203]) ).
fof(f245,plain,
( pair(projection1,projection1) = pair(projection1,s)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f244,f233]) ).
fof(f268,plain,
( s = apply(projection2,pair(projection1,projection1))
| ~ spl0_2 ),
inference(superposition,[],[f3,f245]) ).
fof(f270,plain,
( projection1 = s
| ~ spl0_2 ),
inference(forward_demodulation,[],[f268,f3]) ).
fof(f282,plain,
( projection1 = apply(eq,pair(apply(k,projection1),apply(k,projection2)))
| ~ spl0_2 ),
inference(superposition,[],[f15,f270]) ).
fof(f283,plain,
( projection1 = apply(eq,pair(apply(k,projection1),k_projection2))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f282,f14]) ).
fof(f284,plain,
( projection1 = apply(eq,pair(k_projection1,k_projection2))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f283,f13]) ).
fof(f301,plain,
( projection1 = projection2
| k_projection1 = k_projection2
| ~ spl0_2 ),
inference(superposition,[],[f10,f284]) ).
fof(f309,plain,
( k_projection1 = k_projection2
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f301,f12]) ).
fof(f330,plain,
( ! [X0] : projection2 = apply(k_projection1,X0)
| ~ spl0_2 ),
inference(superposition,[],[f45,f309]) ).
fof(f348,plain,
( projection1 = projection2
| ~ spl0_2 ),
inference(superposition,[],[f330,f39]) ).
fof(f361,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f348,f12]) ).
fof(f362,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f361]) ).
fof(f363,plain,
( apply(k,projection2) != k_projection2
| ~ spl0_1
| spl0_2 ),
inference(forward_demodulation,[],[f134,f131]) ).
fof(f367,plain,
( $false
| ~ spl0_1
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f363,f14]) ).
fof(f368,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_contradiction_clause,[],[f367]) ).
cnf(s2,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f137]) ).
cnf(s4,plain,
~ spl0_2,
inference(sat_conversion,[],[f362]) ).
cnf(s5,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f368]) ).
cnf(s6,plain,
~ spl0_1,
inference(rat,[],[s5,s4]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s4,s6]) ).
fof(f374,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL074-3 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.18 % Computer : n015.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Mon Sep 28 21:37:13 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.21 Running first-order model finding
% 0.11/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.26 % (3059754)Will run a generic schedule for satisfiability detection.
% 0.11/0.26 % (3059769)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=175812988:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.26 % (3059765)% WARNING: option uhcvi not known.
% 0.11/0.26 % (3059765)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2578599057:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.26 % (3059766)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1269621409:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.26 % (3059768)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1874039416:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.26 % (3059767)dis+10_1_sil=32000:sp=arity:random_seed=2296620541:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.26 % (3059770)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2998510211:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.26 % (3059764)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2847665550_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.26 % TRYING [1]
% 0.11/0.26 % TRYING [2]
% 0.11/0.26 % TRYING [3]
% 0.11/0.26 % (3059768) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3059754-3059768"...
% 0.11/0.26 % (3059768)...printing done.
% 0.11/0.26 % (3059768)Refutation found. Thanks to Tanya!
% 0.11/0.26 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.26 % (3059768)------------------------------
% 0.11/0.26 % (3059768)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.26 % (3059768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.26 % (3059768)CaDiCaL version: 2.1.3
% 0.11/0.26 % (3059768)Termination reason: Refutation
% 0.11/0.26 % (3059768)Time elapsed: 0.015 s
% 0.11/0.26 % (3059768)Peak memory usage: 12 MB
% 0.11/0.26 % (3059768)Instructions burned: 22 (million)
% 0.11/0.26 % (3059754)Success in time 0.048 s
% 0.11/0.27 % Vampire exiting
%------------------------------------------------------------------------------