%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL004-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 09:37:36 AM UTC 2026
% Result : Unsatisfiable 3.73s 1.45s
% Output : Refutation 3.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 12 unt; 3 def)
% Number of atoms : 46 ( 16 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 33 ( 16 ~; 14 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 7 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_definition) ).
fof(f2,axiom,
! [X0,X1] : apply(apply(k,X0),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_definition) ).
fof(f3,negated_conjecture,
apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) != apply(y,apply(apply(x,x),y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_u_combinator) ).
fof(f5,definition,
( spl0_1
<=> apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) = apply(y,apply(apply(x,x),y)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f7,plain,
( apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) != apply(y,apply(apply(x,x),y))
| spl0_1 ),
inference(avatar_component_clause,[],[f5]) ).
fof(f8,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f3,f5]) ).
fof(f19,plain,
( apply(y,apply(apply(x,x),y)) != apply(apply(apply(apply(k,apply(s,apply(apply(s,k),k))),x),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),y)
| spl0_1 ),
inference(superposition,[],[f7,f1]) ).
fof(f20,plain,
! [X0,X1] : apply(apply(apply(s,k),X0),X1) = X1,
inference(superposition,[],[f2,f1]) ).
fof(f21,plain,
( apply(y,apply(apply(x,x),y)) != apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),y)
| spl0_1 ),
inference(forward_demodulation,[],[f19,f2]) ).
fof(f24,definition,
( spl0_2
<=> apply(y,apply(apply(x,x),y)) = apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),y) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f26,plain,
( apply(y,apply(apply(x,x),y)) != apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),y)
| spl0_2 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f27,plain,
( ~ spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f21,f5,f24]) ).
fof(f93,plain,
( apply(y,apply(apply(x,x),y)) != apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x))),y)
| spl0_2 ),
inference(superposition,[],[f26,f1]) ).
fof(f102,plain,
( apply(y,apply(apply(x,x),y)) != apply(apply(apply(s,apply(apply(s,k),k)),apply(x,x)),y)
| spl0_2 ),
inference(forward_demodulation,[],[f93,f20]) ).
fof(f109,definition,
( spl0_5
<=> apply(y,apply(apply(x,x),y)) = apply(apply(apply(s,apply(apply(s,k),k)),apply(x,x)),y) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f111,plain,
( apply(y,apply(apply(x,x),y)) != apply(apply(apply(s,apply(apply(s,k),k)),apply(x,x)),y)
| spl0_5 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
( ~ spl0_5
| spl0_2 ),
inference(avatar_split_clause,[],[f102,f24,f109]) ).
fof(f282,plain,
( apply(y,apply(apply(x,x),y)) != apply(apply(apply(apply(s,k),k),y),apply(apply(x,x),y))
| spl0_5 ),
inference(superposition,[],[f111,f1]) ).
fof(f283,plain,
( apply(y,apply(apply(x,x),y)) != apply(y,apply(apply(x,x),y))
| spl0_5 ),
inference(forward_demodulation,[],[f282,f20]) ).
fof(f284,plain,
( $false
| spl0_5 ),
inference(trivial_inequality_removal,[],[f283]) ).
fof(f285,plain,
spl0_5,
inference(avatar_contradiction_clause,[],[f284]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f8]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f27]) ).
cnf(s6,plain,
( spl0_2
| ~ spl0_5 ),
inference(sat_conversion,[],[f112]) ).
cnf(s7,plain,
spl0_5,
inference(sat_conversion,[],[f285]) ).
cnf(s9,plain,
spl0_2,
inference(rat,[],[s6,s7]) ).
cnf(s10,plain,
spl0_1,
inference(rat,[],[s2,s9]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s1,s10]) ).
fof(f291,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL004-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 % Computer : n005.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Mon Sep 28 21:29:02 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.29 Running first-order theorem proving
% 0.27/0.29 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
% 3.73/1.45 % (1202127)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.73/1.45 % (1202145)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3953977905:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.73/1.45 % (1202145)First to succeed.
% 3.73/1.45 % (1202145)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1202127"
% 3.73/1.45 % (1202142)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2736902567:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.73/1.45 % (1202141)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1950737419:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.73/1.45 % (1202140)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=3897049784:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.73/1.45 % (1202144)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2819377851:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.73/1.45 % (1202144)Also succeeded, but the first one will report.
% 3.73/1.45 % (1202146)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1358514542:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.73/1.45 % (1202143)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=211496933:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.73/1.45 % (1202146)Also succeeded, but the first one will report.
% 3.73/1.45 % (1202143)Also succeeded, but the first one will report.
% 3.73/1.45 % (1202145)Refutation found. Thanks to Tanya!
% 3.73/1.45 % SZS status Unsatisfiable for theBenchmark
% 3.73/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.73/1.45 % (1202145)------------------------------
% 3.73/1.45 % (1202145)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.73/1.45 % (1202145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.73/1.45 % (1202145)CaDiCaL version: 2.1.3
% 3.73/1.45 % (1202145)Termination reason: Refutation
% 3.73/1.45 % (1202145)Time elapsed: 0.018 s
% 3.73/1.45 % (1202145)Peak memory usage: 89 MB
% 3.73/1.45 % (1202145)Instructions burned: 31 (million)
% 3.73/1.45 % (1202145)------------------------------
% 3.73/1.45 % (1202145)------------------------------
% 3.73/1.45 % (1202127)Success in time 0.41 s
% 3.73/1.45 % Vampire exiting
%------------------------------------------------------------------------------