%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL064-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 09:37:49 AM UTC 2026
% Result : Unsatisfiable 2.58s 0.91s
% Output : Refutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 13 unt; 3 def)
% Number of atoms : 49 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 35 ( 17 ~; 15 |; 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
fof(f2,axiom,
! [X0,X1] : apply(apply(t,X0),X1) = apply(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_definition) ).
fof(f3,negated_conjecture,
apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),apply(apply(b,b),t))),x),y),z) != apply(apply(z,x),y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_v_combinator) ).
fof(f5,definition,
( spl0_1
<=> apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),apply(apply(b,b),t))),x),y),z) = apply(apply(z,x),y) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f7,plain,
( apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),apply(apply(b,b),t))),x),y),z) != apply(apply(z,x),y)
| spl0_1 ),
inference(avatar_component_clause,[],[f5]) ).
fof(f8,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f3,f5]) ).
fof(f9,plain,
( apply(apply(z,x),y) != apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,b),apply(apply(b,b),t)),x)),y),z)
| spl0_1 ),
inference(forward_demodulation,[],[f7,f1]) ).
fof(f10,plain,
( apply(apply(z,x),y) != apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(b,apply(apply(apply(b,b),t),x))),y),z)
| spl0_1 ),
inference(forward_demodulation,[],[f9,f1]) ).
fof(f11,plain,
( apply(apply(z,x),y) != apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(b,apply(b,apply(t,x)))),y),z)
| spl0_1 ),
inference(forward_demodulation,[],[f10,f1]) ).
fof(f13,definition,
( spl0_2
<=> apply(apply(z,x),y) = apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(b,apply(b,apply(t,x)))),y),z) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f15,plain,
( apply(apply(z,x),y) != apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(b,apply(b,apply(t,x)))),y),z)
| spl0_2 ),
inference(avatar_component_clause,[],[f13]) ).
fof(f16,plain,
( ~ spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f11,f5,f13]) ).
fof(f20,plain,
( apply(apply(z,x),y) != apply(apply(apply(apply(b,apply(b,apply(t,x))),apply(apply(b,b),t)),y),z)
| spl0_2 ),
inference(superposition,[],[f15,f2]) ).
fof(f35,plain,
( apply(apply(z,x),y) != apply(apply(apply(b,apply(t,x)),apply(apply(apply(b,b),t),y)),z)
| spl0_2 ),
inference(forward_demodulation,[],[f20,f1]) ).
fof(f42,plain,
( apply(apply(z,x),y) != apply(apply(t,x),apply(apply(apply(apply(b,b),t),y),z))
| spl0_2 ),
inference(forward_demodulation,[],[f35,f1]) ).
fof(f44,plain,
( apply(apply(z,x),y) != apply(apply(t,x),apply(apply(b,apply(t,y)),z))
| spl0_2 ),
inference(forward_demodulation,[],[f42,f1]) ).
fof(f47,definition,
( spl0_6
<=> apply(apply(z,x),y) = apply(apply(t,x),apply(apply(b,apply(t,y)),z)) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f49,plain,
( apply(apply(z,x),y) != apply(apply(t,x),apply(apply(b,apply(t,y)),z))
| spl0_6 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f50,plain,
( ~ spl0_6
| spl0_2 ),
inference(avatar_split_clause,[],[f44,f13,f47]) ).
fof(f53,plain,
! [X2,X0,X1] : apply(X0,apply(X1,X2)) = apply(apply(t,X2),apply(apply(b,X0),X1)),
inference(superposition,[],[f2,f1]) ).
fof(f103,plain,
! [X2,X0,X1] : apply(apply(t,X0),apply(apply(b,apply(t,X1)),X2)) = apply(apply(X2,X0),X1),
inference(superposition,[],[f2,f53]) ).
fof(f114,plain,
( $false
| spl0_6 ),
inference(backward_subsumption_resolution,[],[f49,f103]) ).
fof(f115,plain,
spl0_6,
inference(avatar_contradiction_clause,[],[f114]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f8]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f16]) ).
cnf(s6,plain,
( spl0_2
| ~ spl0_6 ),
inference(sat_conversion,[],[f50]) ).
cnf(s9,plain,
spl0_6,
inference(sat_conversion,[],[f115]) ).
cnf(s10,plain,
spl0_2,
inference(rat,[],[s6,s9]) ).
cnf(s11,plain,
spl0_1,
inference(rat,[],[s2,s10]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s11]) ).
fof(f117,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL064-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n017.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Mon Sep 28 21:27:51 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running first-order theorem proving
% 0.10/0.24 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
% 2.58/0.91 % (4057351)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.58/0.91 % (4057389)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=601661516:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.58/0.91 % (4057391)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=476987841:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.58/0.91 % (4057388)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2683416647:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.58/0.91 % (4057383)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=2058776807:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.58/0.91 % (4057385)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=975077529:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.58/0.91 % (4057386)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2004342855:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.58/0.91 % (4057389)First to succeed.
% 2.58/0.91 % (4057382)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=1039196593:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.58/0.91 % (4057389)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4057351"
% 2.58/0.91 % (4057391)Also succeeded, but the first one will report.
% 2.58/0.91 % (4057386)Also succeeded, but the first one will report.
% 2.58/0.91 % (4057388)Instruction limit reached!
% 2.58/0.91 % (4057388)------------------------------
% 2.58/0.91 % (4057388)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/0.91 % (4057388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.91 % (4057388)CaDiCaL version: 2.1.3
% 2.58/0.91 % (4057388)Termination reason: Instruction limit
% 2.58/0.91 % (4057388)Termination phase: Saturation
% 2.58/0.91 % (4057388)Time elapsed: 0.097 s
% 2.58/0.91 % (4057388)Peak memory usage: 88 MB
% 2.58/0.91 % (4057388)Instructions burned: 183 (million)
% 2.58/0.91 % (4057389)Refutation found. Thanks to Tanya!
% 2.58/0.91 % SZS status Unsatisfiable for theBenchmark
% 2.58/0.91 % SZS output start Proof for theBenchmark
% See solution above
% 2.58/0.91 % (4057389)------------------------------
% 2.58/0.91 % (4057389)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/0.91 % (4057389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.91 % (4057389)CaDiCaL version: 2.1.3
% 2.58/0.91 % (4057389)Termination reason: Refutation
% 2.58/0.91 % (4057389)Time elapsed: 0.004 s
% 2.58/0.91 % (4057389)Peak memory usage: 89 MB
% 2.58/0.91 % (4057389)Instructions burned: 8 (million)
% 2.58/0.91 % (4057389)------------------------------
% 2.58/0.91 % (4057389)------------------------------
% 2.58/0.91 % (4057351)Success in time 0.326 s
% 2.58/0.91 % Vampire exiting
%------------------------------------------------------------------------------