%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL003-14 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 09:37:33 AM UTC 2026
% Result : Unsatisfiable 1.16s 0.79s
% Output : Refutation 1.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 15 unt; 2 def)
% Number of atoms : 38 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 12 ~; 10 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
fof(f2,axiom,
! [X0,X1] : apply(apply(w,X0),X1) = apply(apply(X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_definition) ).
fof(f3,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f4,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
fof(f6,definition,
( spl0_1
<=> apply(strong_fixed_point,fixed_pt) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f8,plain,
( apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt))
| spl0_1 ),
inference(avatar_component_clause,[],[f6]) ).
fof(f9,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f4,f6]) ).
fof(f11,definition,
( spl0_2
<=> strong_fixed_point = apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f13,plain,
( strong_fixed_point = apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f11]) ).
fof(f14,plain,
spl0_2,
inference(avatar_split_clause,[],[f3,f11]) ).
fof(f18,plain,
! [X0] : apply(apply(w,w),X0) = apply(apply(X0,X0),X0),
inference(superposition,[],[f2,f2]) ).
fof(f21,plain,
! [X0,X1] : apply(apply(w,apply(b,X0)),X1) = apply(X0,apply(X1,X1)),
inference(superposition,[],[f2,f1]) ).
fof(f60,plain,
! [X2,X0,X1] : apply(X0,apply(apply(X1,X1),X2)) = apply(apply(apply(w,apply(b,apply(b,X0))),X1),X2),
inference(superposition,[],[f1,f21]) ).
fof(f104,plain,
( ! [X0] : apply(apply(apply(b,apply(w,w)),apply(apply(b,w),b)),apply(b,X0)) = apply(strong_fixed_point,X0)
| ~ spl0_2 ),
inference(superposition,[],[f1,f13]) ).
fof(f117,plain,
( ! [X0] : apply(strong_fixed_point,X0) = apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,X0)))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f104,f1]) ).
fof(f118,plain,
( ! [X0] : apply(strong_fixed_point,X0) = apply(apply(w,w),apply(w,apply(b,apply(b,X0))))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f117,f1]) ).
fof(f1596,plain,
! [X0] : apply(apply(w,w),apply(w,apply(b,apply(b,X0)))) = apply(X0,apply(apply(w,w),apply(w,apply(b,apply(b,X0))))),
inference(superposition,[],[f60,f18]) ).
fof(f1694,plain,
( ! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1596,f118]) ).
fof(f1714,plain,
( $false
| spl0_1
| ~ spl0_2 ),
inference(backward_subsumption_resolution,[],[f8,f1694]) ).
fof(f1716,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_contradiction_clause,[],[f1714]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f9]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f14]) ).
cnf(s69,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f1716]) ).
cnf(s79,plain,
spl0_1,
inference(rat,[],[s69,s2]) ).
cnf(s85,plain,
$false,
inference(rat,[],[s1,s79]) ).
fof(f1727,plain,
$false,
inference(avatar_sat_refutation,[],[s85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL003-14 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n010.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Mon Sep 28 21:29:03 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 Running first-order theorem proving
% 0.09/0.19 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
% 1.16/0.79 % (2368499)Detected a unit-equality problem, will run specialized UEQ schedule.
% 1.16/0.79 % (2368509)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1290041871:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 1.16/0.79 % (2368507)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=393209538:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 1.16/0.79 % (2368505)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=2260020471:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 1.16/0.79 % (2368508)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1155597567:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 1.16/0.79 % (2368506)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2264062419:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 1.16/0.79 % (2368504)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=3188713216:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 1.16/0.79 % (2368510)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=334627556:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 1.16/0.79 % (2368509)First to succeed.
% 1.16/0.79 % (2368509)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2368499"
% 1.16/0.79 % (2368507)Instruction limit reached!
% 1.16/0.79 % (2368507)------------------------------
% 1.16/0.79 % (2368507)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.16/0.79 % (2368507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.79 % (2368507)CaDiCaL version: 2.1.3
% 1.16/0.79 % (2368507)Termination reason: Instruction limit
% 1.16/0.79 % (2368507)Termination phase: Saturation
% 1.16/0.79 % (2368507)Time elapsed: 0.081 s
% 1.16/0.79 % (2368507)Peak memory usage: 89 MB
% 1.16/0.79 % (2368507)Instructions burned: 136 (million)
% 1.16/0.79 % (2368508)Instruction limit reached!
% 1.16/0.79 % (2368508)------------------------------
% 1.16/0.79 % (2368508)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.16/0.79 % (2368508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.79 % (2368508)CaDiCaL version: 2.1.3
% 1.16/0.79 % (2368508)Termination reason: Instruction limit
% 1.16/0.79 % (2368508)Termination phase: Saturation
% 1.16/0.79 % (2368508)Time elapsed: 0.100 s
% 1.16/0.79 % (2368508)Peak memory usage: 89 MB
% 1.16/0.79 % (2368508)Instructions burned: 182 (million)
% 1.16/0.79 % (2368509)Refutation found. Thanks to Tanya!
% 1.16/0.79 % SZS status Unsatisfiable for theBenchmark
% 1.16/0.79 % SZS output start Proof for theBenchmark
% See solution above
% 1.16/0.79 % (2368509)------------------------------
% 1.16/0.79 % (2368509)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.16/0.79 % (2368509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.79 % (2368509)CaDiCaL version: 2.1.3
% 1.16/0.79 % (2368509)Termination reason: Refutation
% 1.16/0.79 % (2368509)Time elapsed: 0.055 s
% 1.16/0.79 % (2368509)Peak memory usage: 91 MB
% 1.16/0.79 % (2368509)Instructions burned: 157 (million)
% 1.16/0.79 % (2368509)------------------------------
% 1.16/0.79 % (2368509)------------------------------
% 1.16/0.79 % (2368499)Success in time 0.317 s
% 1.16/0.79 % Vampire exiting
%------------------------------------------------------------------------------