%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL003-12 : TPTP v9.3.1. Released v2.1.0.
% 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 09:37:33 AM UTC 2026
% Result : Unsatisfiable 2.79s 0.97s
% Output : Refutation 2.79s
% 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/sandbox/benchmark/theBenchmark.p',b_definition) ).
fof(f2,axiom,
! [X0,X1] : apply(apply(w,X0),X1) = apply(apply(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_definition) ).
fof(f3,axiom,
strong_fixed_point = apply(apply(b,apply(w,w)),apply(apply(b,w),apply(apply(b,b),b))),
file('/export/starexec/sandbox/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/sandbox/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(w,w)),apply(apply(b,w),apply(apply(b,b),b))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f13,plain,
( strong_fixed_point = apply(apply(b,apply(w,w)),apply(apply(b,w),apply(apply(b,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(f106,plain,
( ! [X0] : apply(apply(w,w),apply(apply(apply(b,w),apply(apply(b,b),b)),X0)) = apply(strong_fixed_point,X0)
| ~ spl0_2 ),
inference(superposition,[],[f1,f13]) ).
fof(f119,plain,
( ! [X0] : apply(strong_fixed_point,X0) = apply(apply(w,w),apply(w,apply(apply(apply(b,b),b),X0)))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f106,f1]) ).
fof(f130,plain,
( ! [X0] : apply(strong_fixed_point,X0) = apply(apply(w,w),apply(w,apply(b,apply(b,X0))))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f119,f1]) ).
fof(f1604,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(f1702,plain,
( ! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1604,f130]) ).
fof(f1722,plain,
( $false
| spl0_1
| ~ spl0_2 ),
inference(backward_subsumption_resolution,[],[f8,f1702]) ).
fof(f1723,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_contradiction_clause,[],[f1722]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f9]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f14]) ).
cnf(s74,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f1723]) ).
cnf(s81,plain,
spl0_1,
inference(rat,[],[s74,s2]) ).
cnf(s93,plain,
$false,
inference(rat,[],[s1,s81]) ).
fof(f1729,plain,
$false,
inference(avatar_sat_refutation,[],[s93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL003-12 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n017.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 21:24:06 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 2.79/0.97 % (4048741)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.79/0.97 % (4048753)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3504706830:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.79/0.97 % (4048751)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3781994028:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.79/0.97 % (4048750)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3587863364:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.79/0.97 % (4048749)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=1505227262:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.79/0.97 % (4048752)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=55458857:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.79/0.97 % (4048748)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=483708463:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.79/0.97 % (4048754)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2814882665:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.79/0.97 % (4048753)First to succeed.
% 2.79/0.97 % (4048753)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4048741"
% 2.79/0.97 % (4048751)Instruction limit reached!
% 2.79/0.97 % (4048751)------------------------------
% 2.79/0.97 % (4048751)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/0.97 % (4048751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/0.97 % (4048751)CaDiCaL version: 2.1.3
% 2.79/0.97 % (4048751)Termination reason: Instruction limit
% 2.79/0.97 % (4048751)Termination phase: Saturation
% 2.79/0.97 % (4048751)Time elapsed: 0.084 s
% 2.79/0.97 % (4048751)Peak memory usage: 88 MB
% 2.79/0.97 % (4048751)Instructions burned: 137 (million)
% 2.79/0.97 % (4048752)Instruction limit reached!
% 2.79/0.97 % (4048752)------------------------------
% 2.79/0.97 % (4048752)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/0.97 % (4048752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/0.97 % (4048752)CaDiCaL version: 2.1.3
% 2.79/0.97 % (4048752)Termination reason: Instruction limit
% 2.79/0.97 % (4048752)Termination phase: Saturation
% 2.79/0.97 % (4048752)Time elapsed: 0.102 s
% 2.79/0.97 % (4048752)Peak memory usage: 89 MB
% 2.79/0.97 % (4048752)Instructions burned: 181 (million)
% 2.79/0.97 % (4048753)Refutation found. Thanks to Tanya!
% 2.79/0.97 % SZS status Unsatisfiable for theBenchmark
% 2.79/0.97 % SZS output start Proof for theBenchmark
% See solution above
% 2.79/0.97 % (4048753)------------------------------
% 2.79/0.97 % (4048753)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/0.97 % (4048753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/0.97 % (4048753)CaDiCaL version: 2.1.3
% 2.79/0.97 % (4048753)Termination reason: Refutation
% 2.79/0.97 % (4048753)Time elapsed: 0.057 s
% 2.79/0.97 % (4048753)Peak memory usage: 91 MB
% 2.79/0.97 % (4048753)Instructions burned: 158 (million)
% 2.79/0.97 % (4048753)------------------------------
% 2.79/0.97 % (4048753)------------------------------
% 2.79/0.97 % (4048741)Success in time 0.332 s
% 2.79/0.97 % Vampire exiting
%------------------------------------------------------------------------------