%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL042-6 : 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 : n009.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 09:37:42 AM UTC 2026
% Result : Unsatisfiable 7.47s 1.95s
% Output : Refutation 7.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 24 unt; 6 def)
% Number of atoms : 70 ( 28 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 56 ( 28 ~; 24 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 20 !; 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(w1,X0),X1) = apply(apply(X1,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w1_definition) ).
fof(f3,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),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(f5,definition,
sF0 = apply(strong_fixed_point,fixed_pt),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f6,plain,
apply(strong_fixed_point,fixed_pt) = sF0,
inference(reorient_equations,[],[f5]) ).
fof(f7,definition,
sF1 = apply(fixed_pt,sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f8,plain,
apply(fixed_pt,sF0) = sF1,
inference(reorient_equations,[],[f7]) ).
fof(f9,plain,
sF0 != sF1,
inference(definition_folding,[],[f4,f8,f6,f6]) ).
fof(f15,definition,
( spl2_1
<=> apply(strong_fixed_point,fixed_pt) = sF0 ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f17,plain,
( apply(strong_fixed_point,fixed_pt) = sF0
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f15]) ).
fof(f18,plain,
spl2_1,
inference(avatar_split_clause,[],[f6,f15]) ).
fof(f23,plain,
! [X2,X0,X1] : apply(apply(w1,X2),apply(apply(b,X0),X1)) = apply(apply(X0,apply(X1,X2)),X2),
inference(superposition,[],[f2,f1]) ).
fof(f25,definition,
( spl2_2
<=> apply(fixed_pt,sF0) = sF1 ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f27,plain,
( apply(fixed_pt,sF0) = sF1
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f28,plain,
spl2_2,
inference(avatar_split_clause,[],[f8,f25]) ).
fof(f31,definition,
( spl2_3
<=> sF0 = sF1 ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f33,plain,
( sF0 != sF1
| spl2_3 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f34,plain,
~ spl2_3,
inference(avatar_split_clause,[],[f9,f31]) ).
fof(f36,definition,
( spl2_4
<=> strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b)),b) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f38,plain,
( strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b)),b)
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f39,plain,
spl2_4,
inference(avatar_split_clause,[],[f3,f36]) ).
fof(f63,plain,
! [X2,X0,X1] : apply(apply(w1,X0),apply(apply(b,apply(b,X1)),X2)) = apply(X1,apply(apply(X2,X0),X0)),
inference(superposition,[],[f1,f23]) ).
fof(f117,plain,
( ! [X0] : apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b),apply(b,X0)) = apply(strong_fixed_point,X0)
| ~ spl2_4 ),
inference(superposition,[],[f1,f38]) ).
fof(f122,plain,
( ! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(b,apply(w1,w1)),apply(b,w1)),apply(b,apply(b,X0)))
| ~ spl2_4 ),
inference(forward_demodulation,[],[f117,f1]) ).
fof(f126,plain,
( ! [X0] : apply(strong_fixed_point,X0) = apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,X0))))
| ~ spl2_4 ),
inference(forward_demodulation,[],[f122,f1]) ).
fof(f129,plain,
( ! [X0] : apply(strong_fixed_point,X0) = apply(apply(w1,apply(apply(b,apply(b,X0)),w1)),w1)
| ~ spl2_4 ),
inference(forward_demodulation,[],[f126,f23]) ).
fof(f170,plain,
! [X0,X1] : apply(apply(w1,apply(apply(b,apply(b,X0)),X1)),w1) = apply(X0,apply(apply(X1,apply(apply(b,apply(b,X0)),X1)),apply(apply(b,apply(b,X0)),X1))),
inference(superposition,[],[f2,f63]) ).
fof(f203,plain,
! [X0,X1] : apply(apply(w1,apply(apply(b,apply(b,X0)),X1)),w1) = apply(X0,apply(apply(w1,apply(apply(b,apply(b,X0)),X1)),X1)),
inference(forward_demodulation,[],[f170,f2]) ).
fof(f2391,plain,
( ! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0))
| ~ spl2_4 ),
inference(superposition,[],[f203,f129]) ).
fof(f2500,plain,
( sF0 = apply(fixed_pt,sF0)
| ~ spl2_1
| ~ spl2_4 ),
inference(superposition,[],[f2391,f17]) ).
fof(f2584,plain,
( sF0 = sF1
| ~ spl2_1
| ~ spl2_2
| ~ spl2_4 ),
inference(forward_demodulation,[],[f2500,f27]) ).
fof(f2591,plain,
( $false
| ~ spl2_1
| ~ spl2_2
| spl2_3
| ~ spl2_4 ),
inference(forward_subsumption_resolution,[],[f2584,f33]) ).
fof(f2592,plain,
( ~ spl2_1
| ~ spl2_2
| spl2_3
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f2591]) ).
cnf(s1,plain,
spl2_1,
inference(sat_conversion,[],[f18]) ).
cnf(s2,plain,
spl2_2,
inference(sat_conversion,[],[f28]) ).
cnf(s3,plain,
~ spl2_3,
inference(sat_conversion,[],[f34]) ).
cnf(s4,plain,
spl2_4,
inference(sat_conversion,[],[f39]) ).
cnf(s7,plain,
( ~ spl2_1
| ~ spl2_2
| spl2_3
| ~ spl2_4 ),
inference(sat_conversion,[],[f2592]) ).
cnf(s8,plain,
~ spl2_1,
inference(rat,[],[s7,s4,s3,s2]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s8]) ).
fof(f2593,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL042-6 : 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 : n009.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 21:30:30 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 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
% 7.47/1.95 % (3507539)Detected a unit-equality problem, will run specialized UEQ schedule.
% 7.47/1.95 % (3507557)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=2111325126:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 7.47/1.95 % (3507562)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1534456468:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 7.47/1.95 % (3507559)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2923289738:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 7.47/1.95 % (3507558)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=1381132194:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 7.47/1.95 % (3507560)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2390857269:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 7.47/1.95 % (3507561)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2460580720:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 7.47/1.95 % (3507563)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3447069342:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 7.47/1.95 % (3507560)Instruction limit reached!
% 7.47/1.95 % (3507560)------------------------------
% 7.47/1.95 % (3507560)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.47/1.95 % (3507560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.47/1.95 % (3507560)CaDiCaL version: 2.1.3
% 7.47/1.95 % (3507560)Termination reason: Instruction limit
% 7.47/1.95 % (3507560)Termination phase: Saturation
% 7.47/1.95 % (3507560)Time elapsed: 0.135 s
% 7.47/1.95 % (3507560)Peak memory usage: 89 MB
% 7.47/1.95 % (3507560)Instructions burned: 136 (million)
% 7.47/1.95 % (3507561)Instruction limit reached!
% 7.47/1.95 % (3507561)------------------------------
% 7.47/1.95 % (3507561)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.47/1.95 % (3507561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.47/1.95 % (3507561)CaDiCaL version: 2.1.3
% 7.47/1.95 % (3507561)Termination reason: Instruction limit
% 7.47/1.95 % (3507561)Termination phase: Saturation
% 7.47/1.95 % (3507561)Time elapsed: 0.145 s
% 7.47/1.95 % (3507561)Peak memory usage: 89 MB
% 7.47/1.95 % (3507561)Instructions burned: 183 (million)
% 7.47/1.95 % (3507562)Instruction limit reached!
% 7.47/1.95 % (3507562)------------------------------
% 7.47/1.95 % (3507562)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.47/1.95 % (3507562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.47/1.95 % (3507562)CaDiCaL version: 2.1.3
% 7.47/1.95 % (3507562)Termination reason: Instruction limit
% 7.47/1.95 % (3507562)Termination phase: Saturation
% 7.47/1.95 % (3507562)Time elapsed: 0.229 s
% 7.47/1.95 % (3507562)Peak memory usage: 91 MB
% 7.47/1.95 % (3507562)Instructions burned: 258 (million)
% 7.47/1.95 % (3507573)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=568185467:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 7.47/1.95 % (3507574)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1930537952:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 7.47/1.95 % (3507575)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=154395500:i=215:ep=RSTC_2995 on theBenchmark for (2995ds/215Mi)
% 7.47/1.95 % (3507575)Refutation not found, incomplete strategy
% 7.47/1.95 % (3507575)------------------------------
% 7.47/1.95 % (3507575)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.47/1.95 % (3507575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.47/1.95 % (3507575)CaDiCaL version: 2.1.3
% 7.47/1.95 % (3507575)Termination reason: Refutation not found, incomplete strategy
% 7.47/1.95 % (3507575)Time elapsed: 0.001 s
% 7.47/1.95 % (3507575)Peak memory usage: 88 MB
% 7.47/1.95 % (3507575)Instructions burned: 1 (million)
% 7.47/1.95 % (3507575)------------------------------
% 7.47/1.95 % (3507575)------------------------------
% 7.47/1.95 % (3507557)First to succeed.
% 7.47/1.95 % (3507557)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3507539"
% 7.47/1.95 % (3507558)Also succeeded, but the first one will report.
% 7.47/1.95 % (3507597)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=562397054:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2992 on theBenchmark for (2992ds/317Mi)
% 7.47/1.95 % (3507563)Instruction limit reached!
% 7.47/1.95 % (3507563)------------------------------
% 7.47/1.95 % (3507563)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.47/1.95 % (3507563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.47/1.95 % (3507563)CaDiCaL version: 2.1.3
% 7.47/1.95 % (3507563)Termination reason: Instruction limit
% 7.47/1.95 % (3507563)Termination phase: Saturation
% 7.47/1.95 % (3507563)Time elapsed: 0.696 s
% 7.47/1.95 % (3507563)Peak memory usage: 95 MB
% 7.47/1.95 % (3507563)Instructions burned: 1187 (million)
% 7.47/1.95 % (3507557)Refutation found. Thanks to Tanya!
% 7.47/1.95 % SZS status Unsatisfiable for theBenchmark
% 7.47/1.95 % SZS output start Proof for theBenchmark
% See solution above
% 7.47/1.95 % (3507557)------------------------------
% 7.47/1.95 % (3507557)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.47/1.95 % (3507557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.47/1.95 % (3507557)CaDiCaL version: 2.1.3
% 7.47/1.95 % (3507557)Termination reason: Refutation
% 7.47/1.95 % (3507557)Time elapsed: 0.669 s
% 7.47/1.95 % (3507557)Peak memory usage: 137 MB
% 7.47/1.95 % (3507557)Instructions burned: 1674 (million)
% 7.47/1.95 % (3507557)------------------------------
% 7.47/1.95 % (3507557)------------------------------
% 7.47/1.95 % (3507539)Success in time 0.944 s
% 7.47/1.95 % Vampire exiting
%------------------------------------------------------------------------------