%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL042-9 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 09:38:14 AM UTC 2026
% Result : Unsatisfiable 3.70s 0.94s
% Output : Refutation 3.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 20 unt; 2 def)
% Number of atoms : 20 ( 19 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 18 ( 18 !; 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(w1,X0),X1) = apply(apply(X1,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w1_definition) ).
fof(f3,axiom,
strong_fixed_point = apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(b,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(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(f19,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(f21,plain,
! [X0] : apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),apply(apply(b,b),b)),X0)) = apply(strong_fixed_point,X0),
inference(superposition,[],[f1,f3]) ).
fof(f24,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(w1,w1),apply(apply(b,w1),apply(apply(apply(b,b),b),X0))),
inference(forward_demodulation,[],[f21,f1]) ).
fof(f26,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,X0)))),
inference(forward_demodulation,[],[f24,f1]) ).
fof(f215,plain,
! [X0,X1] : apply(apply(X0,apply(X1,X0)),apply(X1,X0)) = apply(apply(w1,X0),apply(apply(b,w1),X1)),
inference(superposition,[],[f2,f19]) ).
fof(f217,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,f19]) ).
fof(f1901,plain,
! [X0] : apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,X0)))) = apply(X0,apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,X0))))),
inference(superposition,[],[f217,f215]) ).
fof(f2126,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0)),
inference(forward_demodulation,[],[f1901,f26]) ).
fof(f2171,plain,
sF0 = apply(fixed_pt,sF0),
inference(superposition,[],[f2126,f6]) ).
fof(f2301,plain,
sF0 = sF1,
inference(superposition,[],[f8,f2171]) ).
fof(f2315,plain,
$false,
inference(forward_subsumption_resolution,[],[f2301,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COL042-9 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.26 % Computer : n002.cluster.edu
% 0.09/0.26 % Model : x86_64 x86_64
% 0.09/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.26 % Memory : 8046.5625MB
% 0.09/0.26 % OS : Linux 6.8.0-71-generic
% 0.09/0.26 % CPULimit : 300
% 0.09/0.26 % WCLimit : 300
% 0.09/0.26 % DateTime : Mon Sep 28 21:33:08 UTC 2026
% 0.09/0.26 % CPUTime :
% 0.09/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.26/0.31 Running first-order model finding
% 0.26/0.31 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.70/0.94 % (795441)Will run a generic schedule for satisfiability detection.
% 3.70/0.94 % (795452)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1041034650:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 3.70/0.94 % (795447)% WARNING: option uhcvi not known.
% 3.70/0.94 % (795449)dis+10_1_sil=32000:sp=arity:random_seed=3256240546:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 3.70/0.94 % (795446)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1679840978_3000 on theBenchmark for (3000ds/0Mi)
% 3.70/0.94 % (795451)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3793791302:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 3.70/0.94 % (795448)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3962135791:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 3.70/0.94 % (795450)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3735494523:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 3.70/0.94 % (795447)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4083891817:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 3.70/0.94 % TRYING [1]
% 3.70/0.94 % TRYING [2]
% 3.70/0.94 % TRYING [3]
% 3.70/0.94 % TRYING [4]
% 3.70/0.94 % (795452)Instruction limit reached!
% 3.70/0.94 % (795452)------------------------------
% 3.70/0.94 % (795452)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.70/0.94 % (795452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/0.94 % (795452)CaDiCaL version: 2.1.3
% 3.70/0.94 % (795452)Termination reason: Instruction limit
% 3.70/0.94 % (795452)Termination phase: Saturation
% 3.70/0.94 % (795452)Time elapsed: 0.082 s
% 3.70/0.94 % (795452)Peak memory usage: 12 MB
% 3.70/0.94 % (795452)Instructions burned: 159 (million)
% 3.70/0.94 % TRYING [5]
% 3.70/0.94 % (795462)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2828590131:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 3.70/0.94 % TRYING [1]
% 3.70/0.94 % TRYING [2]
% 3.70/0.94 % TRYING [3]
% 3.70/0.94 % TRYING [4]
% 3.70/0.94 % (795449)Instruction limit reached!
% 3.70/0.94 % (795449)------------------------------
% 3.70/0.94 % (795449)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.70/0.94 % (795449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/0.94 % (795449)CaDiCaL version: 2.1.3
% 3.70/0.94 % (795449)Termination reason: Instruction limit
% 3.70/0.94 % (795449)Termination phase: Saturation
% 3.70/0.94 % (795449)Time elapsed: 0.098 s
% 3.70/0.94 % (795449)Peak memory usage: 12 MB
% 3.70/0.94 % (795449)Instructions burned: 106 (million)
% 3.70/0.94 % (795450)Instruction limit reached!
% 3.70/0.94 % (795450)------------------------------
% 3.70/0.94 % (795450)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.70/0.94 % (795450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/0.94 % (795450)CaDiCaL version: 2.1.3
% 3.70/0.94 % (795450)Termination reason: Instruction limit
% 3.70/0.94 % (795450)Termination phase: Saturation
% 3.70/0.94 % (795450)Time elapsed: 0.119 s
% 3.70/0.94 % (795450)Peak memory usage: 12 MB
% 3.70/0.94 % (795450)Instructions burned: 116 (million)
% 3.70/0.94 % (795464)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1225578343:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 3.70/0.94 % TRYING [5]
% 3.70/0.94 % (795451)Instruction limit reached!
% 3.70/0.94 % (795451)------------------------------
% 3.70/0.94 % (795451)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.70/0.94 % (795451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/0.94 % (795451)CaDiCaL version: 2.1.3
% 3.70/0.94 % (795451)Termination reason: Instruction limit
% 3.70/0.94 % (795451)Termination phase: Saturation
% 3.70/0.94 % (795451)Time elapsed: 0.134 s
% 3.70/0.94 % (795451)Peak memory usage: 13 MB
% 3.70/0.94 % (795451)Instructions burned: 131 (million)
% 3.70/0.94 % (795465)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=969034065:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 3.70/0.94 % (795468)ott-21_1_sil=16000:fs=off:random_seed=2299216424:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.70/0.94 % (795464)Instruction limit reached!
% 3.70/0.94 % (795464)------------------------------
% 3.70/0.94 % (795464)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.70/0.94 % (795464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/0.94 % (795464)CaDiCaL version: 2.1.3
% 3.70/0.94 % (795464)Termination reason: Instruction limit
% 3.70/0.94 % (795464)Termination phase: Saturation
% 3.70/0.94 % (795464)Time elapsed: 0.138 s
% 3.70/0.94 % (795464)Peak memory usage: 13 MB
% 3.70/0.94 % (795464)Instructions burned: 131 (million)
% 3.70/0.94 % (795468)Instruction limit reached!
% 3.70/0.94 % (795468)------------------------------
% 3.70/0.94 % (795468)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.70/0.94 % (795468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/0.94 % (795468)CaDiCaL version: 2.1.3
% 3.70/0.94 % (795468)Termination reason: Instruction limit
% 3.70/0.94 % (795468)Termination phase: Saturation
% 3.70/0.94 % (795468)Time elapsed: 0.133 s
% 3.70/0.94 % (795468)Peak memory usage: 11 MB
% 3.70/0.94 % (795468)Instructions burned: 182 (million)
% 3.70/0.94 % (795473)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=986031451:i=477:bd=all_2996 on theBenchmark for (2996ds/477Mi)
% 3.70/0.94 % (795474)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=4267272107:fmbsr=1.3:i=865:ins=25_2996 on theBenchmark for (2996ds/865Mi)
% 3.70/0.94 % TRYING [1]
% 3.70/0.94 % TRYING [2]
% 3.70/0.94 % TRYING [3]
% 3.70/0.94 % TRYING [4]
% 3.70/0.94 % TRYING [5]
% 3.70/0.94 % TRYING [6]
% 3.70/0.94 % (795462)Instruction limit reached!
% 3.70/0.94 % (795462)------------------------------
% 3.70/0.94 % (795462)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.70/0.94 % (795462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/0.94 % (795462)CaDiCaL version: 2.1.3
% 3.70/0.94 % (795462)Termination reason: Instruction limit
% 3.70/0.94 % (795462)Termination phase: Finite model building constraint generation
% 3.70/0.94 % (795462)Time elapsed: 0.353 s
% 3.70/0.94 % (795462)Peak memory usage: 14 MB
% 3.70/0.94 % (795462)Instructions burned: 717 (million)
% 3.70/0.94 % (795478)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=887817659:i=1179_2995 on theBenchmark for (2995ds/1179Mi)
% 3.70/0.94 % TRYING [6]
% 3.70/0.94 % TRYING [6]
% 3.70/0.94 % (795478) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-795441-795478"...
% 3.70/0.94 % (795478)...printing done.
% 3.70/0.94 % (795478)Refutation found. Thanks to Tanya!
% 3.70/0.94 % SZS status Unsatisfiable for theBenchmark
% 3.70/0.94 % SZS output start Proof for theBenchmark
% See solution above
% 3.70/0.94 % (795478)------------------------------
% 3.70/0.94 % (795478)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.70/0.94 % (795478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/0.94 % (795478)CaDiCaL version: 2.1.3
% 3.70/0.94 % (795478)Termination reason: Refutation
% 3.70/0.94 % (795478)Time elapsed: 0.114 s
% 3.70/0.94 % (795478)Peak memory usage: 15 MB
% 3.70/0.94 % (795478)Instructions burned: 204 (million)
% 3.70/0.94 % (795441)Success in time 0.614 s
% 3.70/0.94 % Vampire exiting
%------------------------------------------------------------------------------