%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL003-14 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 09:38:06 AM UTC 2026
% Result : Unsatisfiable 1.83s 0.58s
% Output : Refutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 13 unt; 0 def)
% Number of atoms : 13 ( 12 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 1 ( 1 ~; 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 16 ( 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(apply(b,apply(w,w)),apply(apply(b,w),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,plain,
! [X0] : apply(apply(w,w),X0) = apply(apply(X0,X0),X0),
inference(superposition,[],[f2,f2]) ).
fof(f10,plain,
! [X0,X1] : apply(apply(w,apply(b,X0)),X1) = apply(X0,apply(X1,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f13,plain,
! [X0] : apply(apply(apply(b,apply(w,w)),apply(apply(b,w),b)),apply(b,X0)) = apply(strong_fixed_point,X0),
inference(superposition,[],[f1,f3]) ).
fof(f70,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,f10]) ).
fof(f310,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,X0))),
inference(superposition,[],[f1,f13]) ).
fof(f318,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(w,w),apply(w,apply(b,apply(b,X0)))),
inference(forward_demodulation,[],[f310,f1]) ).
fof(f3028,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,[],[f70,f5]) ).
fof(f3259,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0)),
inference(forward_demodulation,[],[f3028,f318]) ).
fof(f3311,plain,
$false,
inference(backward_subsumption_resolution,[],[f4,f3259]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL003-14 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 % Computer : n007.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Mon Sep 28 21:26:40 UTC 2026
% 0.07/0.21 % CPUTime :
% 0.07/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.26 Running first-order model finding
% 0.07/0.26 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.83/0.58 % (2865120)Will run a generic schedule for satisfiability detection.
% 1.83/0.58 % (2865128)dis+10_1_sil=32000:sp=arity:random_seed=4038302895:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.83/0.58 % (2865126)% WARNING: option uhcvi not known.
% 1.83/0.58 % (2865126)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3694889744:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.83/0.58 % (2865127)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1748989252:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.83/0.58 % (2865129)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3089122409:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.83/0.58 % (2865125)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1000158820_2999 on theBenchmark for (2999ds/0Mi)
% 1.83/0.58 % (2865131)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=731830244:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.83/0.58 % (2865130)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=523631512:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.83/0.58 % TRYING [1]
% 1.83/0.58 % TRYING [2]
% 1.83/0.58 % TRYING [3]
% 1.83/0.58 % TRYING [4]
% 1.83/0.58 % (2865128)Instruction limit reached!
% 1.83/0.58 % (2865128)------------------------------
% 1.83/0.58 % (2865128)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.58 % (2865128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.58 % (2865128)CaDiCaL version: 2.1.3
% 1.83/0.58 % (2865128)Termination reason: Instruction limit
% 1.83/0.58 % (2865128)Termination phase: Saturation
% 1.83/0.58 % (2865128)Time elapsed: 0.050 s
% 1.83/0.58 % (2865128)Peak memory usage: 12 MB
% 1.83/0.58 % (2865128)Instructions burned: 104 (million)
% 1.83/0.58 % (2865139)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3176767472:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.83/0.58 % TRYING [1]
% 1.83/0.58 % TRYING [2]
% 1.83/0.58 % TRYING [3]
% 1.83/0.58 % TRYING [4]
% 1.83/0.58 % TRYING [5]
% 1.83/0.58 % (2865129)Instruction limit reached!
% 1.83/0.58 % (2865129)------------------------------
% 1.83/0.58 % (2865129)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.58 % (2865129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.58 % (2865129)CaDiCaL version: 2.1.3
% 1.83/0.58 % (2865129)Termination reason: Instruction limit
% 1.83/0.58 % (2865129)Termination phase: Saturation
% 1.83/0.58 % (2865129)Time elapsed: 0.117 s
% 1.83/0.58 % (2865129)Peak memory usage: 12 MB
% 1.83/0.58 % (2865129)Instructions burned: 116 (million)
% 1.83/0.58 % (2865130)Instruction limit reached!
% 1.83/0.58 % (2865130)------------------------------
% 1.83/0.58 % (2865130)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.58 % (2865130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.58 % (2865130)CaDiCaL version: 2.1.3
% 1.83/0.58 % (2865130)Termination reason: Instruction limit
% 1.83/0.58 % (2865130)Termination phase: Saturation
% 1.83/0.58 % (2865130)Time elapsed: 0.130 s
% 1.83/0.58 % (2865130)Peak memory usage: 13 MB
% 1.83/0.58 % (2865130)Instructions burned: 132 (million)
% 1.83/0.58 % TRYING [5]
% 1.83/0.58 % (2865131)Instruction limit reached!
% 1.83/0.58 % (2865131)------------------------------
% 1.83/0.58 % (2865131)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.58 % (2865131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.58 % (2865131)CaDiCaL version: 2.1.3
% 1.83/0.58 % (2865131)Termination reason: Instruction limit
% 1.83/0.58 % (2865131)Termination phase: Saturation
% 1.83/0.58 % (2865131)Time elapsed: 0.155 s
% 1.83/0.58 % (2865131)Peak memory usage: 12 MB
% 1.83/0.58 % (2865131)Instructions burned: 159 (million)
% 1.83/0.58 % (2865141)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2896932223:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.83/0.58 % (2865142)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=2061183972:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.83/0.58 % (2865143)ott-21_1_sil=16000:fs=off:random_seed=3633919405:i=180:av=off:fsr=off_2997 on theBenchmark for (2997ds/180Mi)
% 1.83/0.58 % (2865126) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2865120-2865126"...
% 1.83/0.58 % (2865126)...printing done.
% 1.83/0.58 % (2865126)Refutation found. Thanks to Tanya!
% 1.83/0.58 % SZS status Unsatisfiable for theBenchmark
% 1.83/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 1.83/0.58 % (2865126)------------------------------
% 1.83/0.58 % (2865126)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.58 % (2865126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.58 % (2865126)CaDiCaL version: 2.1.3
% 1.83/0.58 % (2865126)Termination reason: Refutation
% 1.83/0.58 % (2865126)Time elapsed: 0.242 s
% 1.83/0.58 % (2865126)Peak memory usage: 13 MB
% 1.83/0.58 % (2865126)Instructions burned: 267 (million)
% 1.83/0.58 % (2865120)Success in time 0.297 s
% 1.83/0.58 % Vampire exiting
%------------------------------------------------------------------------------