%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL003-16 : 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 : n004.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 1.71s 0.56s
% Output : Refutation 1.71s
% 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 : 8 ( 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/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(apply(b,apply(w,w)),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(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(f22,plain,
! [X0] : apply(apply(apply(b,apply(apply(b,apply(w,w)),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(f234,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(b,apply(w,w)),w),apply(b,apply(b,X0))),
inference(superposition,[],[f22,f1]) ).
fof(f740,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(w,w),apply(w,apply(b,apply(b,X0)))),
inference(superposition,[],[f234,f1]) ).
fof(f3533,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(f3785,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0)),
inference(forward_demodulation,[],[f3533,f740]) ).
fof(f3846,plain,
$false,
inference(backward_subsumption_resolution,[],[f4,f3785]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL003-16 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n004.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 21:28:52 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 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
% 1.71/0.56 % (803754)Will run a generic schedule for satisfiability detection.
% 1.71/0.56 % (803762)dis+10_1_sil=32000:sp=arity:random_seed=3683586769:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 1.71/0.56 % (803760)% WARNING: option uhcvi not known.
% 1.71/0.56 % (803765)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1799454319:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 1.71/0.56 % (803759)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1325166558_3000 on theBenchmark for (3000ds/0Mi)
% 1.71/0.56 % (803760)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=15882385:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 1.71/0.56 % (803761)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2286465154:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 1.71/0.56 % (803763)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=164287151:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 1.71/0.56 % (803764)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1890577562:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 1.71/0.56 % TRYING [1]
% 1.71/0.56 % TRYING [2]
% 1.71/0.56 % TRYING [3]
% 1.71/0.56 % TRYING [4]
% 1.71/0.56 % (803762)Instruction limit reached!
% 1.71/0.56 % (803762)------------------------------
% 1.71/0.56 % (803762)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.71/0.56 % (803762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.71/0.56 % (803762)CaDiCaL version: 2.1.3
% 1.71/0.56 % (803762)Termination reason: Instruction limit
% 1.71/0.56 % (803762)Termination phase: Saturation
% 1.71/0.56 % (803762)Time elapsed: 0.051 s
% 1.71/0.56 % (803762)Peak memory usage: 12 MB
% 1.71/0.56 % (803762)Instructions burned: 104 (million)
% 1.71/0.56 % (803774)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=630234162:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.71/0.56 % TRYING [1]
% 1.71/0.56 % TRYING [2]
% 1.71/0.56 % TRYING [3]
% 1.71/0.56 % TRYING [4]
% 1.71/0.56 % TRYING [5]
% 1.71/0.56 % (803763)Instruction limit reached!
% 1.71/0.56 % (803763)------------------------------
% 1.71/0.56 % (803763)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.71/0.56 % (803763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.71/0.56 % (803763)CaDiCaL version: 2.1.3
% 1.71/0.56 % (803763)Termination reason: Instruction limit
% 1.71/0.56 % (803763)Termination phase: Saturation
% 1.71/0.56 % (803763)Time elapsed: 0.109 s
% 1.71/0.56 % (803763)Peak memory usage: 12 MB
% 1.71/0.56 % (803763)Instructions burned: 116 (million)
% 1.71/0.56 % TRYING [5]
% 1.71/0.56 % (803764)Instruction limit reached!
% 1.71/0.56 % (803764)------------------------------
% 1.71/0.56 % (803764)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.71/0.56 % (803764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.71/0.56 % (803764)CaDiCaL version: 2.1.3
% 1.71/0.56 % (803764)Termination reason: Instruction limit
% 1.71/0.56 % (803764)Termination phase: Saturation
% 1.71/0.56 % (803764)Time elapsed: 0.121 s
% 1.71/0.56 % (803764)Peak memory usage: 12 MB
% 1.71/0.56 % (803764)Instructions burned: 131 (million)
% 1.71/0.56 % (803782)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3146381082:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.71/0.56 % (803765)Instruction limit reached!
% 1.71/0.56 % (803765)------------------------------
% 1.71/0.56 % (803765)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.71/0.56 % (803765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.71/0.56 % (803765)CaDiCaL version: 2.1.3
% 1.71/0.56 % (803765)Termination reason: Instruction limit
% 1.71/0.56 % (803765)Termination phase: Saturation
% 1.71/0.56 % (803765)Time elapsed: 0.148 s
% 1.71/0.56 % (803765)Peak memory usage: 12 MB
% 1.71/0.56 % (803765)Instructions burned: 159 (million)
% 1.71/0.56 % (803783)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=2265385460:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.71/0.56 % (803785)ott-21_1_sil=16000:fs=off:random_seed=4259249617:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.71/0.56 % (803782)Instruction limit reached!
% 1.71/0.56 % (803782)------------------------------
% 1.71/0.56 % (803782)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.71/0.56 % (803782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.71/0.56 % (803782)CaDiCaL version: 2.1.3
% 1.71/0.56 % (803782)Termination reason: Instruction limit
% 1.71/0.56 % (803782)Termination phase: Saturation
% 1.71/0.56 % (803782)Time elapsed: 0.138 s
% 1.71/0.56 % (803782)Peak memory usage: 13 MB
% 1.71/0.56 % (803782)Instructions burned: 132 (million)
% 1.71/0.56 % (803760) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-803754-803760"...
% 1.71/0.56 % (803760)...printing done.
% 1.71/0.56 % (803760)Refutation found. Thanks to Tanya!
% 1.71/0.56 % SZS status Unsatisfiable for theBenchmark
% 1.71/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 1.71/0.56 % (803760)------------------------------
% 1.71/0.56 % (803760)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.71/0.56 % (803760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.71/0.56 % (803760)CaDiCaL version: 2.1.3
% 1.71/0.56 % (803760)Termination reason: Refutation
% 1.71/0.56 % (803760)Time elapsed: 0.274 s
% 1.71/0.56 % (803760)Peak memory usage: 13 MB
% 1.71/0.56 % (803760)Instructions burned: 309 (million)
% 1.71/0.56 % (803754)Success in time 0.311 s
% 1.71/0.56 % Vampire exiting
%------------------------------------------------------------------------------