%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n001.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 0.19s 0.33s
% Output : Refutation 0.19s
% 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(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(f5,plain,
! [X0] : apply(apply(w,w),X0) = apply(apply(X0,X0),X0),
inference(superposition,[],[f2,f2]) ).
fof(f16,plain,
! [X0,X1] : apply(apply(w,apply(b,X0)),X1) = apply(X0,apply(X1,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f44,plain,
! [X0] : apply(apply(w,w),apply(apply(apply(b,w),apply(apply(b,b),b)),X0)) = apply(strong_fixed_point,X0),
inference(superposition,[],[f1,f3]) ).
fof(f47,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(w,w),apply(w,apply(apply(apply(b,b),b),X0))),
inference(forward_demodulation,[],[f44,f1]) ).
fof(f48,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(w,w),apply(w,apply(b,apply(b,X0)))),
inference(forward_demodulation,[],[f47,f1]) ).
fof(f72,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,f16]) ).
fof(f2979,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,[],[f72,f5]) ).
fof(f3209,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0)),
inference(forward_demodulation,[],[f2979,f48]) ).
fof(f3261,plain,
$false,
inference(backward_subsumption_resolution,[],[f4,f3209]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.08/0.18 % Computer : n001.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 21:34:34 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.22 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
% 0.19/0.33 % (773020)Will run a generic schedule for satisfiability detection.
% 0.19/0.33 % (773026)% WARNING: option uhcvi not known.
% 0.19/0.33 % (773026)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2288352947:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.33 % (773025)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3090318012_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.33 % (773027)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2988863444:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.33 % (773028)dis+10_1_sil=32000:sp=arity:random_seed=1304295871:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.33 % (773029)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=469779180:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.33 % (773031)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=69753929:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.33 % (773030)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3754641803:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.33 % TRYING [1]
% 0.19/0.33 % TRYING [2]
% 0.19/0.33 % TRYING [3]
% 0.19/0.33 % TRYING [4]
% 0.19/0.33 % (773028)Instruction limit reached!
% 0.19/0.33 % (773028)------------------------------
% 0.19/0.33 % (773028)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.33 % (773028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.33 % (773028)CaDiCaL version: 2.1.3
% 0.19/0.33 % (773028)Termination reason: Instruction limit
% 0.19/0.33 % (773028)Termination phase: Saturation
% 0.19/0.33 % (773028)Time elapsed: 0.056 s
% 0.19/0.33 % (773028)Peak memory usage: 12 MB
% 0.19/0.33 % (773028)Instructions burned: 104 (million)
% 0.19/0.33 % (773026) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-773020-773026"...
% 0.19/0.33 % (773026)...printing done.
% 0.19/0.33 % (773026)Refutation found. Thanks to Tanya!
% 0.19/0.33 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.33 % (773026)------------------------------
% 0.19/0.33 % (773026)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.33 % (773026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.33 % (773026)CaDiCaL version: 2.1.3
% 0.19/0.33 % (773026)Termination reason: Refutation
% 0.19/0.33 % (773026)Time elapsed: 0.074 s
% 0.19/0.33 % (773026)Peak memory usage: 13 MB
% 0.19/0.33 % (773026)Instructions burned: 265 (million)
% 0.19/0.33 % (773020)Success in time 0.102 s
% 0.19/0.33 % Vampire exiting
%------------------------------------------------------------------------------