%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL063-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 09:38:19 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.15s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 5 ( 5 !; 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(t,X0),X1) = apply(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t_definition) ).
fof(f3,negated_conjecture,
apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))),x),y),z) != apply(apply(z,y),x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_f_combinator) ).
fof(f4,plain,
apply(apply(z,y),x) != apply(apply(apply(apply(t,t),apply(apply(apply(b,b),apply(apply(b,b),t)),x)),y),z),
inference(superposition,[],[f3,f1]) ).
fof(f5,plain,
apply(apply(z,y),x) != apply(apply(apply(apply(apply(apply(b,b),apply(apply(b,b),t)),x),t),y),z),
inference(forward_demodulation,[],[f4,f2]) ).
fof(f6,plain,
apply(apply(z,y),x) != apply(apply(apply(apply(b,apply(apply(apply(b,b),t),x)),t),y),z),
inference(forward_demodulation,[],[f5,f1]) ).
fof(f7,plain,
apply(apply(z,y),x) != apply(apply(apply(apply(apply(b,b),t),x),apply(t,y)),z),
inference(forward_demodulation,[],[f6,f1]) ).
fof(f8,plain,
apply(apply(z,y),x) != apply(apply(apply(b,apply(t,x)),apply(t,y)),z),
inference(forward_demodulation,[],[f7,f1]) ).
fof(f9,plain,
apply(apply(z,y),x) != apply(apply(t,x),apply(apply(t,y),z)),
inference(forward_demodulation,[],[f8,f1]) ).
fof(f10,plain,
apply(apply(z,y),x) != apply(apply(apply(t,y),z),x),
inference(forward_demodulation,[],[f9,f2]) ).
fof(f11,plain,
apply(apply(z,y),x) != apply(apply(z,y),x),
inference(forward_demodulation,[],[f10,f2]) ).
fof(f12,plain,
$false,
inference(trivial_inequality_removal,[],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COL063-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Mon Sep 28 21:32:00 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.13 Running first-order model finding
% 0.08/0.13 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
% 0.08/0.15 % (3803423)Will run a generic schedule for satisfiability detection.
% 0.08/0.15 % (3803429)% WARNING: option uhcvi not known.
% 0.08/0.15 % (3803431)dis+10_1_sil=32000:sp=arity:random_seed=3361054575:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.15 % (3803430)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2777203400:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.15 % (3803428)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3633968170_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.15 % (3803429)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3698676360:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.15 % (3803432)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2636592701:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.15 % (3803433)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=922513010:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.15 % (3803434)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1827088203:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.15 % (3803431) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3803423-3803431"...
% 0.08/0.15 % (3803430) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3803423-3803430"...
% 0.08/0.15 % (3803429) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3803423-3803429"...
% 0.08/0.15 % TRYING [1]
% 0.08/0.15 % (3803432) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3803423-3803432"...
% 0.08/0.15 % TRYING [2]
% 0.08/0.15 % (3803430)...printing done.
% 0.08/0.15 % (3803431)...printing done.
% 0.08/0.15 % (3803433) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3803423-3803433"...
% 0.08/0.15 % TRYING [3]
% 0.08/0.15 % (3803429)...printing done.
% 0.08/0.15 % (3803432)...printing done.
% 0.08/0.15 % (3803431)Refutation found. Thanks to Tanya!
% 0.08/0.15 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.15 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.15 % (3803431)------------------------------
% 0.08/0.15 % (3803431)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.15 % (3803431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.15 % (3803431)CaDiCaL version: 2.1.3
% 0.08/0.15 % (3803431)Termination reason: Refutation
% 0.08/0.15 % (3803431)Time elapsed: 0.001 s
% 0.08/0.15 % (3803431)Peak memory usage: 11 MB
% 0.08/0.15 % (3803431)Instructions burned: 1 (million)
% 0.08/0.15 % (3803423)Success in time 0.022 s
% 0.08/0.15 % Vampire exiting
%------------------------------------------------------------------------------