%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL043-2 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 09:38:15 AM UTC 2026
% Result : Unsatisfiable 0.91s 0.50s
% Output : Refutation 0.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 17 unt; 0 def)
% Number of atoms : 19 ( 16 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 10 ~; 1 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 26 !; 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,
! [X2,X0,X1] : apply(apply(apply(h,X0),X1),X2) = apply(apply(apply(X0,X1),X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_definition) ).
fof(f3,axiom,
! [X0] :
( fixed_point(X0)
| apply(X0,fixed_pt) != apply(fixed_pt,apply(X0,fixed_pt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f4,negated_conjecture,
~ fixed_point(apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
fof(f5,plain,
apply(apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b),fixed_pt) != apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b),fixed_pt)),
inference(resolution,[],[f3,f4]) ).
fof(f6,plain,
apply(apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b),apply(b,fixed_pt)) != apply(fixed_pt,apply(apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b),apply(b,fixed_pt))),
inference(forward_demodulation,[],[f5,f1]) ).
fof(f7,plain,
apply(apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h),apply(b,apply(b,fixed_pt))) != apply(fixed_pt,apply(apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h),apply(b,apply(b,fixed_pt)))),
inference(forward_demodulation,[],[f6,f1]) ).
fof(f9,plain,
! [X2,X3,X0,X1] : apply(apply(apply(h,apply(apply(b,X0),X1)),X2),X3) = apply(apply(apply(X0,apply(X1,X2)),X3),X2),
inference(superposition,[],[f2,f1]) ).
fof(f12,plain,
! [X2,X0,X1] : apply(apply(apply(h,apply(b,X0)),X1),X2) = apply(apply(X0,apply(X1,X2)),X1),
inference(superposition,[],[f2,f1]) ).
fof(f184,plain,
! [X2,X0,X1] : apply(X0,apply(apply(X1,X2),X1)) = apply(apply(apply(h,apply(b,apply(b,X0))),X1),X2),
inference(superposition,[],[f1,f12]) ).
fof(f590,plain,
! [X2,X3,X0,X1,X4,X5] : apply(apply(apply(h,apply(apply(b,X4),apply(apply(h,apply(apply(b,X0),X1)),X2))),X3),X5) = apply(apply(apply(X4,apply(apply(apply(X0,apply(X1,X2)),X3),X2)),X5),X3),
inference(superposition,[],[f9,f9]) ).
fof(f655,plain,
apply(apply(apply(apply(apply(b,h),apply(b,b)),apply(apply(h,apply(apply(b,h),apply(b,b))),h)),apply(b,apply(b,fixed_pt))),h) != apply(fixed_pt,apply(apply(apply(apply(apply(b,h),apply(b,b)),apply(apply(h,apply(apply(b,h),apply(b,b))),h)),apply(b,apply(b,fixed_pt))),h)),
inference(superposition,[],[f7,f9]) ).
fof(f677,plain,
! [X2,X0,X1] : apply(apply(X0,X1),apply(X2,X1)) = apply(apply(apply(h,apply(apply(b,b),X0)),X1),X2),
inference(superposition,[],[f1,f9]) ).
fof(f699,plain,
apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h) != apply(fixed_pt,apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h)),
inference(forward_demodulation,[],[f655,f1]) ).
fof(f714,plain,
apply(apply(apply(b,apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h)),h),apply(b,apply(b,fixed_pt))) != apply(fixed_pt,apply(apply(apply(b,apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h)),h),apply(b,apply(b,fixed_pt)))),
inference(forward_demodulation,[],[f699,f590]) ).
fof(f715,plain,
apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt))))),
inference(forward_demodulation,[],[f714,f1]) ).
fof(f716,plain,
apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt))))),
inference(forward_demodulation,[],[f715,f677]) ).
fof(f717,plain,
$false,
inference(forward_subsumption_resolution,[],[f716,f184]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL043-2 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.26/0.31 % Computer : n019.cluster.edu
% 0.26/0.31 % Model : x86_64 x86_64
% 0.26/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.26/0.31 % Memory : 8046.5625MB
% 0.26/0.31 % OS : Linux 6.8.0-71-generic
% 0.26/0.31 % CPULimit : 300
% 0.26/0.31 % WCLimit : 300
% 0.26/0.31 % DateTime : Mon Sep 28 21:30:48 UTC 2026
% 0.26/0.32 % CPUTime :
% 0.26/0.32 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.26/0.37 Running first-order model finding
% 0.26/0.37 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
% 0.91/0.50 % (297356)Will run a generic schedule for satisfiability detection.
% 0.91/0.50 % (297361)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=826846855_2999 on theBenchmark for (2999ds/0Mi)
% 0.91/0.50 % TRYING [1]
% 0.91/0.50 % TRYING [2]
% 0.91/0.50 % TRYING [3]
% 0.91/0.50 % (297362)% WARNING: option uhcvi not known.
% 0.91/0.50 % TRYING [4]
% 0.91/0.50 % (297362)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4124499106:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.91/0.50 % (297365)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3628995117:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.91/0.50 % (297363)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2119639729:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.91/0.50 % (297364)dis+10_1_sil=32000:sp=arity:random_seed=3931677863:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.91/0.50 % (297366)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2243131373:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.91/0.50 % (297367)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2717621840:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.91/0.50 % TRYING [5]
% 0.91/0.50 % (297365) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-297356-297365"...
% 0.91/0.50 % (297365)...printing done.
% 0.91/0.50 % (297365)Refutation found. Thanks to Tanya!
% 0.91/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.91/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.91/0.50 % (297365)------------------------------
% 0.91/0.50 % (297365)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.50 % (297365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.50 % (297365)CaDiCaL version: 2.1.3
% 0.91/0.50 % (297365)Termination reason: Refutation
% 0.91/0.50 % (297365)Time elapsed: 0.064 s
% 0.91/0.50 % (297365)Peak memory usage: 12 MB
% 0.91/0.50 % (297365)Instructions burned: 62 (million)
% 0.91/0.50 % (297356)Success in time 0.115 s
% 0.91/0.50 % Vampire exiting
%------------------------------------------------------------------------------