%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LDA001-1 : TPTP v9.3.1. Released v1.0.0.
% 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 12:01:28 PM UTC 2026
% Result : Unsatisfiable 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 24 unt; 0 def)
% Number of atoms : 24 ( 23 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 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 : 9 ( 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : f(X0,f(X1,X2)) = f(f(X0,X1),f(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
fof(f2,axiom,
n2 = f(n1,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
fof(f3,axiom,
n3 = f(n2,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
fof(f4,axiom,
u = f(n2,n2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
fof(f5,negated_conjecture,
f(f(n3,n2),u) != f(f(u,u),u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
fof(f6,plain,
! [X0] : f(n1,f(n1,X0)) = f(n2,f(n1,X0)),
inference(superposition,[],[f1,f2]) ).
fof(f7,plain,
! [X0] : f(n2,f(n1,X0)) = f(n3,f(n2,X0)),
inference(superposition,[],[f1,f3]) ).
fof(f8,plain,
! [X0] : f(n2,f(n2,X0)) = f(u,f(n2,X0)),
inference(superposition,[],[f1,f4]) ).
fof(f10,plain,
! [X0] : f(n1,f(X0,n1)) = f(f(n1,X0),n2),
inference(superposition,[],[f1,f2]) ).
fof(f12,plain,
! [X0] : f(n2,f(X0,n2)) = f(f(n2,X0),u),
inference(superposition,[],[f1,f4]) ).
fof(f14,plain,
f(n2,n2) = f(n1,n2),
inference(superposition,[],[f6,f2]) ).
fof(f18,plain,
u = f(n1,n2),
inference(forward_demodulation,[],[f14,f4]) ).
fof(f19,plain,
f(n2,f(n1,n1)) = f(n3,n3),
inference(superposition,[],[f7,f3]) ).
fof(f23,plain,
f(n2,n2) = f(n3,n3),
inference(forward_demodulation,[],[f19,f2]) ).
fof(f24,plain,
u = f(n3,n3),
inference(forward_demodulation,[],[f23,f4]) ).
fof(f26,plain,
f(u,u) = f(n2,u),
inference(superposition,[],[f8,f4]) ).
fof(f33,plain,
f(n1,f(n2,n1)) = f(u,n2),
inference(superposition,[],[f10,f18]) ).
fof(f37,plain,
f(u,n2) = f(n1,n3),
inference(forward_demodulation,[],[f33,f3]) ).
fof(f46,plain,
! [X0] : f(n3,f(X0,n3)) = f(f(n3,X0),u),
inference(superposition,[],[f1,f24]) ).
fof(f468,plain,
f(f(u,u),u) != f(n3,f(n2,n3)),
inference(superposition,[],[f5,f46]) ).
fof(f478,plain,
f(f(u,u),u) != f(n2,f(n1,n3)),
inference(forward_demodulation,[],[f468,f7]) ).
fof(f483,plain,
f(f(u,u),u) != f(n2,f(u,n2)),
inference(forward_demodulation,[],[f478,f37]) ).
fof(f486,plain,
f(n2,f(u,n2)) != f(f(n2,u),u),
inference(forward_demodulation,[],[f483,f26]) ).
fof(f488,plain,
$false,
inference(forward_subsumption_resolution,[],[f486,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LDA001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n004.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 17:10:07 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.43 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
% 0.18/0.48 % (3759444)Will run a generic schedule for satisfiability detection.
% 0.18/0.48 % (3759455)% WARNING: option uhcvi not known.
% 0.18/0.48 % (3759455)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3408031582:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.48 % (3759457)dis+10_1_sil=32000:sp=arity:random_seed=4202511437:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.48 % (3759456)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3878569171:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.48 % (3759459)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4046815587:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.48 % (3759458)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=585779792:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.48 % (3759454)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=765822789_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.48 % TRYING [1]
% 0.18/0.48 % (3759455) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3759444-3759455"...
% 0.18/0.48 % TRYING [2]
% 0.18/0.48 % TRYING [3]
% 0.18/0.48 % (3759460)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=370909073:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.48 % (3759455)...printing done.
% 0.18/0.48 % (3759455)Refutation found. Thanks to Tanya!
% 0.18/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.48 % (3759455)------------------------------
% 0.18/0.48 % (3759455)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.48 % (3759455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.48 % (3759455)CaDiCaL version: 2.1.3
% 0.18/0.48 % (3759455)Termination reason: Refutation
% 0.18/0.48 % (3759455)Time elapsed: 0.009 s
% 0.18/0.48 % (3759455)Peak memory usage: 11 MB
% 0.18/0.48 % (3759455)Instructions burned: 29 (million)
% 0.18/0.48 % (3759444)Success in time 0.041 s
% 0.18/0.48 % Vampire exiting
%------------------------------------------------------------------------------