%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LDA002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:01:24 PM UTC 2026
% Result : Unsatisfiable 0.23s 1.91s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 82 ( 82 unt; 1 def)
% Number of atoms : 82 ( 77 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-2 aty)
% Number of variables : 20 ( 20 !; 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,axiom,
u1 = f(u,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
fof(f6,axiom,
u2 = f(u,n2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
fof(f7,axiom,
u3 = f(u,n3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
fof(f8,axiom,
uu = f(u,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
fof(f9,axiom,
a = f(f(n3,n2),u2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
fof(f10,axiom,
b = f(u1,u3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10) ).
fof(f11,axiom,
v = f(uu,uu),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11) ).
fof(f12,negated_conjecture,
f(a,v) != f(b,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
fof(f13,definition,
~ sP0(f(a,v)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f14,plain,
sP0(f(b,v)),
inference(inequality_splitting,[],[f12,f13]) ).
fof(f16,plain,
! [X0] : f(n2,f(n2,X0)) = f(u,f(n2,X0)),
inference(superposition,[],[f1,f4]) ).
fof(f18,plain,
! [X0] : f(n1,f(n1,X0)) = f(n2,f(n1,X0)),
inference(superposition,[],[f1,f2]) ).
fof(f19,plain,
! [X0] : f(n2,f(n1,X0)) = f(n3,f(n2,X0)),
inference(superposition,[],[f1,f3]) ).
fof(f20,plain,
! [X0] : f(u,f(n1,X0)) = f(u1,f(u,X0)),
inference(superposition,[],[f1,f5]) ).
fof(f21,plain,
! [X0] : f(u,f(n3,X0)) = f(u3,f(u,X0)),
inference(superposition,[],[f1,f7]) ).
fof(f22,plain,
! [X0] : f(u,f(u,X0)) = f(uu,f(u,X0)),
inference(superposition,[],[f1,f8]) ).
fof(f23,plain,
! [X0] : f(f(n3,n2),f(u2,X0)) = f(a,f(f(n3,n2),X0)),
inference(superposition,[],[f1,f9]) ).
fof(f24,plain,
! [X0] : f(u1,f(u3,X0)) = f(b,f(u1,X0)),
inference(superposition,[],[f1,f10]) ).
fof(f27,plain,
! [X0] : f(n2,f(X0,n2)) = f(f(n2,X0),u),
inference(superposition,[],[f1,f4]) ).
fof(f30,plain,
! [X0] : f(n2,f(X0,n1)) = f(f(n2,X0),n3),
inference(superposition,[],[f1,f3]) ).
fof(f33,plain,
! [X0] : f(u,f(X0,u)) = f(f(u,X0),uu),
inference(superposition,[],[f1,f8]) ).
fof(f37,plain,
! [X0] : f(n1,f(n1,X0)) = f(n3,f(n2,X0)),
inference(backward_demodulation,[],[f19,f18]) ).
fof(f39,plain,
f(u,u) = f(n2,u),
inference(superposition,[],[f16,f4]) ).
fof(f44,plain,
uu = f(n2,u),
inference(forward_demodulation,[],[f39,f8]) ).
fof(f48,plain,
f(n2,n2) = f(n1,n2),
inference(superposition,[],[f18,f2]) ).
fof(f53,plain,
u = f(n1,n2),
inference(forward_demodulation,[],[f48,f4]) ).
fof(f56,plain,
f(n2,uu) = f(u,uu),
inference(superposition,[],[f16,f44]) ).
fof(f65,plain,
f(n2,u) = f(n1,u),
inference(superposition,[],[f18,f53]) ).
fof(f67,plain,
! [X0] : f(u,f(n1,X0)) = f(n1,f(n2,X0)),
inference(superposition,[],[f1,f53]) ).
fof(f68,plain,
! [X0] : f(u1,f(u,X0)) = f(n1,f(n2,X0)),
inference(backward_demodulation,[],[f20,f67]) ).
fof(f69,plain,
uu = f(n1,u),
inference(forward_demodulation,[],[f65,f44]) ).
fof(f85,plain,
f(uu,uu) = f(u,uu),
inference(superposition,[],[f22,f8]) ).
fof(f88,plain,
v = f(u,uu),
inference(forward_demodulation,[],[f85,f11]) ).
fof(f91,plain,
v = f(n2,uu),
inference(backward_demodulation,[],[f56,f88]) ).
fof(f99,plain,
f(n2,uu) = f(n1,uu),
inference(superposition,[],[f18,f69]) ).
fof(f102,plain,
v = f(n1,uu),
inference(forward_demodulation,[],[f99,f91]) ).
fof(f111,plain,
f(n2,f(n1,n2)) = f(n3,u),
inference(superposition,[],[f27,f3]) ).
fof(f120,plain,
f(n1,f(n1,n2)) = f(n3,u),
inference(forward_demodulation,[],[f111,f18]) ).
fof(f123,plain,
f(n1,u) = f(n3,u),
inference(forward_demodulation,[],[f120,f53]) ).
fof(f125,plain,
uu = f(n3,u),
inference(forward_demodulation,[],[f123,f69]) ).
fof(f126,plain,
f(u,uu) = f(u3,f(u,u)),
inference(superposition,[],[f21,f125]) ).
fof(f127,plain,
! [X0] : f(n3,f(X0,u)) = f(f(n3,X0),uu),
inference(superposition,[],[f1,f125]) ).
fof(f129,plain,
f(u,uu) = f(u3,uu),
inference(forward_demodulation,[],[f126,f8]) ).
fof(f130,plain,
v = f(u3,uu),
inference(forward_demodulation,[],[f129,f88]) ).
fof(f171,plain,
f(n2,f(n1,n1)) = f(n3,n3),
inference(superposition,[],[f30,f3]) ).
fof(f181,plain,
f(n1,f(n1,n1)) = f(n3,n3),
inference(forward_demodulation,[],[f171,f18]) ).
fof(f183,plain,
f(n1,n2) = f(n3,n3),
inference(forward_demodulation,[],[f181,f2]) ).
fof(f185,plain,
u = f(n3,n3),
inference(forward_demodulation,[],[f183,f53]) ).
fof(f188,plain,
! [X0] : f(u,f(n3,X0)) = f(n3,f(n3,X0)),
inference(superposition,[],[f1,f185]) ).
fof(f250,plain,
f(u,f(n2,u)) = f(u2,uu),
inference(superposition,[],[f33,f6]) ).
fof(f251,plain,
f(u1,uu) = f(u,f(n1,u)),
inference(superposition,[],[f33,f5]) ).
fof(f252,plain,
f(u,f(n3,u)) = f(u3,uu),
inference(superposition,[],[f33,f7]) ).
fof(f260,plain,
v = f(u,f(n3,u)),
inference(forward_demodulation,[],[f252,f130]) ).
fof(f261,plain,
f(u1,uu) = f(n1,f(n2,u)),
inference(forward_demodulation,[],[f251,f67]) ).
fof(f262,plain,
f(n2,f(n2,u)) = f(u2,uu),
inference(forward_demodulation,[],[f250,f16]) ).
fof(f264,plain,
v = f(n3,f(n3,u)),
inference(forward_demodulation,[],[f260,f188]) ).
fof(f265,plain,
f(n1,uu) = f(u1,uu),
inference(forward_demodulation,[],[f261,f44]) ).
fof(f266,plain,
f(n2,uu) = f(u2,uu),
inference(forward_demodulation,[],[f262,f44]) ).
fof(f268,plain,
v = f(n3,uu),
inference(forward_demodulation,[],[f264,f125]) ).
fof(f269,plain,
v = f(u1,uu),
inference(forward_demodulation,[],[f265,f102]) ).
fof(f270,plain,
v = f(u2,uu),
inference(forward_demodulation,[],[f266,f91]) ).
fof(f272,plain,
! [X0] : f(n3,f(X0,uu)) = f(f(n3,X0),v),
inference(superposition,[],[f1,f268]) ).
fof(f285,plain,
f(b,v) = f(u1,f(u3,uu)),
inference(superposition,[],[f24,f269]) ).
fof(f288,plain,
f(b,v) = f(u1,v),
inference(forward_demodulation,[],[f285,f130]) ).
fof(f290,plain,
sP0(f(u1,v)),
inference(backward_demodulation,[],[f14,f288]) ).
fof(f353,plain,
f(u1,v) = f(n1,f(n2,uu)),
inference(superposition,[],[f68,f88]) ).
fof(f360,plain,
f(u1,v) = f(n1,v),
inference(forward_demodulation,[],[f353,f91]) ).
fof(f407,plain,
f(a,f(f(n3,n2),uu)) = f(f(n3,n2),v),
inference(superposition,[],[f23,f270]) ).
fof(f410,plain,
f(n3,f(n2,uu)) = f(a,f(f(n3,n2),uu)),
inference(forward_demodulation,[],[f407,f272]) ).
fof(f412,plain,
f(n3,f(n2,uu)) = f(a,f(n3,f(n2,u))),
inference(forward_demodulation,[],[f410,f127]) ).
fof(f414,plain,
f(n3,f(n2,uu)) = f(a,f(n1,f(n1,u))),
inference(forward_demodulation,[],[f412,f37]) ).
fof(f416,plain,
f(n3,f(n2,uu)) = f(a,f(n1,uu)),
inference(forward_demodulation,[],[f414,f69]) ).
fof(f418,plain,
f(a,v) = f(n3,f(n2,uu)),
inference(forward_demodulation,[],[f416,f102]) ).
fof(f420,plain,
f(a,v) = f(n1,f(n1,uu)),
inference(forward_demodulation,[],[f418,f37]) ).
fof(f421,plain,
f(a,v) = f(n1,v),
inference(forward_demodulation,[],[f420,f102]) ).
fof(f422,plain,
f(a,v) = f(u1,v),
inference(forward_demodulation,[],[f421,f360]) ).
fof(f423,plain,
~ sP0(f(u1,v)),
inference(backward_demodulation,[],[f13,f422]) ).
fof(f424,plain,
$false,
inference(forward_subsumption_resolution,[],[f423,f290]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LDA002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 % Computer : n008.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sun Sep 27 17:10:54 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.48 Running first-order theorem proving
% 0.22/0.49 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/1.91 % (1466656)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.23/1.91 % (1466663)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1474966931:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 0.23/1.91 % (1466667)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=4193309851:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 0.23/1.91 % (1466666)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1060722804:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 0.23/1.91 % (1466664)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2388828396:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 0.23/1.91 % (1466661)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=2960946692:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 0.23/1.91 % (1466665)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=695485537:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 0.23/1.91 % (1466662)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2568158476:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 0.23/1.91 % (1466665)Refutation not found, incomplete strategy
% 0.23/1.91 % (1466665)------------------------------
% 0.23/1.91 % (1466665)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.23/1.91 % (1466665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/1.91 % (1466665)CaDiCaL version: 2.1.3
% 0.23/1.91 % (1466665)Termination reason: Refutation not found, incomplete strategy
% 0.23/1.91 % (1466665)Time elapsed: 0.002 s
% 0.23/1.91 % (1466665)Peak memory usage: 87 MB
% 0.23/1.91 % (1466665)Instructions burned: 1 (million)
% 0.23/1.91 % (1466664)First to succeed.
% 0.23/1.91 % (1466664)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1466656"
% 0.23/1.91 % (1466666)Instruction limit reached!
% 0.23/1.91 % (1466666)------------------------------
% 0.23/1.91 % (1466666)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.23/1.91 % (1466666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/1.91 % (1466666)CaDiCaL version: 2.1.3
% 0.23/1.91 % (1466666)Termination reason: Instruction limit
% 0.23/1.91 % (1466666)Termination phase: Saturation
% 0.23/1.91 % (1466666)Time elapsed: 0.253 s
% 0.23/1.91 % (1466666)Peak memory usage: 91 MB
% 0.23/1.91 % (1466666)Instructions burned: 257 (million)
% 0.23/1.91 % (1466667)Also succeeded, but the first one will report.
% 0.23/1.91 % (1466665)------------------------------
% 0.23/1.91 % (1466665)------------------------------
% 0.23/1.91 % (1466664)Refutation found. Thanks to Tanya!
% 0.23/1.91 % SZS status Unsatisfiable for theBenchmark
% 0.23/1.91 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/1.91 % (1466664)------------------------------
% 0.23/1.91 % (1466664)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.23/1.91 % (1466664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/1.91 % (1466664)CaDiCaL version: 2.1.3
% 0.23/1.91 % (1466664)Termination reason: Refutation
% 0.23/1.91 % (1466664)Time elapsed: 0.029 s
% 0.23/1.91 % (1466664)Peak memory usage: 88 MB
% 0.23/1.91 % (1466664)Instructions burned: 27 (million)
% 0.23/1.91 % (1466664)------------------------------
% 0.23/1.91 % (1466664)------------------------------
% 0.23/1.91 % (1466656)Success in time 0.722 s
% 0.23/1.91 % Vampire exiting
%------------------------------------------------------------------------------