%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LDA002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 0.52s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 67 ( 67 unt; 0 def)
% Number of atoms : 67 ( 66 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-2 aty)
% Number of variables : 16 ( 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : f(X0,f(X1,X2)) = f(f(X0,X1),f(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
fof(f2,axiom,
n2 = f(n1,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
fof(f3,axiom,
n3 = f(n2,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
fof(f4,axiom,
u = f(n2,n2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
fof(f5,axiom,
u1 = f(u,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
fof(f6,axiom,
u2 = f(u,n2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
fof(f7,axiom,
u3 = f(u,n3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7) ).
fof(f8,axiom,
uu = f(u,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8) ).
fof(f9,axiom,
a = f(f(n3,n2),u2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9) ).
fof(f10,axiom,
b = f(u1,u3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_10) ).
fof(f11,axiom,
v = f(uu,uu),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_11) ).
fof(f12,negated_conjecture,
f(a,v) != f(b,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
fof(f14,plain,
! [X0] : f(n2,f(n2,X0)) = f(u,f(n2,X0)),
inference(superposition,[],[f1,f4]) ).
fof(f16,plain,
! [X0] : f(n1,f(n1,X0)) = f(n2,f(n1,X0)),
inference(superposition,[],[f1,f2]) ).
fof(f17,plain,
! [X0] : f(n2,f(n1,X0)) = f(n3,f(n2,X0)),
inference(superposition,[],[f1,f3]) ).
fof(f18,plain,
! [X0] : f(u,f(n1,X0)) = f(u1,f(u,X0)),
inference(superposition,[],[f1,f5]) ).
fof(f20,plain,
! [X0] : f(u,f(u,X0)) = f(uu,f(u,X0)),
inference(superposition,[],[f1,f8]) ).
fof(f21,plain,
! [X0] : f(f(n3,n2),f(u2,X0)) = f(a,f(f(n3,n2),X0)),
inference(superposition,[],[f1,f9]) ).
fof(f23,plain,
! [X0] : f(uu,f(uu,X0)) = f(v,f(uu,X0)),
inference(superposition,[],[f1,f11]) ).
fof(f26,plain,
! [X0] : f(u,f(X0,n2)) = f(f(u,X0),u2),
inference(superposition,[],[f1,f6]) ).
fof(f27,plain,
! [X0] : f(n1,f(X0,n1)) = f(f(n1,X0),n2),
inference(superposition,[],[f1,f2]) ).
fof(f31,plain,
! [X0] : f(u,f(X0,u)) = f(f(u,X0),uu),
inference(superposition,[],[f1,f8]) ).
fof(f34,plain,
! [X0] : f(uu,f(X0,uu)) = f(f(uu,X0),v),
inference(superposition,[],[f1,f11]) ).
fof(f35,plain,
f(u,u) = f(n2,u),
inference(superposition,[],[f14,f4]) ).
fof(f40,plain,
uu = f(n2,u),
inference(forward_demodulation,[],[f35,f8]) ).
fof(f44,plain,
f(n2,uu) = f(u,uu),
inference(superposition,[],[f14,f40]) ).
fof(f53,plain,
f(n2,n2) = f(n1,n2),
inference(superposition,[],[f16,f2]) ).
fof(f56,plain,
u = f(n1,n2),
inference(forward_demodulation,[],[f53,f4]) ).
fof(f57,plain,
f(n2,u) = f(n1,u),
inference(superposition,[],[f16,f56]) ).
fof(f60,plain,
uu = f(n1,u),
inference(forward_demodulation,[],[f57,f40]) ).
fof(f67,plain,
f(n2,f(n1,n2)) = f(n3,u),
inference(superposition,[],[f17,f4]) ).
fof(f75,plain,
f(n2,u) = f(n3,u),
inference(forward_demodulation,[],[f67,f56]) ).
fof(f77,plain,
uu = f(n3,u),
inference(forward_demodulation,[],[f75,f40]) ).
fof(f80,plain,
! [X0] : f(n3,f(X0,u)) = f(f(n3,X0),uu),
inference(superposition,[],[f1,f77]) ).
fof(f93,plain,
f(u1,u3) = f(u,f(n1,n3)),
inference(superposition,[],[f18,f7]) ).
fof(f101,plain,
b = f(u,f(n1,n3)),
inference(forward_demodulation,[],[f93,f10]) ).
fof(f158,plain,
f(u,u2) = f(uu,u2),
inference(superposition,[],[f20,f6]) ).
fof(f161,plain,
f(uu,uu) = f(u,uu),
inference(superposition,[],[f20,f8]) ).
fof(f168,plain,
f(uu,uu) = f(n2,uu),
inference(forward_demodulation,[],[f161,f44]) ).
fof(f171,plain,
v = f(n2,uu),
inference(forward_demodulation,[],[f168,f11]) ).
fof(f224,plain,
f(uu,v) = f(v,v),
inference(superposition,[],[f23,f11]) ).
fof(f265,plain,
f(u,f(n2,n2)) = f(u2,u2),
inference(superposition,[],[f26,f6]) ).
fof(f277,plain,
f(n2,f(n2,n2)) = f(u2,u2),
inference(forward_demodulation,[],[f265,f14]) ).
fof(f279,plain,
f(n2,u) = f(u2,u2),
inference(forward_demodulation,[],[f277,f4]) ).
fof(f280,plain,
uu = f(u2,u2),
inference(forward_demodulation,[],[f279,f40]) ).
fof(f290,plain,
f(u,n2) = f(n1,f(n2,n1)),
inference(superposition,[],[f27,f56]) ).
fof(f299,plain,
f(u,n2) = f(n1,n3),
inference(forward_demodulation,[],[f290,f3]) ).
fof(f300,plain,
u2 = f(n1,n3),
inference(forward_demodulation,[],[f299,f6]) ).
fof(f301,plain,
b = f(u,u2),
inference(superposition,[],[f101,f300]) ).
fof(f513,plain,
f(u,f(n2,u)) = f(u2,uu),
inference(superposition,[],[f31,f6]) ).
fof(f527,plain,
f(n2,f(n2,u)) = f(u2,uu),
inference(forward_demodulation,[],[f513,f14]) ).
fof(f535,plain,
f(n2,uu) = f(u2,uu),
inference(forward_demodulation,[],[f527,f40]) ).
fof(f538,plain,
v = f(u2,uu),
inference(forward_demodulation,[],[f535,f171]) ).
fof(f609,plain,
f(uu,f(u2,uu)) = f(f(u,u2),v),
inference(superposition,[],[f34,f158]) ).
fof(f616,plain,
f(b,v) = f(uu,f(u2,uu)),
inference(forward_demodulation,[],[f609,f301]) ).
fof(f623,plain,
f(b,v) = f(uu,v),
inference(forward_demodulation,[],[f616,f538]) ).
fof(f632,plain,
f(a,v) != f(uu,v),
inference(superposition,[],[f12,f623]) ).
fof(f1562,plain,
f(f(n3,n2),uu) = f(a,f(f(n3,n2),u2)),
inference(superposition,[],[f21,f280]) ).
fof(f1570,plain,
f(f(n3,n2),uu) = f(a,a),
inference(forward_demodulation,[],[f1562,f9]) ).
fof(f1573,plain,
f(n3,f(n2,u)) = f(a,a),
inference(forward_demodulation,[],[f1570,f80]) ).
fof(f1575,plain,
f(n2,f(n1,u)) = f(a,a),
inference(forward_demodulation,[],[f1573,f17]) ).
fof(f1577,plain,
f(n2,uu) = f(a,a),
inference(forward_demodulation,[],[f1575,f60]) ).
fof(f1578,plain,
v = f(a,a),
inference(forward_demodulation,[],[f1577,f171]) ).
fof(f1579,plain,
! [X0] : f(a,f(X0,a)) = f(f(a,X0),v),
inference(superposition,[],[f1,f1578]) ).
fof(f2439,plain,
f(a,v) = f(v,v),
inference(superposition,[],[f1579,f1578]) ).
fof(f2442,plain,
f(a,v) = f(uu,v),
inference(forward_demodulation,[],[f2439,f224]) ).
fof(f2443,plain,
$false,
inference(forward_subsumption_resolution,[],[f2442,f632]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LDA002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n004.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 17:10:07 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 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
% 0.18/0.52 % (3759522)Will run a generic schedule for satisfiability detection.
% 0.18/0.52 % (3759533)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=758382651:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.18/0.52 % (3759529)% WARNING: option uhcvi not known.
% 0.18/0.52 % (3759528)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3288970598_3000 on theBenchmark for (3000ds/0Mi)
% 0.18/0.52 % (3759531)dis+10_1_sil=32000:sp=arity:random_seed=2066904609:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.18/0.52 % (3759530)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=313866102:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.18/0.52 % (3759534)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=496649544:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.18/0.52 % (3759532)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=954356093:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.18/0.52 % (3759529)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=858367966:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.18/0.52 % TRYING [1]
% 0.18/0.52 % TRYING [2]
% 0.18/0.52 % TRYING [3]
% 0.18/0.52 % TRYING [4]
% 0.18/0.52 % TRYING [5]
% 0.18/0.52 % (3759533)Instruction limit reached!
% 0.18/0.52 % (3759533)------------------------------
% 0.18/0.52 % (3759533)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.52 % (3759533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.52 % (3759533)CaDiCaL version: 2.1.3
% 0.18/0.52 % (3759533)Termination reason: Instruction limit
% 0.18/0.52 % (3759533)Termination phase: Saturation
% 0.18/0.52 % (3759533)Time elapsed: 0.041 s
% 0.18/0.52 % (3759533)Peak memory usage: 12 MB
% 0.18/0.52 % (3759533)Instructions burned: 133 (million)
% 0.18/0.52 % (3759566)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3863616032:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.18/0.52 % TRYING [1]
% 0.18/0.52 % TRYING [2]
% 0.18/0.52 % TRYING [3]
% 0.18/0.52 % TRYING [4]
% 0.18/0.52 % TRYING [5]
% 0.18/0.52 % (3759531)Instruction limit reached!
% 0.18/0.52 % (3759531)------------------------------
% 0.18/0.52 % (3759531)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.52 % (3759531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.52 % (3759531)CaDiCaL version: 2.1.3
% 0.18/0.52 % (3759531)Termination reason: Instruction limit
% 0.18/0.52 % (3759531)Termination phase: Saturation
% 0.18/0.52 % (3759531)Time elapsed: 0.055 s
% 0.18/0.52 % (3759531)Peak memory usage: 12 MB
% 0.18/0.52 % (3759531)Instructions burned: 105 (million)
% 0.18/0.52 % (3759530) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3759522-3759530"...
% 0.18/0.52 % TRYING [6]
% 0.18/0.52 % (3759530)...printing done.
% 0.18/0.52 % (3759530)Refutation found. Thanks to Tanya!
% 0.18/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.52 % (3759530)------------------------------
% 0.18/0.52 % (3759530)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.52 % (3759530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.52 % (3759530)CaDiCaL version: 2.1.3
% 0.18/0.52 % (3759530)Termination reason: Refutation
% 0.18/0.52 % (3759530)Time elapsed: 0.063 s
% 0.18/0.52 % (3759530)Peak memory usage: 12 MB
% 0.18/0.52 % (3759530)Instructions burned: 125 (million)
% 0.18/0.52 % (3759522)Success in time 0.087 s
% 0.18/0.52 % Vampire exiting
%------------------------------------------------------------------------------