%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n011.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 4.83s 1.89s
% Output : Refutation 4.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 64 ( 64 unt; 9 def)
% Number of atoms : 64 ( 63 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-3 aty)
% Number of variables : 33 ( 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [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,negated_conjecture,
n2 = f(n1,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
fof(f3,negated_conjecture,
n3 = f(n2,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
fof(f4,negated_conjecture,
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,definition,
! [X2,X0,X1] : sF0(X0,X1,X2) = f(X0,f(X1,X2)),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f7,plain,
! [X2,X0,X1] : f(X0,f(X1,X2)) = sF0(X0,X1,X2),
inference(reorient_equations,[],[f6]) ).
fof(f8,definition,
! [X2,X0,X1] : sF1(X0,X1,X2) = f(f(X0,X1),f(X0,X2)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f9,plain,
! [X2,X0,X1] : f(f(X0,X1),f(X0,X2)) = sF1(X0,X1,X2),
inference(reorient_equations,[],[f8]) ).
fof(f10,plain,
! [X2,X0,X1] : sF0(X0,X1,X2) = sF1(X0,X1,X2),
inference(definition_folding,[],[f1,f9,f7]) ).
fof(f11,definition,
sF2 = f(n1,n1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f12,plain,
f(n1,n1) = sF2,
inference(reorient_equations,[],[f11]) ).
fof(f13,plain,
n2 = sF2,
inference(definition_folding,[],[f2,f12]) ).
fof(f14,definition,
sF3 = f(n2,n1),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f15,plain,
f(n2,n1) = sF3,
inference(reorient_equations,[],[f14]) ).
fof(f16,plain,
n3 = sF3,
inference(definition_folding,[],[f3,f15]) ).
fof(f17,definition,
sF4 = f(n2,n2),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f18,plain,
f(n2,n2) = sF4,
inference(reorient_equations,[],[f17]) ).
fof(f19,plain,
u = sF4,
inference(definition_folding,[],[f4,f18]) ).
fof(f20,definition,
sF5 = f(n3,n2),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f21,plain,
f(n3,n2) = sF5,
inference(reorient_equations,[],[f20]) ).
fof(f22,definition,
sF6 = f(sF5,u),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f23,plain,
f(sF5,u) = sF6,
inference(reorient_equations,[],[f22]) ).
fof(f24,definition,
sF7 = f(u,u),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f25,plain,
f(u,u) = sF7,
inference(reorient_equations,[],[f24]) ).
fof(f26,definition,
sF8 = f(sF7,u),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f27,plain,
f(sF7,u) = sF8,
inference(reorient_equations,[],[f26]) ).
fof(f28,plain,
sF6 != sF8,
inference(definition_folding,[],[f5,f27,f25,f23,f21]) ).
fof(f29,plain,
! [X2,X0,X1] : f(f(X0,X1),f(X0,X2)) = sF0(X0,X1,X2),
inference(forward_demodulation,[],[f10,f9]) ).
fof(f30,plain,
! [X2,X0,X1] : f(X0,f(X1,X2)) = f(f(X0,X1),f(X0,X2)),
inference(forward_demodulation,[],[f29,f7]) ).
fof(f32,plain,
! [X0] : f(n3,f(n2,X0)) = f(sF5,f(n3,X0)),
inference(superposition,[],[f30,f21]) ).
fof(f34,plain,
! [X0] : f(n2,f(n1,X0)) = f(sF3,f(n2,X0)),
inference(superposition,[],[f30,f15]) ).
fof(f41,plain,
! [X0] : f(n2,f(X0,n2)) = f(f(n2,X0),sF4),
inference(superposition,[],[f30,f18]) ).
fof(f42,plain,
! [X0] : f(n2,f(X0,n1)) = f(f(n2,X0),sF3),
inference(superposition,[],[f30,f15]) ).
fof(f43,plain,
! [X0] : f(n1,f(X0,n1)) = f(f(n1,X0),sF2),
inference(superposition,[],[f30,f12]) ).
fof(f47,plain,
! [X0] : f(n1,f(X0,n1)) = f(f(n1,X0),n2),
inference(forward_demodulation,[],[f43,f13]) ).
fof(f48,plain,
! [X0] : f(n2,f(X0,n1)) = f(f(n2,X0),n3),
inference(forward_demodulation,[],[f42,f16]) ).
fof(f49,plain,
! [X0] : f(n2,f(X0,n2)) = f(f(n2,X0),u),
inference(forward_demodulation,[],[f41,f19]) ).
fof(f51,plain,
! [X0] : f(n3,f(n2,X0)) = f(n2,f(n1,X0)),
inference(forward_demodulation,[],[f34,f16]) ).
fof(f111,plain,
f(n1,sF2) = f(sF2,n2),
inference(superposition,[],[f47,f12]) ).
fof(f114,plain,
f(n2,n2) = f(n1,n2),
inference(forward_demodulation,[],[f111,f13]) ).
fof(f115,plain,
sF4 = f(n1,n2),
inference(forward_demodulation,[],[f114,f18]) ).
fof(f116,plain,
u = f(n1,n2),
inference(forward_demodulation,[],[f115,f19]) ).
fof(f117,plain,
f(n1,f(n2,n1)) = f(u,n2),
inference(superposition,[],[f47,f116]) ).
fof(f120,plain,
f(u,n2) = f(n1,sF3),
inference(forward_demodulation,[],[f117,f15]) ).
fof(f121,plain,
f(u,n2) = f(n1,n3),
inference(forward_demodulation,[],[f120,f16]) ).
fof(f126,plain,
f(n2,f(n1,n1)) = f(sF3,n3),
inference(superposition,[],[f48,f15]) ).
fof(f129,plain,
f(n2,f(n1,n1)) = f(n3,n3),
inference(forward_demodulation,[],[f126,f16]) ).
fof(f131,plain,
f(n3,n3) = f(n2,sF2),
inference(forward_demodulation,[],[f129,f12]) ).
fof(f133,plain,
f(n2,n2) = f(n3,n3),
inference(forward_demodulation,[],[f131,f13]) ).
fof(f135,plain,
sF4 = f(n3,n3),
inference(forward_demodulation,[],[f133,f18]) ).
fof(f136,plain,
u = f(n3,n3),
inference(forward_demodulation,[],[f135,f19]) ).
fof(f138,plain,
f(sF5,u) = f(n3,f(n2,n3)),
inference(superposition,[],[f32,f136]) ).
fof(f141,plain,
sF6 = f(n3,f(n2,n3)),
inference(forward_demodulation,[],[f138,f23]) ).
fof(f155,plain,
f(n2,sF4) = f(sF4,u),
inference(superposition,[],[f49,f18]) ).
fof(f160,plain,
f(u,u) = f(n2,u),
inference(forward_demodulation,[],[f155,f19]) ).
fof(f162,plain,
sF7 = f(n2,u),
inference(forward_demodulation,[],[f160,f25]) ).
fof(f163,plain,
f(sF7,u) = f(n2,f(u,n2)),
inference(superposition,[],[f49,f162]) ).
fof(f167,plain,
sF8 = f(n2,f(u,n2)),
inference(forward_demodulation,[],[f163,f27]) ).
fof(f237,plain,
sF6 = f(n2,f(n1,n3)),
inference(superposition,[],[f141,f51]) ).
fof(f243,plain,
sF6 = f(n2,f(u,n2)),
inference(forward_demodulation,[],[f237,f121]) ).
fof(f248,plain,
sF6 = sF8,
inference(forward_demodulation,[],[f243,f167]) ).
fof(f260,plain,
sF6 != sF6,
inference(superposition,[],[f28,f248]) ).
fof(f261,plain,
$false,
inference(trivial_inequality_removal,[],[f260]) ).
%------------------------------------------------------------------------------
%----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 THM
% 0.14/0.41 % Computer : n011.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sun Sep 27 17:10:15 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.47 Running first-order theorem proving
% 0.14/0.47 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
% 4.83/1.89 % (2633995)Detected a unit-equality problem, will run specialized UEQ schedule.
% 4.83/1.89 % (2634005)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=2304942328:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 4.83/1.89 % (2634008)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2182357665:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 4.83/1.89 % (2634008)First to succeed.
% 4.83/1.89 % (2634008)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2633995"
% 4.83/1.89 % (2634004)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=3002828192:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 4.83/1.89 % (2634007)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=102279091:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 4.83/1.89 % (2634006)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3268646279:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 4.83/1.89 % (2634007)Also succeeded, but the first one will report.
% 4.83/1.89 % (2634010)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=4003245587:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 4.83/1.89 % (2634009)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=555306552:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 4.83/1.89 % (2634010)Also succeeded, but the first one will report.
% 4.83/1.89 % (2634008)Refutation found. Thanks to Tanya!
% 4.83/1.89 % SZS status Unsatisfiable for theBenchmark
% 4.83/1.89 % SZS output start Proof for theBenchmark
% See solution above
% 4.83/1.90 % (2634008)------------------------------
% 4.83/1.90 % (2634008)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.83/1.90 % (2634008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.83/1.90 % (2634008)CaDiCaL version: 2.1.3
% 4.83/1.90 % (2634008)Termination reason: Refutation
% 4.83/1.90 % (2634008)Time elapsed: 0.010 s
% 4.83/1.90 % (2634008)Peak memory usage: 88 MB
% 4.83/1.90 % (2634008)Instructions burned: 13 (million)
% 4.83/1.90 % (2634008)------------------------------
% 4.83/1.90 % (2634008)------------------------------
% 4.83/1.90 % (2633995)Success in time 0.569 s
% 4.83/1.90 % Vampire exiting
%------------------------------------------------------------------------------