%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL058-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 09:37:46 AM UTC 2026
% Result : Unsatisfiable 2.78s 1.19s
% Output : Refutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 42 ( 42 unt; 10 def)
% Number of atoms : 42 ( 41 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 32 ( 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0,X1] : response(response(lark,X0),X1) = response(X0,response(X1,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lark_exists) ).
fof(f2,negated_conjecture,
response(response(response(lark,response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(lark,response(lark,lark))),response(response(lark,response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(lark,response(lark,lark)))) != response(response(lark,response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(lark,response(lark,lark))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_the_bird_exists) ).
fof(f3,plain,
response(response(lark,response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(lark,response(lark,lark))) != response(response(response(lark,response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(lark,response(lark,lark))),response(response(lark,response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(lark,response(lark,lark)))),
inference(reorient_equations,[],[f2]) ).
fof(f4,definition,
! [X0] : sF0(X0) = response(lark,X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f5,plain,
! [X0] : response(lark,X0) = sF0(X0),
inference(reorient_equations,[],[f4]) ).
fof(f6,definition,
! [X0,X1] : sF1(X0,X1) = response(sF0(X0),X1),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f7,plain,
! [X0,X1] : response(sF0(X0),X1) = sF1(X0,X1),
inference(reorient_equations,[],[f6]) ).
fof(f8,definition,
! [X1] : sF2(X1) = response(X1,X1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f9,plain,
! [X1] : response(X1,X1) = sF2(X1),
inference(reorient_equations,[],[f8]) ).
fof(f10,definition,
! [X0,X1] : sF3(X0,X1) = response(X0,sF2(X1)),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f11,plain,
! [X0,X1] : response(X0,sF2(X1)) = sF3(X0,X1),
inference(reorient_equations,[],[f10]) ).
fof(f12,plain,
! [X0,X1] : sF1(X0,X1) = sF3(X0,X1),
inference(definition_folding,[],[f1,f11,f9,f7,f5]) ).
fof(f13,definition,
sF4 = response(lark,lark),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f14,plain,
response(lark,lark) = sF4,
inference(reorient_equations,[],[f13]) ).
fof(f15,definition,
sF5 = response(lark,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f16,plain,
response(lark,sF4) = sF5,
inference(reorient_equations,[],[f15]) ).
fof(f17,definition,
sF6 = response(sF5,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f18,plain,
response(sF5,sF5) = sF6,
inference(reorient_equations,[],[f17]) ).
fof(f19,definition,
sF7 = response(lark,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f20,plain,
response(lark,sF6) = sF7,
inference(reorient_equations,[],[f19]) ).
fof(f21,definition,
sF8 = response(sF7,sF5),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f22,plain,
response(sF7,sF5) = sF8,
inference(reorient_equations,[],[f21]) ).
fof(f23,definition,
sF9 = response(sF8,sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f24,plain,
response(sF8,sF8) = sF9,
inference(reorient_equations,[],[f23]) ).
fof(f25,plain,
sF8 != sF9,
inference(definition_folding,[],[f3,f24,f22,f16,f14,f20,f18,f16,f14,f16,f14,f22,f16,f14,f20,f18,f16,f14,f16,f14,f22,f16,f14,f20,f18,f16,f14,f16,f14]) ).
fof(f26,plain,
! [X0,X1] : sF1(X0,X1) = response(X0,sF2(X1)),
inference(forward_demodulation,[],[f12,f11]) ).
fof(f27,plain,
! [X0,X1] : response(X0,response(X1,X1)) = sF1(X0,X1),
inference(forward_demodulation,[],[f26,f9]) ).
fof(f28,plain,
! [X0,X1] : response(X0,response(X1,X1)) = response(sF0(X0),X1),
inference(forward_demodulation,[],[f27,f7]) ).
fof(f29,plain,
! [X0,X1] : response(response(lark,X0),X1) = response(X0,response(X1,X1)),
inference(forward_demodulation,[],[f28,f5]) ).
fof(f30,plain,
! [X0] : response(sF6,response(X0,X0)) = response(sF7,X0),
inference(superposition,[],[f29,f20]) ).
fof(f31,plain,
! [X0] : response(sF4,response(X0,X0)) = response(sF5,X0),
inference(superposition,[],[f29,f16]) ).
fof(f33,plain,
! [X0,X1] : response(response(X0,X0),response(X1,X1)) = response(response(response(lark,lark),X0),X1),
inference(superposition,[],[f29,f29]) ).
fof(f36,plain,
! [X0,X1] : response(response(X0,X0),response(X1,X1)) = response(response(sF4,X0),X1),
inference(forward_demodulation,[],[f33,f14]) ).
fof(f40,plain,
sF8 = response(sF6,response(sF5,sF5)),
inference(superposition,[],[f22,f30]) ).
fof(f41,plain,
sF8 = response(sF6,sF6),
inference(forward_demodulation,[],[f40,f18]) ).
fof(f44,plain,
sF6 = response(sF4,sF6),
inference(superposition,[],[f31,f18]) ).
fof(f67,plain,
! [X0] : response(sF8,response(X0,X0)) = response(response(sF4,sF6),X0),
inference(superposition,[],[f36,f41]) ).
fof(f93,plain,
! [X0] : response(sF8,response(X0,X0)) = response(sF6,X0),
inference(forward_demodulation,[],[f67,f44]) ).
fof(f108,plain,
sF8 = response(sF8,sF8),
inference(superposition,[],[f93,f41]) ).
fof(f110,plain,
sF8 = sF9,
inference(forward_demodulation,[],[f108,f24]) ).
fof(f113,plain,
sF8 != sF8,
inference(superposition,[],[f25,f110]) ).
fof(f114,plain,
$false,
inference(trivial_inequality_removal,[],[f113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL058-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n006.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 21:31:10 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.78/1.18 % (227542)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.78/1.18 % (227557)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1230557473:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.78/1.18 % (227557)First to succeed.
% 2.78/1.18 % (227557)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-227542"
% 2.78/1.18 % (227559)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=711357767:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.78/1.18 % (227558)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2372054087:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.78/1.18 % (227555)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3256158883:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.78/1.18 % (227553)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=280730726:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.78/1.19 % (227556)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=417592546:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.78/1.19 % (227554)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=2581338367:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.78/1.19 % (227556)Also succeeded, but the first one will report.
% 2.78/1.19 % (227558)Also succeeded, but the first one will report.
% 2.78/1.19 % (227559)Also succeeded, but the first one will report.
% 2.78/1.19 % (227557)Refutation found. Thanks to Tanya!
% 2.78/1.19 % SZS status Unsatisfiable for theBenchmark
% 2.78/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 2.78/1.19 % (227557)------------------------------
% 2.78/1.19 % (227557)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.19 % (227557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.19 % (227557)CaDiCaL version: 2.1.3
% 2.78/1.19 % (227557)Termination reason: Refutation
% 2.78/1.19 % (227557)Time elapsed: 0.003 s
% 2.78/1.19 % (227557)Peak memory usage: 88 MB
% 2.78/1.19 % (227557)Instructions burned: 7 (million)
% 2.78/1.19 % (227557)------------------------------
% 2.78/1.19 % (227557)------------------------------
% 2.78/1.19 % (227542)Success in time 0.297 s
% 2.78/1.19 % Vampire exiting
%------------------------------------------------------------------------------