%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LAT394-2 : TPTP v9.3.1. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 11:47:35 AM UTC 2026
% Result : Unsatisfiable 6.42s 1.85s
% Output : Refutation 6.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 2
% Syntax : Number of formulae : 42 ( 42 unt; 0 def)
% Number of atoms : 42 ( 41 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 93 ( 93 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] : f(f(f(f(X0,X1),f(X1,X2)),X3),f(X1,f(f(X1,f(f(X0,X0),X0)),X2))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos) ).
fof(f2,negated_conjecture,
f(x0,f(x0,x0)) != f(x1,f(x1,x1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f5,plain,
! [X2,X3,X0,X1] : f(f(X0,X3),f(X0,f(f(X0,f(f(f(f(X1,X0),f(X0,X2)),f(f(X1,X0),f(X0,X2))),f(f(X1,X0),f(X0,X2)))),f(f(X0,f(f(X1,X1),X1)),X2)))) = X0,
inference(superposition,[],[f1,f1]) ).
fof(f6,plain,
! [X2,X3,X0,X1] : f(X0,X2) = f(X0,f(f(X0,X2),f(f(f(X0,X2),f(f(f(X1,X0),f(X1,X0)),f(X1,X0))),X3))),
inference(superposition,[],[f1,f1]) ).
fof(f12,plain,
! [X2,X0,X1] : f(f(X1,X0),f(X0,X2)) = f(f(X1,X0),f(f(f(X1,X0),f(X0,X2)),X0)),
inference(superposition,[],[f6,f1]) ).
fof(f14,plain,
! [X2,X0,X1] : f(X0,X1) = f(X0,f(f(X0,X1),f(f(f(X2,X0),f(X2,X0)),f(X2,X0)))),
inference(superposition,[],[f6,f6]) ).
fof(f26,plain,
! [X2,X0,X1] : f(f(f(f(X1,X0),f(X0,X2)),X0),f(X0,X0)) = X0,
inference(superposition,[],[f12,f1]) ).
fof(f44,plain,
! [X0] : f(f(X0,X0),f(X0,X0)) = X0,
inference(superposition,[],[f26,f1]) ).
fof(f57,plain,
! [X0,X1] : f(f(X0,X1),f(X0,f(f(X0,f(f(X0,X0),X0)),X0))) = X0,
inference(superposition,[],[f1,f44]) ).
fof(f85,plain,
! [X0,X1] : f(X0,X1) = f(X0,f(f(X0,X1),f(X0,X1))),
inference(superposition,[],[f6,f57]) ).
fof(f100,plain,
! [X2,X3,X0,X1] : f(f(f(f(X1,X0),f(X0,X2)),X3),f(X0,X0)) = X0,
inference(superposition,[],[f85,f1]) ).
fof(f101,plain,
! [X0,X1] : f(f(X0,X1),f(X0,X0)) = X0,
inference(superposition,[],[f85,f57]) ).
fof(f170,plain,
! [X2,X0,X1] : f(f(X0,X1),f(X1,f(f(X1,f(f(X0,X0),X0)),X2))) = X1,
inference(superposition,[],[f1,f5]) ).
fof(f200,plain,
! [X0,X1] : f(X0,X0) = f(f(f(X0,X0),X1),X0),
inference(superposition,[],[f101,f44]) ).
fof(f219,plain,
! [X2,X0] : f(X0,f(f(X0,X0),X2)) = f(X0,f(f(X0,f(f(X0,X0),X2)),f(X0,X0))),
inference(superposition,[],[f12,f101]) ).
fof(f230,plain,
! [X2,X0] : f(X0,X0) = f(X0,f(f(X0,X0),X2)),
inference(forward_demodulation,[],[f219,f101]) ).
fof(f242,plain,
! [X0,X1] : f(f(X0,X0),f(X0,X0)) = f(f(X0,X0),f(X0,X1)),
inference(superposition,[],[f12,f200]) ).
fof(f271,plain,
! [X0,X1] : f(f(X0,X0),f(X0,X1)) = X0,
inference(forward_demodulation,[],[f242,f101]) ).
fof(f278,plain,
! [X0,X1] : f(X0,X1) = f(f(f(X0,X1),f(X0,X1)),X0),
inference(superposition,[],[f271,f57]) ).
fof(f877,plain,
! [X0,X1] : f(f(X0,X1),f(X1,X1)) = X1,
inference(superposition,[],[f100,f101]) ).
fof(f1042,plain,
! [X0,X1] : f(f(X0,X0),f(X1,X0)) = X0,
inference(superposition,[],[f278,f877]) ).
fof(f1078,plain,
! [X0,X1] : f(X0,X0) = f(X0,f(X1,f(X0,X0))),
inference(superposition,[],[f1042,f44]) ).
fof(f1754,plain,
! [X0,X1] : f(f(X0,X1),f(X1,f(f(X0,X0),X0))) = X1,
inference(superposition,[],[f170,f170]) ).
fof(f1811,plain,
! [X0,X1] : f(X1,X0) = f(X0,f(f(X1,X0),f(f(f(X1,X0),f(f(f(X1,X0),f(X1,X0)),f(X1,X0))),f(X1,X0)))),
inference(superposition,[],[f57,f170]) ).
fof(f1820,plain,
! [X0,X1] : f(X1,X0) = f(X0,f(f(X1,X0),f(f(f(X1,X0),f(X1,X0)),f(X1,X0)))),
inference(forward_demodulation,[],[f1811,f230]) ).
fof(f1831,plain,
! [X0,X1] : f(X1,X0) = f(X0,f(f(X1,X0),f(X1,X0))),
inference(forward_demodulation,[],[f1820,f230]) ).
fof(f1858,plain,
! [X0,X1] : f(f(f(X0,X0),X1),f(X1,f(X0,f(X0,X0)))) = X1,
inference(superposition,[],[f1754,f44]) ).
fof(f2212,plain,
! [X0,X1] : f(X0,X1) = f(X0,f(f(X0,X1),f(X0,f(X0,X0)))),
inference(superposition,[],[f14,f44]) ).
fof(f2522,plain,
! [X2,X0,X1] : f(f(f(f(X1,X0),f(X0,f(X0,f(X0,X0)))),X2),f(X0,f(f(X1,X1),X1))) = X0,
inference(superposition,[],[f1,f2212]) ).
fof(f2580,plain,
! [X2,X0,X1] : f(f(f(f(X1,X0),f(X0,X0)),X2),f(X0,f(f(X1,X1),X1))) = X0,
inference(forward_demodulation,[],[f2522,f1078]) ).
fof(f2587,plain,
! [X2,X0,X1] : f(f(X0,X2),f(X0,f(f(X1,X1),X1))) = X0,
inference(forward_demodulation,[],[f2580,f877]) ).
fof(f2850,plain,
! [X0,X1] : f(X0,X0) = f(X0,f(f(X1,X1),X1)),
inference(superposition,[],[f85,f2587]) ).
fof(f2969,plain,
! [X0,X1] : f(f(X0,X0),f(f(X1,X1),X1)) = X0,
inference(superposition,[],[f2850,f44]) ).
fof(f2978,plain,
! [X0,X1] : f(X1,X1) = f(X1,f(X0,f(X0,X0))),
inference(superposition,[],[f2850,f44]) ).
fof(f3335,plain,
! [X0,X1] : f(f(X1,X1),f(X0,f(X0,X0))) = X1,
inference(superposition,[],[f2969,f44]) ).
fof(f3718,plain,
! [X0,X1] : f(X0,X0) = f(f(X1,f(X1,X1)),f(f(X0,X0),f(X0,X0))),
inference(superposition,[],[f1831,f2978]) ).
fof(f3768,plain,
! [X0,X1] : f(X0,X0) = f(f(X1,f(X1,X1)),X0),
inference(forward_demodulation,[],[f3718,f101]) ).
fof(f5879,plain,
! [X0,X1] : f(X1,f(X1,X1)) = f(f(f(X0,X0),f(X1,f(X1,X1))),f(f(X0,f(X0,X0)),f(X0,f(X0,X0)))),
inference(superposition,[],[f1858,f3768]) ).
fof(f5882,plain,
! [X0,X1] : f(X1,f(X1,X1)) = f(X0,f(f(X0,f(X0,X0)),f(X0,f(X0,X0)))),
inference(forward_demodulation,[],[f5879,f3335]) ).
fof(f5950,plain,
! [X0,X1] : f(X0,f(X0,X0)) = f(X1,f(X1,X1)),
inference(forward_demodulation,[],[f5882,f85]) ).
fof(f9617,plain,
! [X0] : f(x0,f(x0,x0)) != f(X0,f(X0,X0)),
inference(superposition,[],[f2,f5950]) ).
fof(f9751,plain,
$false,
inference(forward_subsumption_resolution,[],[f9617,f5950]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT394-2 : TPTP v9.3.1. Released v5.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n018.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 15:16:38 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 6.42/1.85 % (2493272)Detected a unit-equality problem, will run specialized UEQ schedule.
% 6.42/1.85 % (2493281)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1085979772:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 6.42/1.85 % (2493277)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=557825093:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 6.42/1.85 % (2493279)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2200248930:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 6.42/1.85 % (2493278)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=1607987997:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 6.42/1.85 % (2493283)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=121438386:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 6.42/1.85 % (2493280)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3856259242:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 6.42/1.85 % (2493282)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3004976226:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 6.42/1.85 % (2493281)Instruction limit reached!
% 6.42/1.85 % (2493281)------------------------------
% 6.42/1.85 % (2493281)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/1.85 % (2493281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/1.85 % (2493281)CaDiCaL version: 2.1.3
% 6.42/1.85 % (2493281)Termination reason: Instruction limit
% 6.42/1.85 % (2493281)Termination phase: Saturation
% 6.42/1.85 % (2493281)Time elapsed: 0.054 s
% 6.42/1.85 % (2493281)Peak memory usage: 89 MB
% 6.42/1.85 % (2493281)Instructions burned: 182 (million)
% 6.42/1.85 % (2493280)Instruction limit reached!
% 6.42/1.85 % (2493280)------------------------------
% 6.42/1.85 % (2493280)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/1.85 % (2493280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/1.85 % (2493280)CaDiCaL version: 2.1.3
% 6.42/1.85 % (2493280)Termination reason: Instruction limit
% 6.42/1.85 % (2493280)Termination phase: Saturation
% 6.42/1.85 % (2493280)Time elapsed: 0.081 s
% 6.42/1.85 % (2493280)Peak memory usage: 88 MB
% 6.42/1.85 % (2493280)Instructions burned: 138 (million)
% 6.42/1.85 % (2493291)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2565905179:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 6.42/1.85 % (2493282)Instruction limit reached!
% 6.42/1.85 % (2493282)------------------------------
% 6.42/1.85 % (2493282)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/1.85 % (2493282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/1.85 % (2493282)CaDiCaL version: 2.1.3
% 6.42/1.85 % (2493282)Termination reason: Instruction limit
% 6.42/1.85 % (2493282)Termination phase: Saturation
% 6.42/1.85 % (2493282)Time elapsed: 0.160 s
% 6.42/1.85 % (2493282)Peak memory usage: 89 MB
% 6.42/1.85 % (2493282)Instructions burned: 258 (million)
% 6.42/1.85 % (2493292)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=564709724:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 6.42/1.85 % (2493294)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1771435353:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 6.42/1.85 % (2493283)First to succeed.
% 6.42/1.85 % (2493283)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2493272"
% 6.42/1.85 % (2493294)Instruction limit reached!
% 6.42/1.85 % (2493294)------------------------------
% 6.42/1.85 % (2493294)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/1.85 % (2493294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/1.85 % (2493294)CaDiCaL version: 2.1.3
% 6.42/1.85 % (2493294)Termination reason: Instruction limit
% 6.42/1.85 % (2493294)Termination phase: Saturation
% 6.42/1.85 % (2493294)Time elapsed: 0.094 s
% 6.42/1.85 % (2493294)Peak memory usage: 98 MB
% 6.42/1.85 % (2493294)Instructions burned: 215 (million)
% 6.42/1.85 % (2493297)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=1514968080:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2994 on theBenchmark for (2994ds/317Mi)
% 6.42/1.85 % (2493291)Also succeeded, but the first one will report.
% 6.42/1.85 % (2493283)Refutation found. Thanks to Tanya!
% 6.42/1.85 % SZS status Unsatisfiable for theBenchmark
% 6.42/1.85 % SZS output start Proof for theBenchmark
% See solution above
% 6.42/1.85 % (2493283)------------------------------
% 6.42/1.85 % (2493283)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/1.85 % (2493283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/1.85 % (2493283)CaDiCaL version: 2.1.3
% 6.42/1.85 % (2493283)Termination reason: Refutation
% 6.42/1.85 % (2493283)Time elapsed: 0.400 s
% 6.42/1.85 % (2493283)Peak memory usage: 94 MB
% 6.42/1.85 % (2493283)Instructions burned: 703 (million)
% 6.42/1.85 % (2493283)------------------------------
% 6.42/1.85 % (2493283)------------------------------
% 6.42/1.85 % (2493272)Success in time 0.826 s
% 6.42/1.85 % Vampire exiting
%------------------------------------------------------------------------------