%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO075-1 : TPTP v9.3.1. Released v2.6.0.
% 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 09:36:01 AM UTC 2026
% Result : Unsatisfiable 5.92s 1.71s
% Output : Refutation 5.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 19 unt; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 10 ( 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 : 33 ( 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : nand(nand(X0,nand(nand(X1,X0),X0)),nand(X1,nand(X2,X0))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sh_1) ).
fof(f2,negated_conjecture,
nand(nand(a,a),nand(b,a)) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_meredith_2_basis_1) ).
fof(f3,plain,
a != nand(nand(a,a),nand(b,a)),
inference(reorient_equations,[],[f2]) ).
fof(f5,plain,
! [X2,X3,X0,X1] : nand(nand(nand(X0,nand(X1,X2)),nand(nand(X3,nand(X0,nand(X1,X2))),nand(X0,nand(X1,X2)))),nand(X3,X0)) = X3,
inference(superposition,[],[f1,f1]) ).
fof(f6,plain,
! [X2,X0,X1] : nand(X2,nand(nand(X0,X2),X2)) = nand(nand(nand(X1,X2),nand(nand(nand(X2,nand(nand(X0,X2),X2)),nand(X1,X2)),nand(X1,X2))),X0),
inference(superposition,[],[f1,f1]) ).
fof(f11,plain,
! [X3,X0,X1] : nand(nand(X0,nand(nand(X3,X0),X0)),nand(X3,nand(X1,nand(nand(X0,X1),X1)))) = X3,
inference(superposition,[],[f5,f1]) ).
fof(f42,plain,
! [X0,X1] : nand(X0,nand(nand(X0,X0),X0)) = nand(nand(X1,nand(nand(nand(X0,nand(nand(X0,X0),X0)),X1),X1)),X0),
inference(superposition,[],[f11,f1]) ).
fof(f55,plain,
! [X0,X1] : nand(nand(X0,nand(nand(X0,X0),X0)),nand(X0,nand(X0,nand(nand(X0,X0),X0)))) = nand(nand(X1,nand(nand(nand(nand(X0,nand(nand(X0,X0),X0)),nand(X0,nand(X0,nand(nand(X0,X0),X0)))),X1),X1)),nand(X0,nand(nand(X0,X0),X0))),
inference(superposition,[],[f42,f1]) ).
fof(f75,plain,
! [X0,X1] : nand(nand(X1,nand(nand(X0,X1),X1)),nand(X0,nand(nand(X0,X0),X0))) = X0,
inference(forward_demodulation,[],[f55,f11]) ).
fof(f120,plain,
! [X0] : nand(X0,nand(nand(X0,X0),X0)) = nand(nand(nand(X0,nand(nand(X0,X0),X0)),nand(X0,nand(X0,nand(nand(X0,X0),X0)))),X0),
inference(superposition,[],[f42,f75]) ).
fof(f135,plain,
! [X0] : nand(X0,X0) = nand(X0,nand(nand(X0,X0),X0)),
inference(forward_demodulation,[],[f120,f11]) ).
fof(f151,plain,
! [X0,X1] : nand(nand(X0,X0),nand(X0,nand(X1,X0))) = X0,
inference(superposition,[],[f1,f135]) ).
fof(f152,plain,
! [X0,X1] : nand(nand(X1,nand(nand(X0,X1),X1)),nand(X0,X0)) = X0,
inference(superposition,[],[f75,f135]) ).
fof(f153,plain,
! [X0,X1] : nand(X0,X0) = nand(nand(X1,nand(nand(nand(X0,X0),X1),X1)),X0),
inference(superposition,[],[f42,f135]) ).
fof(f525,plain,
! [X0,X1] : nand(X1,nand(nand(nand(nand(X0,X1),nand(X0,X1)),X1),X1)) = nand(nand(nand(X0,X1),nand(nand(nand(X0,X1),nand(X0,X1)),nand(X0,X1))),nand(nand(X0,X1),nand(X0,X1))),
inference(superposition,[],[f6,f153]) ).
fof(f536,plain,
! [X0,X1] : nand(X0,X1) = nand(X1,nand(nand(nand(nand(X0,X1),nand(X0,X1)),X1),X1)),
inference(forward_demodulation,[],[f525,f152]) ).
fof(f742,plain,
! [X0,X1] : nand(nand(X1,X1),nand(X0,X1)) = X1,
inference(superposition,[],[f151,f536]) ).
fof(f816,plain,
a != a,
inference(superposition,[],[f3,f742]) ).
fof(f857,plain,
$false,
inference(trivial_inequality_removal,[],[f816]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : BOO075-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.28 % Computer : n008.cluster.edu
% 0.11/0.28 % Model : x86_64 x86_64
% 0.11/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.28 % Memory : 8046.5625MB
% 0.11/0.28 % OS : Linux 6.8.0-71-generic
% 0.11/0.28 % CPULimit : 300
% 0.11/0.28 % WCLimit : 300
% 0.11/0.28 % DateTime : Mon Sep 28 21:08:39 UTC 2026
% 0.12/0.28 % CPUTime :
% 0.12/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.33 Running first-order theorem proving
% 0.12/0.33 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
% 5.92/1.71 % (2653526)Detected a unit-equality problem, will run specialized UEQ schedule.
% 5.92/1.71 % (2653534)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3643093665:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 5.92/1.71 % (2653535)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1584650862:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 5.92/1.71 % (2653533)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=953028173:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 5.92/1.71 % (2653532)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=2113540368:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 5.92/1.71 % (2653531)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=3629410393:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 5.92/1.71 % (2653534)Instruction limit reached!
% 5.92/1.71 % (2653534)------------------------------
% 5.92/1.71 % (2653534)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.92/1.71 % (2653534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.92/1.71 % (2653534)CaDiCaL version: 2.1.3
% 5.92/1.71 % (2653534)Termination reason: Instruction limit
% 5.92/1.71 % (2653534)Termination phase: Saturation
% 5.92/1.71 % (2653534)Time elapsed: 0.068 s
% 5.92/1.71 % (2653534)Peak memory usage: 88 MB
% 5.92/1.71 % (2653534)Instructions burned: 137 (million)
% 5.92/1.71 % (2653537)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1180002383:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 5.92/1.71 % (2653536)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1564573384:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 5.92/1.71 % (2653537)First to succeed.
% 5.92/1.71 % (2653537)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2653526"
% 5.92/1.71 % (2653535)Instruction limit reached!
% 5.92/1.71 % (2653535)------------------------------
% 5.92/1.71 % (2653535)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.92/1.71 % (2653535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.92/1.71 % (2653535)CaDiCaL version: 2.1.3
% 5.92/1.71 % (2653535)Termination reason: Instruction limit
% 5.92/1.71 % (2653535)Termination phase: Saturation
% 5.92/1.71 % (2653535)Time elapsed: 0.163 s
% 5.92/1.71 % (2653535)Peak memory usage: 89 MB
% 5.92/1.71 % (2653535)Instructions burned: 181 (million)
% 5.92/1.71 % (2653536)Also succeeded, but the first one will report.
% 5.92/1.71 % (2653543)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=635551772:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 5.92/1.71 % (2653546)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1631028559:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 5.92/1.71 % (2653537)Refutation found. Thanks to Tanya!
% 5.92/1.71 % SZS status Unsatisfiable for theBenchmark
% 5.92/1.71 % SZS output start Proof for theBenchmark
% See solution above
% 5.92/1.71 % (2653537)------------------------------
% 5.92/1.71 % (2653537)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.92/1.71 % (2653537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.92/1.71 % (2653537)CaDiCaL version: 2.1.3
% 5.92/1.71 % (2653537)Termination reason: Refutation
% 5.92/1.71 % (2653537)Time elapsed: 0.053 s
% 5.92/1.71 % (2653537)Peak memory usage: 88 MB
% 5.92/1.71 % (2653537)Instructions burned: 56 (million)
% 5.92/1.71 % (2653537)------------------------------
% 5.92/1.71 % (2653537)------------------------------
% 5.92/1.71 % (2653526)Success in time 0.734 s
% 5.92/1.71 % Vampire exiting
%------------------------------------------------------------------------------