%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN986+1.003 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 02:06:08 PM UTC 2026
% Result : Theorem 3.94s 1.60s
% Output : Refutation 5.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 3
% Syntax : Number of formulae : 52 ( 8 unt; 0 def)
% Number of atoms : 140 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 212 ( 124 ~; 80 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 16 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 143 ( 135 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : r(X0,zero,succ(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp1) ).
fof(f2,axiom,
! [X0,X1,X2,X3] :
( r(X0,X1,X2)
=> ( r(X2,X1,X3)
=> r(X0,succ(X1),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp2) ).
fof(f3,conjecture,
? [X0,X1,X2,X3] :
( r(zero,zero,X0)
& r(zero,X0,X1)
& r(zero,X1,X2)
& r(zero,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ck) ).
fof(f4,negated_conjecture,
~ ? [X0,X1,X2,X3] :
( r(zero,zero,X0)
& r(zero,X0,X1)
& r(zero,X1,X2)
& r(zero,X2,X3) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [X0,X1,X2,X3] :
( r(X0,succ(X1),X3)
| ~ r(X2,X1,X3)
| ~ r(X0,X1,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f6,plain,
! [X0,X1,X2,X3] :
( r(X0,succ(X1),X3)
| ~ r(X2,X1,X3)
| ~ r(X0,X1,X2) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
! [X0,X1,X2,X3] :
( ~ r(zero,zero,X0)
| ~ r(zero,X0,X1)
| ~ r(zero,X1,X2)
| ~ r(zero,X2,X3) ),
inference(ennf_transformation,[],[f4]) ).
fof(f8,plain,
! [X0] : r(X0,zero,succ(X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f9,plain,
! [X2,X3,X0,X1] :
( r(X0,succ(X1),X3)
| ~ r(X2,X1,X3)
| ~ r(X0,X1,X2) ),
inference(cnf_transformation,[],[f6]) ).
fof(f10,plain,
! [X2,X3,X0,X1] :
( ~ r(zero,zero,X0)
| ~ r(zero,X0,X1)
| ~ r(zero,X1,X2)
| ~ r(zero,X2,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ r(zero,succ(zero),X0)
| ~ r(zero,X0,X1)
| ~ r(zero,X1,X2) ),
inference(resolution,[],[f8,f10]) ).
fof(f43,plain,
! [X2,X3,X0,X1] :
( ~ r(zero,zero,X3)
| ~ r(zero,X1,X2)
| ~ r(X3,zero,X0)
| ~ r(zero,X0,X1) ),
inference(resolution,[],[f31,f9]) ).
fof(f60,plain,
! [X2,X0,X1] :
( ~ r(succ(zero),zero,X2)
| ~ r(zero,X0,X1)
| ~ r(zero,X2,X0) ),
inference(resolution,[],[f43,f8]) ).
fof(f69,plain,
! [X0,X1] :
( ~ r(zero,succ(succ(zero)),X0)
| ~ r(zero,X0,X1) ),
inference(resolution,[],[f60,f8]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ~ r(zero,succ(zero),X2)
| ~ r(X2,succ(zero),X0)
| ~ r(zero,X0,X1) ),
inference(resolution,[],[f69,f9]) ).
fof(f77,plain,
! [X2,X3,X0,X1] :
( ~ r(zero,zero,X3)
| ~ r(zero,X1,X2)
| ~ r(X3,zero,X0)
| ~ r(X0,succ(zero),X1) ),
inference(resolution,[],[f71,f9]) ).
fof(f85,plain,
! [X2,X0,X1] :
( ~ r(succ(zero),zero,X2)
| ~ r(zero,X0,X1)
| ~ r(X2,succ(zero),X0) ),
inference(resolution,[],[f77,f8]) ).
fof(f91,plain,
! [X0,X1] :
( ~ r(succ(succ(zero)),succ(zero),X0)
| ~ r(zero,X0,X1) ),
inference(resolution,[],[f85,f8]) ).
fof(f96,plain,
! [X2,X0,X1] :
( ~ r(succ(succ(zero)),zero,X2)
| ~ r(X2,zero,X0)
| ~ r(zero,X0,X1) ),
inference(resolution,[],[f91,f9]) ).
fof(f102,plain,
! [X0,X1] :
( ~ r(succ(succ(succ(zero))),zero,X0)
| ~ r(zero,X0,X1) ),
inference(resolution,[],[f96,f8]) ).
fof(f112,plain,
! [X0] : ~ r(zero,succ(succ(succ(succ(zero)))),X0),
inference(resolution,[],[f102,f8]) ).
fof(f113,plain,
! [X0,X1] :
( ~ r(zero,succ(succ(succ(zero))),X0)
| ~ r(X0,succ(succ(succ(zero))),X1) ),
inference(resolution,[],[f112,f9]) ).
fof(f114,plain,
! [X2,X0,X1] :
( ~ r(zero,succ(succ(zero)),X2)
| ~ r(X2,succ(succ(zero)),X0)
| ~ r(X0,succ(succ(succ(zero))),X1) ),
inference(resolution,[],[f113,f9]) ).
fof(f117,plain,
! [X2,X3,X0,X1] :
( ~ r(zero,succ(zero),X3)
| ~ r(X1,succ(succ(succ(zero))),X2)
| ~ r(X3,succ(zero),X0)
| ~ r(X0,succ(succ(zero)),X1) ),
inference(resolution,[],[f114,f9]) ).
fof(f121,plain,
! [X2,X3,X0,X1,X4] :
( ~ r(zero,zero,X4)
| ~ r(X2,succ(zero),X3)
| ~ r(X3,succ(succ(zero)),X0)
| ~ r(X4,zero,X2)
| ~ r(X0,succ(succ(succ(zero))),X1) ),
inference(resolution,[],[f117,f9]) ).
fof(f125,plain,
! [X2,X3,X0,X1] :
( ~ r(succ(zero),zero,X0)
| ~ r(X1,succ(succ(zero)),X2)
| ~ r(X0,succ(zero),X1)
| ~ r(X2,succ(succ(succ(zero))),X3) ),
inference(resolution,[],[f121,f8]) ).
fof(f129,plain,
! [X2,X0,X1] :
( ~ r(succ(succ(zero)),succ(zero),X0)
| ~ r(X0,succ(succ(zero)),X1)
| ~ r(X1,succ(succ(succ(zero))),X2) ),
inference(resolution,[],[f125,f8]) ).
fof(f131,plain,
! [X2,X3,X0,X1] :
( ~ r(succ(succ(zero)),zero,X3)
| ~ r(X1,succ(succ(succ(zero))),X2)
| ~ r(X3,zero,X0)
| ~ r(X0,succ(succ(zero)),X1) ),
inference(resolution,[],[f129,f9]) ).
fof(f133,plain,
! [X2,X0,X1] :
( ~ r(succ(succ(succ(zero))),zero,X2)
| ~ r(X0,succ(succ(succ(zero))),X1)
| ~ r(X2,succ(succ(zero)),X0) ),
inference(resolution,[],[f131,f8]) ).
fof(f137,plain,
! [X0,X1] :
( ~ r(succ(succ(succ(succ(zero)))),succ(succ(zero)),X0)
| ~ r(X0,succ(succ(succ(zero))),X1) ),
inference(resolution,[],[f133,f8]) ).
fof(f139,plain,
! [X2,X0,X1] :
( ~ r(succ(succ(succ(succ(zero)))),succ(zero),X2)
| ~ r(X2,succ(zero),X0)
| ~ r(X0,succ(succ(succ(zero))),X1) ),
inference(resolution,[],[f137,f9]) ).
fof(f141,plain,
! [X2,X3,X0,X1] :
( ~ r(succ(succ(succ(succ(zero)))),zero,X3)
| ~ r(X1,succ(succ(succ(zero))),X2)
| ~ r(X3,zero,X0)
| ~ r(X0,succ(zero),X1) ),
inference(resolution,[],[f139,f9]) ).
fof(f155,plain,
! [X2,X0,X1] :
( ~ r(succ(succ(succ(succ(succ(zero))))),zero,X2)
| ~ r(X0,succ(succ(succ(zero))),X1)
| ~ r(X2,succ(zero),X0) ),
inference(resolution,[],[f141,f8]) ).
fof(f167,plain,
! [X0,X1] :
( ~ r(succ(succ(succ(succ(succ(succ(zero)))))),succ(zero),X0)
| ~ r(X0,succ(succ(succ(zero))),X1) ),
inference(resolution,[],[f155,f8]) ).
fof(f170,plain,
! [X2,X0,X1] :
( ~ r(succ(succ(succ(succ(succ(succ(zero)))))),zero,X2)
| ~ r(X2,zero,X0)
| ~ r(X0,succ(succ(succ(zero))),X1) ),
inference(resolution,[],[f167,f9]) ).
fof(f171,plain,
! [X0,X1] :
( ~ r(succ(succ(succ(succ(succ(succ(succ(zero))))))),zero,X0)
| ~ r(X0,succ(succ(succ(zero))),X1) ),
inference(resolution,[],[f170,f8]) ).
fof(f181,plain,
! [X0] : ~ r(succ(succ(succ(succ(succ(succ(succ(succ(zero)))))))),succ(succ(succ(zero))),X0),
inference(resolution,[],[f171,f8]) ).
fof(f182,plain,
! [X0,X1] :
( ~ r(succ(succ(succ(succ(succ(succ(succ(succ(zero)))))))),succ(succ(zero)),X0)
| ~ r(X0,succ(succ(zero)),X1) ),
inference(resolution,[],[f181,f9]) ).
fof(f183,plain,
! [X2,X0,X1] :
( ~ r(succ(succ(succ(succ(succ(succ(succ(succ(zero)))))))),succ(zero),X2)
| ~ r(X2,succ(zero),X0)
| ~ r(X0,succ(succ(zero)),X1) ),
inference(resolution,[],[f182,f9]) ).
fof(f186,plain,
! [X2,X3,X0,X1] :
( ~ r(succ(succ(succ(succ(succ(succ(succ(succ(zero)))))))),zero,X3)
| ~ r(X1,succ(succ(zero)),X2)
| ~ r(X3,zero,X0)
| ~ r(X0,succ(zero),X1) ),
inference(resolution,[],[f183,f9]) ).
fof(f201,plain,
! [X2,X0,X1] :
( ~ r(succ(succ(succ(succ(succ(succ(succ(succ(succ(zero))))))))),zero,X2)
| ~ r(X0,succ(succ(zero)),X1)
| ~ r(X2,succ(zero),X0) ),
inference(resolution,[],[f186,f8]) ).
fof(f211,plain,
! [X0,X1] :
( ~ r(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(zero)))))))))),succ(zero),X0)
| ~ r(X0,succ(succ(zero)),X1) ),
inference(resolution,[],[f201,f8]) ).
fof(f214,plain,
! [X2,X0,X1] :
( ~ r(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(zero)))))))))),zero,X2)
| ~ r(X2,zero,X0)
| ~ r(X0,succ(succ(zero)),X1) ),
inference(resolution,[],[f211,f9]) ).
fof(f215,plain,
! [X0,X1] :
( ~ r(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(zero))))))))))),zero,X0)
| ~ r(X0,succ(succ(zero)),X1) ),
inference(resolution,[],[f214,f8]) ).
fof(f226,plain,
! [X0] : ~ r(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(zero)))))))))))),succ(succ(zero)),X0),
inference(resolution,[],[f215,f8]) ).
fof(f228,plain,
! [X0,X1] :
( ~ r(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(zero)))))))))))),succ(zero),X0)
| ~ r(X0,succ(zero),X1) ),
inference(resolution,[],[f226,f9]) ).
fof(f229,plain,
! [X2,X0,X1] :
( ~ r(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(zero)))))))))))),zero,X2)
| ~ r(X2,zero,X0)
| ~ r(X0,succ(zero),X1) ),
inference(resolution,[],[f228,f9]) ).
fof(f232,plain,
! [X0,X1] :
( ~ r(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(zero))))))))))))),zero,X0)
| ~ r(X0,succ(zero),X1) ),
inference(resolution,[],[f229,f8]) ).
fof(f242,plain,
! [X0] : ~ r(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(zero)))))))))))))),succ(zero),X0),
inference(resolution,[],[f232,f8]) ).
fof(f244,plain,
! [X0,X1] :
( ~ r(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(zero)))))))))))))),zero,X0)
| ~ r(X0,zero,X1) ),
inference(resolution,[],[f242,f9]) ).
fof(f245,plain,
! [X0] : ~ r(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(zero))))))))))))))),zero,X0),
inference(resolution,[],[f244,f8]) ).
fof(f249,plain,
$false,
inference(resolution,[],[f245,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN986+1.003 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 % Computer : n008.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Mon Sep 28 17:20:24 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.27 Running first-order theorem proving
% 0.10/0.27 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
% 3.94/1.60 % (2405302)Detected formulas, will run a generic FOF schedule.
% 3.94/1.60 % (2405307)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=822831584:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.94/1.60 % (2405313)dis-21_1_sil=8000:lcm=predicate:random_seed=3867433897:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.94/1.60 % (2405310)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3337552717:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.94/1.60 % (2405309)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3622127162:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.94/1.60 % (2405308)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3116274761:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.94/1.60 % (2405310)Refutation not found, incomplete strategy
% 3.94/1.60 % (2405310)------------------------------
% 3.94/1.60 % (2405310)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.60 % (2405310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.60 % (2405310)CaDiCaL version: 2.1.3
% 3.94/1.60 % (2405310)Termination reason: Refutation not found, incomplete strategy
% 3.94/1.60 % (2405310)Time elapsed: 0.002 s
% 3.94/1.60 % (2405310)Peak memory usage: 88 MB
% 3.94/1.60 % (2405311)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1046010322:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.94/1.60 % (2405312)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2008462037:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.94/1.60 % (2405312)First to succeed.
% 3.94/1.60 % (2405312)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2405302"
% 3.94/1.60 % (2405313)Instruction limit reached!
% 3.94/1.60 % (2405313)------------------------------
% 3.94/1.60 % (2405313)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.60 % (2405313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.60 % (2405313)CaDiCaL version: 2.1.3
% 3.94/1.60 % (2405313)Termination reason: Instruction limit
% 3.94/1.60 % (2405313)Termination phase: Saturation
% 3.94/1.60 % (2405313)Time elapsed: 0.129 s
% 3.94/1.60 % (2405313)Peak memory usage: 88 MB
% 3.94/1.60 % (2405313)Instructions burned: 129 (million)
% 3.94/1.60 % (2405311)Instruction limit reached!
% 3.94/1.60 % (2405311)------------------------------
% 3.94/1.60 % (2405311)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.60 % (2405311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.60 % (2405311)CaDiCaL version: 2.1.3
% 3.94/1.60 % (2405311)Termination reason: Instruction limit
% 3.94/1.60 % (2405311)Termination phase: Saturation
% 3.94/1.60 % (2405311)Time elapsed: 0.093 s
% 3.94/1.60 % (2405311)Peak memory usage: 87 MB
% 3.94/1.60 % (2405311)Instructions burned: 120 (million)
% 3.94/1.60 % (2405322)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3594797937:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 3.94/1.60 % (2405321)lrs+10_1_sil=8000:sp=occurrence:random_seed=1180950344:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 3.94/1.60 % (2405322)Also succeeded, but the first one will report.
% 3.94/1.60 % (2405321)Also succeeded, but the first one will report.
% 3.94/1.60 % (2405310)------------------------------
% 3.94/1.60 % (2405310)------------------------------
% 3.94/1.60 % (2405312)Refutation found. Thanks to Tanya!
% 3.94/1.60 % SZS status Theorem for theBenchmark
% 3.94/1.60 % SZS output start Proof for theBenchmark
% See solution above
% 5.92/1.84 % (2405312)------------------------------
% 5.92/1.84 % (2405312)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.92/1.84 % (2405312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.92/1.84 % (2405312)CaDiCaL version: 2.1.3
% 5.92/1.84 % (2405312)Termination reason: Refutation
% 5.92/1.84 % (2405312)Time elapsed: 0.013 s
% 5.92/1.84 % (2405312)Peak memory usage: 89 MB
% 5.92/1.84 % (2405312)Instructions burned: 10 (million)
% 5.92/1.84 % (2405312)------------------------------
% 5.92/1.84 % (2405312)------------------------------
% 5.92/1.84 % (2405302)Success in time 0.708 s
% 5.92/1.84 % Vampire exiting
%------------------------------------------------------------------------------