%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN073+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 12:26:44 PM UTC 2026
% Result : Theorem 3.38s 1.22s
% Output : Refutation 3.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 10 unt; 2 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 87 ( 43 ~; 32 |; 10 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 46 ( 41 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0,X1] :
( ! [X2] :
( ! [X3] :
( ~ id(X3,X2)
| ~ r2(X0,X3) )
| ~ r2(X1,X2) )
| id(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3a) ).
fof(f18,axiom,
! [X0,X1] :
( ! [X2] :
( ~ id(X2,X1)
| ~ r1(X2) )
| ~ r2(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7a) ).
fof(f19,conjecture,
! [X0] :
( ! [X1] :
( ! [X2] :
( ~ r1(X2)
| ~ r2(X2,X1) )
| ~ id(X1,X0) )
| ! [X3] :
( ! [X4] :
( ~ r1(X4)
| ~ r2(X4,X3) )
| ~ r2(X3,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oneunidtwo) ).
fof(f20,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( ! [X2] :
( ~ r1(X2)
| ~ r2(X2,X1) )
| ~ id(X1,X0) )
| ! [X3] :
( ! [X4] :
( ~ r1(X4)
| ~ r2(X4,X3) )
| ~ r2(X3,X0) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( r1(X2)
& r2(X2,X1) )
& id(X1,X0) )
& ? [X3] :
( ? [X4] :
( r1(X4)
& r2(X4,X3) )
& r2(X3,X0) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f22,plain,
( r1(sK2)
& r2(sK2,sK1)
& id(sK1,sK0)
& r1(sK4)
& r2(sK4,sK3)
& r2(sK3,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f21]) ).
fof(f26,plain,
r2(sK3,sK0),
inference(cnf_transformation,[],[f22]) ).
fof(f27,plain,
r2(sK4,sK3),
inference(cnf_transformation,[],[f22]) ).
fof(f29,plain,
id(sK1,sK0),
inference(cnf_transformation,[],[f22]) ).
fof(f30,plain,
r2(sK2,sK1),
inference(cnf_transformation,[],[f22]) ).
fof(f31,plain,
r1(sK2),
inference(cnf_transformation,[],[f22]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ id(X2,X1)
| ~ r1(X2)
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( ~ id(X3,X2)
| ~ r2(X0,X3)
| ~ r2(X1,X2)
| id(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f57,plain,
! [X2,X1] :
( ~ id(X2,X1)
| ~ r1(X2)
| sP10(X1) ),
inference(cnf_transformation,[],[f57_D]) ).
fof(f57_D,definition,
! [X1] :
( ! [X2] :
( ~ id(X2,X1)
| ~ r1(X2) )
<=> ~ sP10(X1) ),
introduced(definition,[new_symbols(definition,[sP10])],[general_splitting_component_introduction]) ).
fof(f58,plain,
! [X0,X1] :
( ~ r2(X0,X1)
| ~ sP10(X1) ),
inference(general_splitting,[],[f35,f57_D]) ).
fof(f59,plain,
! [X2,X3,X1] :
( ~ r2(X1,X2)
| ~ id(X3,X2)
| sP11(X3,X1) ),
inference(cnf_transformation,[],[f59_D]) ).
fof(f59_D,definition,
! [X1,X3] :
( ! [X2] :
( ~ r2(X1,X2)
| ~ id(X3,X2) )
<=> ~ sP11(X3,X1) ),
introduced(definition,[new_symbols(definition,[sP11])],[general_splitting_component_introduction]) ).
fof(f60,plain,
! [X3,X0,X1] :
( ~ sP11(X3,X1)
| id(X0,X1)
| ~ r2(X0,X3) ),
inference(general_splitting,[],[f48,f59_D]) ).
fof(f74,plain,
! [X0] :
( ~ id(X0,sK0)
| sP11(X0,sK3) ),
inference(resolution,[],[f26,f59]) ).
fof(f76,plain,
~ sP10(sK3),
inference(resolution,[],[f27,f58]) ).
fof(f107,plain,
sP11(sK1,sK3),
inference(resolution,[],[f74,f29]) ).
fof(f111,plain,
! [X0] :
( ~ r2(X0,sK1)
| id(X0,sK3) ),
inference(resolution,[],[f107,f60]) ).
fof(f129,plain,
id(sK2,sK3),
inference(resolution,[],[f111,f30]) ).
fof(f138,plain,
( ~ r1(sK2)
| sP10(sK3) ),
inference(resolution,[],[f129,f57]) ).
fof(f140,plain,
sP10(sK3),
inference(forward_subsumption_resolution,[],[f138,f31]) ).
fof(f142,plain,
$false,
inference(forward_subsumption_resolution,[],[f140,f76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN073+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 21:55:30 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 3.38/1.22 % (2439362)Detected formulas, will run a generic FOF schedule.
% 3.38/1.22 % (2439372)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3645991978:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.38/1.22 % (2439373)dis-21_1_sil=8000:lcm=predicate:random_seed=4144592268: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)
% 3.38/1.22 % (2439370)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4146889829:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.38/1.22 % (2439367)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=368929986:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.38/1.22 % (2439369)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=2228700088:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.38/1.22 % (2439368)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=4240872934:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.38/1.22 % (2439371)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1160367628:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.38/1.22 % (2439370)First to succeed.
% 3.38/1.22 % (2439370)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2439362"
% 3.38/1.22 % (2439371)Also succeeded, but the first one will report.
% 3.38/1.22 % (2439373)Also succeeded, but the first one will report.
% 3.38/1.22 % (2439372)Also succeeded, but the first one will report.
% 3.38/1.22 % (2439370)Refutation found. Thanks to Tanya!
% 3.38/1.22 % SZS status Theorem for theBenchmark
% 3.38/1.22 % SZS output start Proof for theBenchmark
% See solution above
% 3.38/1.22 % (2439370)------------------------------
% 3.38/1.22 % (2439370)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.22 % (2439370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.22 % (2439370)CaDiCaL version: 2.1.3
% 3.38/1.22 % (2439370)Termination reason: Refutation
% 3.38/1.22 % (2439370)Time elapsed: 0.003 s
% 3.38/1.22 % (2439370)Peak memory usage: 88 MB
% 3.38/1.22 % (2439370)Instructions burned: 3 (million)
% 3.38/1.22 % (2439370)------------------------------
% 3.38/1.22 % (2439370)------------------------------
% 3.38/1.22 % (2439362)Success in time 0.421 s
% 3.38/1.22 % Vampire exiting
%------------------------------------------------------------------------------