%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM018+1 : 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 : 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 09:39:24 AM UTC 2026
% Result : Theorem 3.47s 1.22s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 10 unt; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 40 ( 19 ~; 15 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 19 ( 14 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0] :
( ( aRewritingSystem0(X0)
& isTerminating0(X0) )
=> ! [X1] :
( aElement0(X1)
=> ? [X2] : aNormalFormOfIn0(X2,X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTermNF) ).
fof(f15,axiom,
aRewritingSystem0(xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656) ).
fof(f16,axiom,
( isLocallyConfluent0(xR)
& isTerminating0(xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656_01) ).
fof(f22,axiom,
( aElement0(xw)
& sdtmndtasgtdt0(xu,xR,xw)
& sdtmndtasgtdt0(xv,xR,xw) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__799) ).
fof(f23,conjecture,
? [X0] : aNormalFormOfIn0(X0,xw,xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f24,negated_conjecture,
~ ? [X0] : aNormalFormOfIn0(X0,xw,xR),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f47,plain,
! [X0] :
( ! [X1] :
( ? [X2] : aNormalFormOfIn0(X2,X1,X0)
| ~ aElement0(X1) )
| ~ aRewritingSystem0(X0)
| ~ isTerminating0(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( ? [X2] : aNormalFormOfIn0(X2,X1,X0)
| ~ aElement0(X1) )
| ~ aRewritingSystem0(X0)
| ~ isTerminating0(X0) ),
inference(flattening,[],[f47]) ).
fof(f51,plain,
! [X0] : ~ aNormalFormOfIn0(X0,xw,xR),
inference(ennf_transformation,[],[f24]) ).
fof(f79,plain,
! [X0] :
( ! [X1] :
( aNormalFormOfIn0(sK16(X0,X1),X1,X0)
| ~ aElement0(X1) )
| ~ aRewritingSystem0(X0)
| ~ isTerminating0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X2,sK16(X0,X1))],[f48]) ).
fof(f125,plain,
! [X0,X1] :
( ~ isTerminating0(X0)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X0)
| aNormalFormOfIn0(sK16(X0,X1),X1,X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f126,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f15]) ).
fof(f127,plain,
isTerminating0(xR),
inference(cnf_transformation,[],[f16]) ).
fof(f145,plain,
aElement0(xw),
inference(cnf_transformation,[],[f22]) ).
fof(f146,plain,
! [X0] : ~ aNormalFormOfIn0(X0,xw,xR),
inference(cnf_transformation,[],[f51]) ).
fof(f149,plain,
! [X0] :
( ~ aElement0(X0)
| ~ aRewritingSystem0(xR)
| aNormalFormOfIn0(sK16(xR,X0),X0,xR) ),
inference(resolution,[],[f125,f127]) ).
fof(f150,plain,
! [X0] :
( aNormalFormOfIn0(sK16(xR,X0),X0,xR)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f149,f126]) ).
fof(f151,plain,
~ aElement0(xw),
inference(resolution,[],[f150,f146]) ).
fof(f158,plain,
$false,
inference(forward_subsumption_resolution,[],[f151,f145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM018+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.16 % Computer : n006.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Mon Sep 28 21:45:40 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 Running first-order theorem proving
% 0.08/0.19 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
% 3.47/1.22 % (238054)Detected formulas, will run a generic FOF schedule.
% 3.47/1.22 % (238061)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=3000913864:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.47/1.22 % (238064)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2193218370:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.47/1.22 % (238064)First to succeed.
% 3.47/1.22 % (238064)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-238054"
% 3.47/1.22 % (238062)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3731865075:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.47/1.22 % (238060)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=4059759:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.47/1.22 % (238059)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=3699321309:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.47/1.22 % (238063)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=286584858:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.47/1.22 % (238063)Also succeeded, but the first one will report.
% 3.47/1.22 % (238062)Also succeeded, but the first one will report.
% 3.47/1.22 % (238065)dis-21_1_sil=8000:lcm=predicate:random_seed=2538413795: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)
% 3.47/1.22 % (238065)Also succeeded, but the first one will report.
% 3.47/1.22 % (238064)Refutation found. Thanks to Tanya!
% 3.47/1.22 % SZS status Theorem for theBenchmark
% 3.47/1.22 % SZS output start Proof for theBenchmark
% See solution above
% 3.47/1.23 % (238064)------------------------------
% 3.47/1.23 % (238064)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.23 % (238064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.23 % (238064)CaDiCaL version: 2.1.3
% 3.47/1.23 % (238064)Termination reason: Refutation
% 3.47/1.23 % (238064)Time elapsed: 0.004 s
% 3.47/1.23 % (238064)Peak memory usage: 89 MB
% 3.47/1.23 % (238064)Instructions burned: 4 (million)
% 3.47/1.23 % (238064)------------------------------
% 3.47/1.23 % (238064)------------------------------
% 3.47/1.23 % (238054)Success in time 0.405 s
% 3.47/1.23 % Vampire exiting
%------------------------------------------------------------------------------