%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM659_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:16:17 PM UTC 2026
% Result : Theorem 2.44s 1.22s
% Output : Refutation 2.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 11 unt; 0 typ; 1 def)
% Number of atoms : 29 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 12 ~; 7 |; 1 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 8 ( 8 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
nat: $tType ).
tff(func_def_0,type,
x: nat ).
tff(func_def_1,type,
y: nat ).
tff(pred_def_1,type,
less: ( nat * nat ) > $o ).
tff(pred_def_2,type,
more: ( nat * nat ) > $o ).
tff(pred_def_3,type,
sP0: nat > $o ).
tff(f1,axiom,
~ ( ~ less(x,y)
=> ( x = y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).
tff(f3,axiom,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ~ more(X0,X1)
=> less(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10a) ).
tff(f4,conjecture,
more(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10k) ).
tff(f5,negated_conjecture,
~ more(x,y),
inference(negated_conjecture,[status(cth)],[f4]) ).
tff(f8,plain,
~ more(x,y),
inference(flattening,[],[f5]) ).
tff(f9,plain,
( ( x != y )
& ~ less(x,y) ),
inference(ennf_transformation,[],[f1]) ).
tff(f10,plain,
! [X0: nat,X1: nat] :
( less(X0,X1)
| more(X0,X1)
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f11,plain,
! [X0: nat,X1: nat] :
( less(X0,X1)
| more(X0,X1)
| ( X0 = X1 ) ),
inference(flattening,[],[f10]) ).
tff(f12,plain,
~ more(x,y),
inference(cnf_transformation,[],[f8]) ).
tff(f13,plain,
~ less(x,y),
inference(cnf_transformation,[],[f9]) ).
tff(f14,plain,
x != y,
inference(cnf_transformation,[],[f9]) ).
tff(f15,plain,
! [X0: nat,X1: nat] :
( more(X0,X1)
| less(X0,X1)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f11]) ).
tff(f16,definition,
~ sP0(x),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
tff(f17,plain,
sP0(y),
inference(inequality_splitting,[],[f14,f16]) ).
tff(f18,plain,
( less(x,y)
| ( x = y ) ),
inference(resolution,[],[f12,f15]) ).
tff(f19,plain,
x = y,
inference(forward_subsumption_resolution,[],[f18,f13]) ).
tff(f22,plain,
sP0(x),
inference(superposition,[],[f17,f19]) ).
tff(f23,plain,
$false,
inference(forward_subsumption_resolution,[],[f22,f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM659_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 21:03:07 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.44/1.22 % (3199224)Detected formulas, will run a generic FOF schedule.
% 2.44/1.22 % (3199232)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2138233783:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.44/1.22 % (3199232)First to succeed.
% 2.44/1.22 % (3199232)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3199224"
% 2.44/1.22 % (3199229)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=68139472:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.44/1.22 % (3199231)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=3389839241:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.44/1.22 % (3199230)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=1610626759:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.44/1.22 % (3199234)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2691979241:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.44/1.22 % (3199234)Also succeeded, but the first one will report.
% 2.44/1.22 % (3199233)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3649870764:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.44/1.22 % (3199235)dis-21_1_sil=8000:lcm=predicate:random_seed=2803742800: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)
% 2.44/1.22 % (3199233)Also succeeded, but the first one will report.
% 2.44/1.22 % (3199235)Also succeeded, but the first one will report.
% 2.44/1.22 % (3199232)Refutation found. Thanks to Tanya!
% 2.44/1.22 % SZS status Theorem for theBenchmark
% 2.44/1.22 % SZS output start Proof for theBenchmark
% See solution above
% 2.44/1.22 % (3199232)------------------------------
% 2.44/1.22 % (3199232)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.44/1.22 % (3199232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/1.22 % (3199232)CaDiCaL version: 2.1.3
% 2.44/1.22 % (3199232)Termination reason: Refutation
% 2.44/1.22 % (3199232)Time elapsed: 0.001 s
% 2.44/1.22 % (3199232)Peak memory usage: 88 MB
% 2.44/1.22 % (3199232)------------------------------
% 2.44/1.22 % (3199232)------------------------------
% 2.44/1.22 % (3199224)Success in time 0.272 s
% 2.44/1.22 % Vampire exiting
%------------------------------------------------------------------------------