%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM664_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 12:16:19 PM UTC 2026
% Result : Theorem 2.73s 1.36s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 51 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 44 ( 23 ~; 16 |; 0 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 13 ( 0 sgn 13 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
nat: $tType ).
tff(func_def_0,type,
x: nat ).
tff(func_def_1,type,
y: nat ).
tff(func_def_2,type,
z: nat ).
tff(pred_def_1,type,
less: ( nat * nat ) > $o ).
tff(f1,axiom,
less(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
tff(f2,axiom,
( ~ less(y,z)
=> ( y = z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k) ).
tff(f4,axiom,
! [X0: nat,X1: nat,X2: nat] :
( less(X0,X1)
=> ( less(X1,X2)
=> less(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz15) ).
tff(f5,conjecture,
less(x,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz16b) ).
tff(f6,negated_conjecture,
~ less(x,z),
inference(negated_conjecture,[status(cth)],[f5]) ).
tff(f10,plain,
~ less(x,z),
inference(flattening,[],[f6]) ).
tff(f11,plain,
( ( y = z )
| less(y,z) ),
inference(ennf_transformation,[],[f2]) ).
tff(f13,plain,
! [X0: nat,X1: nat,X2: nat] :
( less(X0,X2)
| ~ less(X1,X2)
| ~ less(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
tff(f14,plain,
! [X0: nat,X1: nat,X2: nat] :
( less(X0,X2)
| ~ less(X1,X2)
| ~ less(X0,X1) ),
inference(flattening,[],[f13]) ).
tff(f15,plain,
less(x,y),
inference(cnf_transformation,[],[f1]) ).
tff(f16,plain,
( ( y = z )
| less(y,z) ),
inference(cnf_transformation,[],[f11]) ).
tff(f18,plain,
! [X2: nat,X0: nat,X1: nat] :
( less(X0,X2)
| ~ less(X1,X2)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
tff(f19,plain,
~ less(x,z),
inference(cnf_transformation,[],[f10]) ).
tff(f24,definition,
( spl0_1
<=> less(y,z) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f26,plain,
( less(y,z)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f24]) ).
tff(f28,definition,
( spl0_2
<=> ( y = z ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f30,plain,
( ( y = z )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f28]) ).
tff(f31,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f16,f28,f24]) ).
tff(f32,plain,
( ~ less(x,y)
| ~ spl0_2 ),
inference(superposition,[],[f19,f30]) ).
tff(f33,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f32,f15]) ).
tff(f34,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f33]) ).
tff(f35,plain,
! [X0: nat] :
( ~ less(x,X0)
| ~ less(X0,z) ),
inference(resolution,[],[f18,f19]) ).
tff(f36,plain,
~ less(y,z),
inference(resolution,[],[f35,f15]) ).
tff(f38,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f36,f26]) ).
tff(f39,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f38]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f31]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f34]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f39]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
tff(f40,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM664_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n019.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 21:01:19 UTC 2026
% 0.09/0.39 % CPUTime :
% 0.09/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 2.73/1.36 % (3398584)Detected formulas, will run a generic FOF schedule.
% 2.73/1.36 % (3398660)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2386294707:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.73/1.36 % (3398660)First to succeed.
% 2.73/1.36 % (3398660)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3398584"
% 2.73/1.36 % (3398654)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=3380525907:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.73/1.36 % (3398656)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=756220110:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.73/1.36 % (3398653)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=1892740915:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.73/1.36 % (3398657)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=480466690:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.73/1.36 % (3398657)Refutation not found, incomplete strategy
% 2.73/1.36 % (3398657)------------------------------
% 2.73/1.36 % (3398657)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.36 % (3398657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.36 % (3398657)CaDiCaL version: 2.1.3
% 2.73/1.36 % (3398657)Termination reason: Refutation not found, incomplete strategy
% 2.73/1.36 % (3398657)Time elapsed: 0.001 s
% 2.73/1.36 % (3398657)Peak memory usage: 88 MB
% 2.73/1.36 % (3398661)dis-21_1_sil=8000:lcm=predicate:random_seed=2874438046: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)
% 2.73/1.36 % (3398659)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1632990163:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.73/1.36 % (3398659)Also succeeded, but the first one will report.
% 2.73/1.36 % (3398661)Instruction limit reached!
% 2.73/1.36 % (3398661)------------------------------
% 2.73/1.36 % (3398661)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.36 % (3398661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.36 % (3398661)CaDiCaL version: 2.1.3
% 2.73/1.36 % (3398661)Termination reason: Instruction limit
% 2.73/1.36 % (3398661)Termination phase: Saturation
% 2.73/1.36 % (3398661)Time elapsed: 0.050 s
% 2.73/1.36 % (3398661)Peak memory usage: 88 MB
% 2.73/1.36 % (3398661)Instructions burned: 132 (million)
% 2.73/1.36 % (3398660)Refutation found. Thanks to Tanya!
% 2.73/1.36 % SZS status Theorem for theBenchmark
% 2.73/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 2.73/1.36 % (3398660)------------------------------
% 2.73/1.36 % (3398660)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.36 % (3398660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.36 % (3398660)CaDiCaL version: 2.1.3
% 2.73/1.36 % (3398660)Termination reason: Refutation
% 2.73/1.36 % (3398660)Time elapsed: 0.002 s
% 2.73/1.36 % (3398660)Peak memory usage: 90 MB
% 2.73/1.36 % (3398660)Instructions burned: 1 (million)
% 2.73/1.36 % (3398660)------------------------------
% 2.73/1.36 % (3398660)------------------------------
% 2.73/1.36 % (3398584)Success in time 0.305 s
% 2.73/1.36 % Vampire exiting
%------------------------------------------------------------------------------