%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM789_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 : n001.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 12:17:02 PM UTC 2026
% Result : Theorem 2.96s 1.27s
% Output : Refutation 2.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 8 unt; 0 typ; 2 def)
% Number of atoms : 66 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 83 ( 46 ~; 18 |; 4 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 7 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 12 ( 0 sgn 12 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
rat: $tType ).
tff(func_def_0,type,
x0: rat ).
tff(func_def_1,type,
y0: rat ).
tff(pred_def_1,type,
less: ( rat * rat ) > $o ).
tff(pred_def_2,type,
more: ( rat * rat ) > $o ).
tff(pred_def_3,type,
is: ( rat * rat ) > $o ).
tff(pred_def_4,type,
sQ0_eqProxy: ( $o * $o ) > $o ).
tff(f1,axiom,
less(x0,y0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
tff(f3,axiom,
! [X0: rat,X1: rat] :
~ ( ( is(X0,X1)
=> ~ more(X0,X1) )
=> ~ ~ ( ( more(X0,X1)
=> ~ less(X0,X1) )
=> ~ ( less(X0,X1)
=> ~ is(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz81b) ).
tff(f4,conjecture,
~ ( ~ more(x0,y0)
=> is(x0,y0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz81h) ).
tff(f5,negated_conjecture,
~ ~ ( ~ more(x0,y0)
=> is(x0,y0) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
tff(f9,plain,
! [X0: rat,X1: rat] :
~ ( ( is(X0,X1)
=> ~ more(X0,X1) )
=> ( ( more(X0,X1)
=> ~ less(X0,X1) )
=> ~ ( less(X0,X1)
=> ~ is(X0,X1) ) ) ),
inference(flattening,[],[f3]) ).
tff(f10,plain,
( ~ more(x0,y0)
=> is(x0,y0) ),
inference(flattening,[],[f5]) ).
tff(f12,plain,
! [X0: rat,X1: rat] :
( ( ~ is(X0,X1)
| ~ less(X0,X1) )
& ( ~ less(X0,X1)
| ~ more(X0,X1) )
& ( ~ more(X0,X1)
| ~ is(X0,X1) ) ),
inference(ennf_transformation,[],[f9]) ).
tff(f13,plain,
! [X0: rat,X1: rat] :
( ( ~ is(X0,X1)
| ~ less(X0,X1) )
& ( ~ less(X0,X1)
| ~ more(X0,X1) )
& ( ~ more(X0,X1)
| ~ is(X0,X1) ) ),
inference(flattening,[],[f12]) ).
tff(f14,plain,
( is(x0,y0)
| more(x0,y0) ),
inference(ennf_transformation,[],[f10]) ).
tff(f15,plain,
less(x0,y0),
inference(cnf_transformation,[],[f1]) ).
tff(f18,plain,
! [X0: rat,X1: rat] :
( ~ more(X0,X1)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
tff(f19,plain,
! [X0: rat,X1: rat] :
( ~ is(X0,X1)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
tff(f20,plain,
( is(x0,y0)
| more(x0,y0) ),
inference(cnf_transformation,[],[f14]) ).
tff(f31,definition,
( spl1_1
<=> more(x0,y0) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
tff(f32,plain,
( more(x0,y0)
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f31]) ).
tff(f34,definition,
( spl1_2
<=> is(x0,y0) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
tff(f35,plain,
( is(x0,y0)
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f34]) ).
tff(f36,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f20,f34,f31]) ).
tff(f38,plain,
( ~ less(x0,y0)
| ~ spl1_2 ),
inference(resolution,[],[f19,f35]) ).
tff(f39,plain,
( $false
| ~ spl1_2 ),
inference(resolution,[],[f38,f15]) ).
tff(f40,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[],[f39]) ).
tff(f41,plain,
( ~ less(x0,y0)
| ~ spl1_1 ),
inference(resolution,[],[f32,f18]) ).
tff(f42,plain,
( $false
| ~ spl1_1 ),
inference(resolution,[],[f41,f15]) ).
tff(f43,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f42]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f36]) ).
cnf(s2,plain,
~ spl1_2,
inference(sat_conversion,[],[f40]) ).
cnf(s3,plain,
~ spl1_1,
inference(sat_conversion,[],[f43]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
tff(f44,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM789_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 % Computer : n001.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sun Sep 27 21:30:32 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.46 Running first-order theorem proving
% 0.14/0.46 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
% 2.96/1.27 % (3965343)Detected formulas, will run a generic FOF schedule.
% 2.96/1.27 % (3965362)dis-21_1_sil=8000:lcm=predicate:random_seed=340507092:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/129Mi)
% 2.96/1.27 % (3965362)First to succeed.
% 2.96/1.27 % (3965362)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3965343"
% 2.96/1.27 % (3965357)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=1483151362:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/134677Mi)
% 2.96/1.27 % (3965359)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1116904099:i=109:sd=1:ins=1:gsp=on:ss=axioms_3000 on theBenchmark for (3000ds/109Mi)
% 2.96/1.27 % (3965356)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=2247162156:i=141193_3000 on theBenchmark for (3000ds/141193Mi)
% 2.96/1.27 % (3965358)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=487212797:i=141695:sd=1:nm=32:gsp=on:ss=included_3000 on theBenchmark for (3000ds/141695Mi)
% 2.96/1.27 % (3965361)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2628214793:s2a=on:i=139:gtg=position_3000 on theBenchmark for (3000ds/139Mi)
% 2.96/1.27 % (3965360)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1076478155:i=119:av=off:ss=axioms_3000 on theBenchmark for (3000ds/119Mi)
% 2.96/1.27 % (3965359)Also succeeded, but the first one will report.
% 2.96/1.27 % (3965360)Also succeeded, but the first one will report.
% 2.96/1.27 % (3965361)Also succeeded, but the first one will report.
% 2.96/1.27 % (3965362)Refutation found. Thanks to Tanya!
% 2.96/1.27 % SZS status Theorem for theBenchmark
% 2.96/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 2.96/1.27 % (3965362)------------------------------
% 2.96/1.27 % (3965362)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.96/1.27 % (3965362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.96/1.27 % (3965362)CaDiCaL version: 2.1.3
% 2.96/1.27 % (3965362)Termination reason: Refutation
% 2.96/1.27 % (3965362)Time elapsed: 0.002 s
% 2.96/1.27 % (3965362)Peak memory usage: 89 MB
% 2.96/1.27 % (3965362)Instructions burned: 1 (million)
% 2.96/1.27 % (3965362)------------------------------
% 2.96/1.27 % (3965362)------------------------------
% 2.96/1.27 % (3965343)Success in time 0.348 s
% 2.96/1.27 % Vampire exiting
%------------------------------------------------------------------------------