%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM742_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 : n020.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 12:16:46 PM UTC 2026
% Result : Theorem 4.80s 1.70s
% Output : Refutation 4.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 15 unt; 0 typ; 2 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 81 ( 41 ~; 31 |; 0 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 41 ( 0 sgn 41 !; 0 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
frac: $tType ).
tff(func_def_0,type,
x: frac ).
tff(func_def_1,type,
y: frac ).
tff(func_def_2,type,
z: frac ).
tff(pred_def_1,type,
lessf: ( frac * frac ) > $o ).
tff(pred_def_2,type,
eq: ( frac * frac ) > $o ).
tff(pred_def_3,type,
sQ0_eqProxy: ( $o * $o ) > $o ).
tff(f1,axiom,
( ~ lessf(x,y)
=> eq(x,y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
tff(f2,axiom,
lessf(y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k) ).
tff(f4,axiom,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( lessf(X0,X1)
=> ( eq(X0,X2)
=> ( eq(X1,X3)
=> lessf(X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz45) ).
tff(f5,axiom,
! [X0: frac,X1: frac] :
( eq(X0,X1)
=> eq(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz38) ).
tff(f6,axiom,
! [X0: frac,X1: frac,X2: frac] :
( lessf(X0,X1)
=> ( lessf(X1,X2)
=> lessf(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz50) ).
tff(f7,axiom,
! [X0: frac] : eq(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz37) ).
tff(f8,conjecture,
lessf(x,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz51a) ).
tff(f9,negated_conjecture,
~ lessf(x,z),
inference(negated_conjecture,[status(cth)],[f8]) ).
tff(f13,plain,
~ lessf(x,z),
inference(flattening,[],[f9]) ).
tff(f14,plain,
( eq(x,y)
| lessf(x,y) ),
inference(ennf_transformation,[],[f1]) ).
tff(f16,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( lessf(X2,X3)
| ~ eq(X1,X3)
| ~ eq(X0,X2)
| ~ lessf(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
tff(f17,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( lessf(X2,X3)
| ~ eq(X1,X3)
| ~ eq(X0,X2)
| ~ lessf(X0,X1) ),
inference(flattening,[],[f16]) ).
tff(f18,plain,
! [X0: frac,X1: frac] :
( eq(X1,X0)
| ~ eq(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
tff(f19,plain,
! [X0: frac,X1: frac,X2: frac] :
( lessf(X0,X2)
| ~ lessf(X1,X2)
| ~ lessf(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
tff(f20,plain,
! [X0: frac,X1: frac,X2: frac] :
( lessf(X0,X2)
| ~ lessf(X1,X2)
| ~ lessf(X0,X1) ),
inference(flattening,[],[f19]) ).
tff(f21,plain,
( eq(x,y)
| lessf(x,y) ),
inference(cnf_transformation,[],[f14]) ).
tff(f22,plain,
lessf(y,z),
inference(cnf_transformation,[],[f2]) ).
tff(f24,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( lessf(X2,X3)
| ~ eq(X1,X3)
| ~ eq(X0,X2)
| ~ lessf(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
tff(f25,plain,
! [X0: frac,X1: frac] :
( eq(X1,X0)
| ~ eq(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
tff(f26,plain,
! [X2: frac,X0: frac,X1: frac] :
( lessf(X0,X2)
| ~ lessf(X1,X2)
| ~ lessf(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
tff(f27,plain,
! [X0: frac] : eq(X0,X0),
inference(cnf_transformation,[],[f7]) ).
tff(f28,plain,
~ lessf(x,z),
inference(cnf_transformation,[],[f13]) ).
tff(f39,definition,
( spl1_1
<=> lessf(x,y) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
tff(f40,plain,
( lessf(x,y)
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f39]) ).
tff(f42,definition,
( spl1_2
<=> eq(x,y) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
tff(f43,plain,
( eq(x,y)
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f42]) ).
tff(f44,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f21,f42,f39]) ).
tff(f47,plain,
! [X0: frac] :
( ~ lessf(X0,z)
| ~ lessf(x,X0) ),
inference(resolution,[],[f26,f28]) ).
tff(f48,plain,
~ lessf(x,y),
inference(resolution,[],[f47,f22]) ).
tff(f51,plain,
! [X0: frac,X1: frac] :
( ~ eq(X0,z)
| ~ eq(X1,x)
| ~ lessf(X1,X0) ),
inference(resolution,[],[f24,f28]) ).
tff(f56,plain,
! [X0: frac] :
( ~ eq(X0,x)
| ~ lessf(X0,z) ),
inference(resolution,[],[f51,f27]) ).
tff(f61,plain,
! [X0: frac] :
( ~ eq(x,X0)
| ~ lessf(X0,z) ),
inference(resolution,[],[f56,f25]) ).
tff(f77,plain,
( ~ lessf(y,z)
| ~ spl1_2 ),
inference(resolution,[],[f61,f43]) ).
tff(f80,plain,
( $false
| ~ spl1_2 ),
inference(resolution,[],[f77,f22]) ).
tff(f83,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[],[f80]) ).
tff(f84,plain,
( $false
| ~ spl1_1 ),
inference(resolution,[],[f40,f48]) ).
tff(f86,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f84]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f44]) ).
cnf(s2,plain,
~ spl1_2,
inference(sat_conversion,[],[f83]) ).
cnf(s3,plain,
~ spl1_1,
inference(sat_conversion,[],[f86]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
tff(f87,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM742_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.37 % Computer : n020.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sun Sep 27 21:16:05 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 4.80/1.70 % (3751127)Detected formulas, will run a generic FOF schedule.
% 4.80/1.70 % (3751146)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=465259201:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.80/1.70 % (3751150)dis-21_1_sil=8000:lcm=predicate:random_seed=4222840316: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)
% 4.80/1.70 % (3751150)First to succeed.
% 4.80/1.70 % (3751150)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3751127"
% 4.80/1.70 % (3751147)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4292548523:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.80/1.70 % (3751148)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1274071351:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.80/1.70 % (3751149)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2458029577:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.80/1.70 % (3751144)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=2578575106:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.80/1.70 % (3751145)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=1880051773:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.80/1.70 % (3751147)Refutation not found, incomplete strategy
% 4.80/1.70 % (3751147)------------------------------
% 4.80/1.70 % (3751147)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.80/1.70 % (3751147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.80/1.70 % (3751147)CaDiCaL version: 2.1.3
% 4.80/1.70 % (3751147)Termination reason: Refutation not found, incomplete strategy
% 4.80/1.70 % (3751147)Time elapsed: 0.001 s
% 4.80/1.70 % (3751147)Peak memory usage: 87 MB
% 4.80/1.70 % (3751148)Also succeeded, but the first one will report.
% 4.80/1.70 % (3751149)Also succeeded, but the first one will report.
% 4.80/1.70 % (3751150)Refutation found. Thanks to Tanya!
% 4.80/1.70 % SZS status Theorem for theBenchmark
% 4.80/1.70 % SZS output start Proof for theBenchmark
% See solution above
% 4.80/1.70 % (3751150)------------------------------
% 4.80/1.70 % (3751150)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.80/1.70 % (3751150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.80/1.70 % (3751150)CaDiCaL version: 2.1.3
% 4.80/1.70 % (3751150)Termination reason: Refutation
% 4.80/1.70 % (3751150)Time elapsed: 0.005 s
% 4.80/1.70 % (3751150)Peak memory usage: 89 MB
% 4.80/1.70 % (3751150)Instructions burned: 2 (million)
% 4.80/1.70 % (3751150)------------------------------
% 4.80/1.70 % (3751150)------------------------------
% 4.80/1.70 % (3751127)Success in time 0.594 s
% 4.80/1.70 % Vampire exiting
%------------------------------------------------------------------------------