%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM691_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 : n002.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 12:16:31 PM UTC 2026
% Result : Theorem 3.33s 1.32s
% Output : Refutation 3.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 52 ( 8 unt; 0 typ; 3 def)
% Number of atoms : 114 ( 20 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 112 ( 50 ~; 45 |; 5 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 42 !; 0 ?; 42 :)
% 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(func_def_3,type,
u: nat ).
tff(func_def_4,type,
pl: ( nat * nat ) > nat ).
tff(pred_def_1,type,
more: ( nat * nat ) > $o ).
tff(pred_def_2,type,
sP0: nat > $o ).
tff(f1,axiom,
( ~ more(x,y)
=> ( x = y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
tff(f2,axiom,
( ~ more(z,u)
=> ( z = u ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).
tff(f4,axiom,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( ~ more(X0,X1)
=> ( X0 = X1 ) )
=> ( more(X2,X3)
=> more(pl(X0,X2),pl(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz22a) ).
tff(f5,axiom,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( more(X0,X1)
=> ( ( ~ more(X2,X3)
=> ( X2 = X3 ) )
=> more(pl(X0,X2),pl(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz22b) ).
tff(f6,conjecture,
( ~ more(pl(x,z),pl(y,u))
=> ( pl(x,z) = pl(y,u) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz23) ).
tff(f7,negated_conjecture,
~ ( ~ more(pl(x,z),pl(y,u))
=> ( pl(x,z) = pl(y,u) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f10,plain,
( ( pl(x,z) != pl(y,u) )
& ~ more(pl(x,z),pl(y,u)) ),
inference(ennf_transformation,[],[f7]) ).
tff(f11,plain,
( ( x = y )
| more(x,y) ),
inference(ennf_transformation,[],[f1]) ).
tff(f12,plain,
( ( z = u )
| more(z,u) ),
inference(ennf_transformation,[],[f2]) ).
tff(f13,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( more(pl(X0,X2),pl(X1,X3))
| ( ( X2 != X3 )
& ~ more(X2,X3) )
| ~ more(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
tff(f14,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( more(pl(X0,X2),pl(X1,X3))
| ( ( X2 != X3 )
& ~ more(X2,X3) )
| ~ more(X0,X1) ),
inference(flattening,[],[f13]) ).
tff(f15,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( more(pl(X0,X2),pl(X1,X3))
| ~ more(X2,X3)
| ( ( X0 != X1 )
& ~ more(X0,X1) ) ),
inference(ennf_transformation,[],[f4]) ).
tff(f16,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( more(pl(X0,X2),pl(X1,X3))
| ~ more(X2,X3)
| ( ( X0 != X1 )
& ~ more(X0,X1) ) ),
inference(flattening,[],[f15]) ).
tff(f17,plain,
~ more(pl(x,z),pl(y,u)),
inference(cnf_transformation,[],[f10]) ).
tff(f18,plain,
pl(x,z) != pl(y,u),
inference(cnf_transformation,[],[f10]) ).
tff(f19,plain,
( more(x,y)
| ( x = y ) ),
inference(cnf_transformation,[],[f11]) ).
tff(f20,plain,
( more(z,u)
| ( z = u ) ),
inference(cnf_transformation,[],[f12]) ).
tff(f21,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( more(pl(X0,X2),pl(X1,X3))
| ~ more(X2,X3)
| ~ more(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
tff(f22,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( more(pl(X0,X2),pl(X1,X3))
| ( X2 != X3 )
| ~ more(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
tff(f24,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( more(pl(X0,X2),pl(X1,X3))
| ~ more(X2,X3)
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f16]) ).
tff(f25,definition,
~ sP0(pl(x,z)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
tff(f26,plain,
sP0(pl(y,u)),
inference(inequality_splitting,[],[f18,f25]) ).
tff(f27,plain,
! [X3: nat,X0: nat,X1: nat] :
( more(pl(X0,X3),pl(X1,X3))
| ~ more(X0,X1) ),
inference(equality_resolution,[],[f22]) ).
tff(f28,plain,
! [X2: nat,X3: nat,X1: nat] :
( more(pl(X1,X2),pl(X1,X3))
| ~ more(X2,X3) ),
inference(equality_resolution,[],[f24]) ).
tff(f30,plain,
( ~ more(z,u)
| ~ more(x,y) ),
inference(resolution,[],[f17,f21]) ).
tff(f32,definition,
( spl1_1
<=> more(x,y) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
tff(f33,plain,
( more(x,y)
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f32]) ).
tff(f34,plain,
( ~ more(x,y)
| spl1_1 ),
inference(avatar_component_clause,[],[f32]) ).
tff(f36,definition,
( spl1_2
<=> more(z,u) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
tff(f38,plain,
( ~ more(z,u)
| spl1_2 ),
inference(avatar_component_clause,[],[f36]) ).
tff(f39,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f30,f36,f32]) ).
tff(f41,plain,
( ( x = y )
| spl1_1 ),
inference(resolution,[],[f34,f19]) ).
tff(f43,plain,
( ~ more(pl(x,z),pl(x,u))
| spl1_1 ),
inference(superposition,[],[f17,f41]) ).
tff(f47,plain,
( ~ more(z,u)
| spl1_1 ),
inference(resolution,[],[f43,f28]) ).
tff(f48,plain,
( ~ spl1_2
| spl1_1 ),
inference(avatar_split_clause,[],[f47,f32,f36]) ).
tff(f49,plain,
( ( z = u )
| spl1_2 ),
inference(resolution,[],[f38,f20]) ).
tff(f50,plain,
( ~ more(pl(x,z),pl(y,z))
| spl1_2 ),
inference(superposition,[],[f17,f49]) ).
tff(f51,plain,
( sP0(pl(y,z))
| spl1_2 ),
inference(superposition,[],[f26,f49]) ).
tff(f57,plain,
( sP0(pl(x,z))
| spl1_1
| spl1_2 ),
inference(forward_demodulation,[],[f51,f41]) ).
tff(f59,plain,
( $false
| spl1_1
| spl1_2 ),
inference(forward_subsumption_resolution,[],[f57,f25]) ).
tff(f60,plain,
( spl1_1
| spl1_2 ),
inference(avatar_contradiction_clause,[],[f59]) ).
tff(f61,plain,
( ~ more(x,y)
| spl1_2 ),
inference(resolution,[],[f50,f27]) ).
tff(f64,plain,
( $false
| ~ spl1_1
| spl1_2 ),
inference(forward_subsumption_resolution,[],[f61,f33]) ).
tff(f65,plain,
( ~ spl1_1
| spl1_2 ),
inference(avatar_contradiction_clause,[],[f64]) ).
cnf(s1,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f39]) ).
cnf(s3,plain,
( spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f48]) ).
cnf(s5,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f60]) ).
cnf(s6,plain,
( ~ spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f65]) ).
cnf(s7,plain,
spl1_1,
inference(rat,[],[s3,s5]) ).
cnf(s8,plain,
spl1_2,
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s8,s7]) ).
tff(f66,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM691_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n002.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 27 21:09:22 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.39 Running first-order theorem proving
% 0.15/0.39 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
% 3.33/1.32 % (3880551)Detected formulas, will run a generic FOF schedule.
% 3.33/1.32 % (3880557)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=223051967:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.33/1.32 % (3880559)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2892676449:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.33/1.32 % (3880559)First to succeed.
% 3.33/1.32 % (3880559)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3880551"
% 3.33/1.32 % (3880558)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=2405783013:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.33/1.32 % (3880556)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=3381795820:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.33/1.32 % (3880561)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1375102232:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.33/1.32 % (3880560)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3094945915:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.33/1.32 % (3880562)dis-21_1_sil=8000:lcm=predicate:random_seed=1909330542: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)
% 3.33/1.32 % (3880562)Refutation not found, incomplete strategy
% 3.33/1.32 % (3880562)------------------------------
% 3.33/1.32 % (3880562)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.33/1.32 % (3880562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/1.32 % (3880562)CaDiCaL version: 2.1.3
% 3.33/1.32 % (3880562)Termination reason: Refutation not found, incomplete strategy
% 3.33/1.32 % (3880562)Time elapsed: 0.001 s
% 3.33/1.32 % (3880562)Peak memory usage: 88 MB
% 3.33/1.32 % (3880562)Instructions burned: 1 (million)
% 3.33/1.32 % (3880560)Also succeeded, but the first one will report.
% 3.33/1.32 % (3880561)Also succeeded, but the first one will report.
% 3.33/1.32 % (3880559)Refutation found. Thanks to Tanya!
% 3.33/1.32 % SZS status Theorem for theBenchmark
% 3.33/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.33/1.32 % (3880559)------------------------------
% 3.33/1.32 % (3880559)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.33/1.32 % (3880559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/1.32 % (3880559)CaDiCaL version: 2.1.3
% 3.33/1.32 % (3880559)Termination reason: Refutation
% 3.33/1.32 % (3880559)Time elapsed: 0.003 s
% 3.33/1.32 % (3880559)Peak memory usage: 90 MB
% 3.33/1.32 % (3880559)Instructions burned: 2 (million)
% 3.33/1.32 % (3880559)------------------------------
% 3.33/1.32 % (3880559)------------------------------
% 3.33/1.32 % (3880551)Success in time 0.399 s
% 3.33/1.32 % Vampire exiting
%------------------------------------------------------------------------------