%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM682_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 : n008.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 12:16:26 PM UTC 2026
% Result : Theorem 3.46s 1.46s
% Output : Refutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 84 ( 17 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 93 ( 47 ~; 27 |; 4 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 37 !; 0 ?; 37 :)
% 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,
pl: ( nat * nat ) > nat ).
tff(pred_def_1,type,
less: ( nat * nat ) > $o ).
tff(pred_def_2,type,
more: ( nat * nat ) > $o ).
tff(f1,axiom,
less(pl(x,z),pl(y,z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
tff(f3,axiom,
! [X0: nat,X1: nat] :
~ ( ( ( X0 = X1 )
=> ~ more(X0,X1) )
=> ~ ~ ( ( more(X0,X1)
=> ~ less(X0,X1) )
=> ~ ( less(X0,X1)
=> ( X0 != X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10b) ).
tff(f4,axiom,
! [X0: nat,X1: nat,X2: nat] :
( more(X0,X1)
=> more(pl(X0,X2),pl(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19a) ).
tff(f6,axiom,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ~ more(X0,X1)
=> less(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10a) ).
tff(f7,conjecture,
less(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz20c) ).
tff(f8,negated_conjecture,
~ less(x,y),
inference(negated_conjecture,[status(cth)],[f7]) ).
tff(f12,plain,
! [X0: nat,X1: nat] :
~ ( ( ( X0 = X1 )
=> ~ more(X0,X1) )
=> ( ( more(X0,X1)
=> ~ less(X0,X1) )
=> ~ ( less(X0,X1)
=> ( X0 != X1 ) ) ) ),
inference(flattening,[],[f3]) ).
tff(f13,plain,
~ less(x,y),
inference(flattening,[],[f8]) ).
tff(f15,plain,
! [X0: nat,X1: nat] :
( ( ( X0 != X1 )
| ~ less(X0,X1) )
& ( ~ less(X0,X1)
| ~ more(X0,X1) )
& ( ~ more(X0,X1)
| ( X0 != X1 ) ) ),
inference(ennf_transformation,[],[f12]) ).
tff(f16,plain,
! [X0: nat,X1: nat] :
( ( ( X0 != X1 )
| ~ less(X0,X1) )
& ( ~ less(X0,X1)
| ~ more(X0,X1) )
& ( ~ more(X0,X1)
| ( X0 != X1 ) ) ),
inference(flattening,[],[f15]) ).
tff(f17,plain,
! [X0: nat,X1: nat,X2: nat] :
( more(pl(X0,X2),pl(X1,X2))
| ~ more(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
tff(f19,plain,
! [X0: nat,X1: nat] :
( less(X0,X1)
| more(X0,X1)
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f6]) ).
tff(f20,plain,
! [X0: nat,X1: nat] :
( less(X0,X1)
| more(X0,X1)
| ( X0 = X1 ) ),
inference(flattening,[],[f19]) ).
tff(f21,plain,
less(pl(x,z),pl(y,z)),
inference(cnf_transformation,[],[f1]) ).
tff(f24,plain,
! [X0: nat,X1: nat] :
( ~ more(X0,X1)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tff(f25,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tff(f26,plain,
! [X2: nat,X0: nat,X1: nat] :
( ~ more(X0,X1)
| more(pl(X0,X2),pl(X1,X2)) ),
inference(cnf_transformation,[],[f17]) ).
tff(f28,plain,
! [X0: nat,X1: nat] :
( more(X0,X1)
| less(X0,X1)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f20]) ).
tff(f29,plain,
~ less(x,y),
inference(cnf_transformation,[],[f13]) ).
tff(f33,plain,
! [X1: nat] : ~ less(X1,X1),
inference(equality_resolution,[],[f25]) ).
tff(f46,plain,
! [X2: nat,X0: nat,X1: nat] :
( less(X0,X2)
| more(pl(X0,X1),pl(X2,X1))
| ( X0 = X2 ) ),
inference(resolution,[],[f26,f28]) ).
tff(f49,plain,
! [X0: nat] :
( more(pl(x,X0),pl(y,X0))
| ( x = y ) ),
inference(resolution,[],[f46,f29]) ).
tff(f52,definition,
( spl0_1
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f54,plain,
( ( x = y )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f52]) ).
tff(f56,definition,
( spl0_2
<=> ! [X0: nat] : more(pl(x,X0),pl(y,X0)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f57,plain,
( ! [X0: nat] : more(pl(x,X0),pl(y,X0))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f56]) ).
tff(f58,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f49,f56,f52]) ).
tff(f60,plain,
( ! [X0: nat] : ~ less(pl(x,X0),pl(y,X0))
| ~ spl0_2 ),
inference(resolution,[],[f57,f24]) ).
tff(f61,plain,
( $false
| ~ spl0_2 ),
inference(resolution,[],[f60,f21]) ).
tff(f63,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f61]) ).
tff(f64,plain,
( less(pl(x,z),pl(x,z))
| ~ spl0_1 ),
inference(superposition,[],[f21,f54]) ).
tff(f66,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f64,f33]) ).
tff(f67,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f66]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f58]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f63]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f67]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
tff(f68,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM682_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 21:04:10 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.46/1.46 % (1595797)Detected formulas, will run a generic FOF schedule.
% 3.46/1.46 % (1595808)dis-21_1_sil=8000:lcm=predicate:random_seed=1799888897: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)
% 3.46/1.46 % (1595808)Instruction limit reached!
% 3.46/1.46 % (1595808)------------------------------
% 3.46/1.46 % (1595808)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.46 % (1595808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.46 % (1595808)CaDiCaL version: 2.1.3
% 3.46/1.46 % (1595808)Termination reason: Instruction limit
% 3.46/1.46 % (1595808)Termination phase: Saturation
% 3.46/1.46 % (1595808)Time elapsed: 0.030 s
% 3.46/1.46 % (1595808)Peak memory usage: 89 MB
% 3.46/1.46 % (1595808)Instructions burned: 134 (million)
% 3.46/1.46 % (1595807)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4290290313:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.46/1.46 % (1595802)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=403162560:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.46/1.46 % (1595803)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=9189462:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.46/1.46 % (1595804)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=477583050:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.46/1.46 % (1595807)First to succeed.
% 3.46/1.46 % (1595807)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1595797"
% 3.46/1.46 % (1595806)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1835224801:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.46/1.46 % (1595805)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1791299069:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.46/1.46 % (1595806)Refutation not found, incomplete strategy
% 3.46/1.46 % (1595806)------------------------------
% 3.46/1.46 % (1595806)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.46 % (1595805)Refutation not found, incomplete strategy
% 3.46/1.46 % (1595805)------------------------------
% 3.46/1.46 % (1595805)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.46 % (1595806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.46 % (1595806)CaDiCaL version: 2.1.3
% 3.46/1.46 % (1595806)Termination reason: Refutation not found, incomplete strategy
% 3.46/1.46 % (1595806)Time elapsed: 0.001 s
% 3.46/1.46 % (1595806)Peak memory usage: 87 MB
% 3.46/1.46 % (1595805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.46 % (1595805)CaDiCaL version: 2.1.3
% 3.46/1.46 % (1595805)Termination reason: Refutation not found, incomplete strategy
% 3.46/1.46 % (1595805)Time elapsed: 0.001 s
% 3.46/1.46 % (1595805)Peak memory usage: 87 MB
% 3.46/1.46 % (1595810)lrs+10_1_sil=8000:sp=occurrence:random_seed=2549005749:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.46/1.46 % (1595810)Also succeeded, but the first one will report.
% 3.46/1.46 % (1595805)------------------------------
% 3.46/1.46 % (1595805)------------------------------
% 3.46/1.46 % (1595806)------------------------------
% 3.46/1.46 % (1595806)------------------------------
% 3.46/1.46 % (1595807)Refutation found. Thanks to Tanya!
% 3.46/1.46 % SZS status Theorem for theBenchmark
% 3.46/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.46/1.46 % (1595807)------------------------------
% 3.46/1.46 % (1595807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.46 % (1595807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.46 % (1595807)CaDiCaL version: 2.1.3
% 3.46/1.46 % (1595807)Termination reason: Refutation
% 3.46/1.46 % (1595807)Time elapsed: 0.003 s
% 3.46/1.46 % (1595807)Peak memory usage: 90 MB
% 3.46/1.46 % (1595807)Instructions burned: 2 (million)
% 3.46/1.46 % (1595807)------------------------------
% 3.46/1.46 % (1595807)------------------------------
% 3.46/1.46 % (1595797)Success in time 0.405 s
% 3.46/1.46 % Vampire exiting
%------------------------------------------------------------------------------