%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM687_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 12:25:21 PM UTC 2026
% Result : Theorem 0.20s 0.53s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 67 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 63 ( 32 ~; 24 |; 0 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 35 !; 0 ?; 35 :)
% 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(f1,axiom,
( ~ more(x,y)
=> ( x = y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
tff(f2,axiom,
more(z,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n) ).
tff(f4,axiom,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( X0 = X1 )
=> ( more(X2,X3)
=> more(pl(X0,X2),pl(X1,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19g) ).
tff(f5,axiom,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( more(X0,X1)
=> ( more(X2,X3)
=> more(pl(X0,X2),pl(X1,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz21) ).
tff(f6,conjecture,
more(pl(x,z),pl(y,u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz22a) ).
tff(f7,negated_conjecture,
~ more(pl(x,z),pl(y,u)),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f10,plain,
~ more(pl(x,z),pl(y,u)),
inference(flattening,[],[f7]) ).
tff(f11,plain,
( ( x = y )
| more(x,y) ),
inference(ennf_transformation,[],[f1]) ).
tff(f13,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( more(pl(X0,X2),pl(X1,X3))
| ~ more(X2,X3)
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f4]) ).
tff(f14,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( more(pl(X0,X2),pl(X1,X3))
| ~ more(X2,X3)
| ( 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)
| ~ more(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
tff(f16,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( more(pl(X0,X2),pl(X1,X3))
| ~ more(X2,X3)
| ~ more(X0,X1) ),
inference(flattening,[],[f15]) ).
tff(f17,plain,
( more(x,y)
| ( x = y ) ),
inference(cnf_transformation,[],[f11]) ).
tff(f18,plain,
more(z,u),
inference(cnf_transformation,[],[f2]) ).
tff(f19,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( X0 != X1 )
| ~ more(X2,X3)
| more(pl(X0,X2),pl(X1,X3)) ),
inference(cnf_transformation,[],[f14]) ).
tff(f20,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,[],[f16]) ).
tff(f21,plain,
~ more(pl(x,z),pl(y,u)),
inference(cnf_transformation,[],[f10]) ).
tff(f22,plain,
! [X2: nat,X3: nat,X1: nat] :
( more(pl(X1,X2),pl(X1,X3))
| ~ more(X2,X3) ),
inference(equality_resolution,[],[f19]) ).
tff(f24,definition,
( spl0_1
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f26,plain,
( ( x = y )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f24]) ).
tff(f28,definition,
( spl0_2
<=> more(x,y) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f30,plain,
( more(x,y)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f28]) ).
tff(f31,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f17,f28,f24]) ).
tff(f32,plain,
( ~ more(z,u)
| ~ more(x,y) ),
inference(resolution,[],[f20,f21]) ).
tff(f33,plain,
~ more(x,y),
inference(forward_subsumption_resolution,[],[f32,f18]) ).
tff(f34,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f33,f30]) ).
tff(f35,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f34]) ).
tff(f38,plain,
( ~ more(pl(x,z),pl(x,u))
| ~ spl0_1 ),
inference(superposition,[],[f21,f26]) ).
tff(f39,plain,
( ~ more(z,u)
| ~ spl0_1 ),
inference(resolution,[],[f38,f22]) ).
tff(f41,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f39,f18]) ).
tff(f42,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f41]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f31]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f35]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f42]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
tff(f43,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM687_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.18/0.44 % Computer : n009.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 27 21:05:45 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.20/0.49 Running first-order model finding
% 0.20/0.49 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.53 % (2388508)Will run a generic schedule for satisfiability detection.
% 0.20/0.53 % (2388517)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1243584137:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.20/0.53 % (2388517) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2388508-2388517"...
% 0.20/0.53 % (2388518)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1598632697:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.20/0.53 % (2388517)...printing done.
% 0.20/0.53 % (2388517)Refutation found. Thanks to Tanya!
% 0.20/0.53 % SZS status Theorem for theBenchmark
% 0.20/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.53 % (2388517)------------------------------
% 0.20/0.53 % (2388517)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.53 % (2388517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.53 % (2388517)CaDiCaL version: 2.1.3
% 0.20/0.53 % (2388517)Termination reason: Refutation
% 0.20/0.53 % (2388517)Time elapsed: 0.002 s
% 0.20/0.53 % (2388517)Peak memory usage: 12 MB
% 0.20/0.53 % (2388517)Instructions burned: 1 (million)
% 0.20/0.53 % (2388508)Success in time 0.023 s
% 0.20/0.53 % Vampire exiting
%------------------------------------------------------------------------------