%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM663_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 12:25:15 PM UTC 2026
% Result : Theorem 0.22s 0.50s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 12 unt; 0 typ; 2 def)
% Number of atoms : 52 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 21 ~; 17 |; 0 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 13 ( 0 sgn 13 !; 0 ?; 13 :)
% 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(pred_def_1,type,
less: ( nat * nat ) > $o ).
tff(f1,axiom,
( ~ less(x,y)
=> ( x = y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
tff(f2,axiom,
less(y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k) ).
tff(f4,axiom,
! [X0: nat,X1: nat,X2: nat] :
( less(X0,X1)
=> ( less(X1,X2)
=> less(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz15) ).
tff(f5,conjecture,
less(x,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz16a) ).
tff(f6,negated_conjecture,
~ less(x,z),
inference(negated_conjecture,[status(cth)],[f5]) ).
tff(f9,plain,
~ less(x,z),
inference(flattening,[],[f6]) ).
tff(f10,plain,
( ( x = y )
| less(x,y) ),
inference(ennf_transformation,[],[f1]) ).
tff(f12,plain,
! [X0: nat,X1: nat,X2: nat] :
( less(X0,X2)
| ~ less(X1,X2)
| ~ less(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
tff(f13,plain,
! [X0: nat,X1: nat,X2: nat] :
( less(X0,X2)
| ~ less(X1,X2)
| ~ less(X0,X1) ),
inference(flattening,[],[f12]) ).
tff(f14,plain,
( less(x,y)
| ( x = y ) ),
inference(cnf_transformation,[],[f10]) ).
tff(f15,plain,
less(y,z),
inference(cnf_transformation,[],[f2]) ).
tff(f16,plain,
! [X2: nat,X0: nat,X1: nat] :
( ~ less(X1,X2)
| ~ less(X0,X1)
| less(X0,X2) ),
inference(cnf_transformation,[],[f13]) ).
tff(f17,plain,
~ less(x,z),
inference(cnf_transformation,[],[f9]) ).
tff(f19,definition,
( spl0_1
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f21,plain,
( ( x = y )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f19]) ).
tff(f23,definition,
( spl0_2
<=> less(x,y) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f25,plain,
( less(x,y)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f23]) ).
tff(f26,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f14,f23,f19]) ).
tff(f27,plain,
! [X0: nat] :
( ~ less(X0,y)
| less(X0,z) ),
inference(resolution,[],[f16,f15]) ).
tff(f29,plain,
( less(x,z)
| ~ spl0_2 ),
inference(resolution,[],[f27,f25]) ).
tff(f30,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f29,f17]) ).
tff(f31,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f30]) ).
tff(f33,plain,
( less(x,z)
| ~ spl0_1 ),
inference(superposition,[],[f15,f21]) ).
tff(f34,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f33,f17]) ).
tff(f35,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f34]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f26]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f31]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f35]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
tff(f36,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM663_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.40 % Computer : n005.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sun Sep 27 21:00:32 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.46 Running first-order model finding
% 0.14/0.46 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.50 % (154770)Will run a generic schedule for satisfiability detection.
% 0.22/0.50 % (154776)% WARNING: option uhcvi not known.
% 0.22/0.50 % (154776)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3440062448:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.50 % (154776) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-154770-154776"...
% 0.22/0.50 % (154776)...printing done.
% 0.22/0.50 % (154777)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=150149211:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.50 % (154776)Refutation found. Thanks to Tanya!
% 0.22/0.50 % SZS status Theorem for theBenchmark
% 0.22/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.50 % (154776)------------------------------
% 0.22/0.50 % (154776)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.50 % (154776)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.50 % (154776)CaDiCaL version: 2.1.3
% 0.22/0.50 % (154776)Termination reason: Refutation
% 0.22/0.50 % (154776)Time elapsed: 0.002 s
% 0.22/0.50 % (154776)Peak memory usage: 12 MB
% 0.22/0.50 % (154776)Instructions burned: 1 (million)
% 0.22/0.50 % (154770)Success in time 0.024 s
% 0.22/0.50 % Vampire exiting
%------------------------------------------------------------------------------