%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM693_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 12:25:23 PM UTC 2026
% Result : Theorem 0.23s 0.51s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 26 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 10 ~; 5 |; 1 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 14 ( 13 !; 1 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
nat: $tType ).
tff(func_def_0,type,
x: nat ).
tff(func_def_1,type,
n_1: nat ).
tff(func_def_2,type,
suc: nat > nat ).
tff(func_def_3,type,
pl: ( nat * nat ) > nat ).
tff(func_def_6,type,
sK0: nat > nat ).
tff(pred_def_1,type,
more: ( nat * nat ) > $o ).
tff(f2,axiom,
! [X0: nat] :
( ( X0 != n_1 )
=> ~ ! [X1: nat] : ( X0 != suc(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz3) ).
tff(f3,axiom,
! [X0: nat,X1: nat] : more(pl(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz18) ).
tff(f4,axiom,
! [X0: nat] : ( suc(X0) = pl(n_1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz4g) ).
tff(f5,conjecture,
( ~ more(x,n_1)
=> ( x = n_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz24) ).
tff(f6,negated_conjecture,
~ ( ~ more(x,n_1)
=> ( x = n_1 ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
tff(f11,plain,
! [X0: nat] :
( ? [X1: nat] : ( suc(X1) = X0 )
| ( n_1 = X0 ) ),
inference(ennf_transformation,[],[f2]) ).
tff(f12,plain,
( ( n_1 != x )
& ~ more(x,n_1) ),
inference(ennf_transformation,[],[f6]) ).
tff(f13,plain,
! [X0: nat] :
( ( suc(sK0(X0)) = X0 )
| ( n_1 = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f11]) ).
tff(f15,plain,
! [X0: nat] :
( ( suc(sK0(X0)) = X0 )
| ( n_1 = X0 ) ),
inference(cnf_transformation,[],[f13]) ).
tff(f16,plain,
! [X0: nat,X1: nat] : more(pl(X0,X1),X0),
inference(cnf_transformation,[],[f3]) ).
tff(f17,plain,
! [X0: nat] : ( suc(X0) = pl(n_1,X0) ),
inference(cnf_transformation,[],[f4]) ).
tff(f18,plain,
~ more(x,n_1),
inference(cnf_transformation,[],[f12]) ).
tff(f19,plain,
n_1 != x,
inference(cnf_transformation,[],[f12]) ).
tff(f22,plain,
! [X0: nat] :
( ( pl(n_1,sK0(X0)) = X0 )
| ( n_1 = X0 ) ),
inference(definition_unfolding,[],[f15,f17]) ).
tff(f26,plain,
! [X0: nat] :
( more(X0,n_1)
| ( n_1 = X0 ) ),
inference(superposition,[],[f16,f22]) ).
tff(f27,plain,
n_1 = x,
inference(resolution,[],[f26,f18]) ).
tff(f28,plain,
$false,
inference(forward_subsumption_resolution,[],[f27,f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM693_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.17/0.42 % Computer : n005.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sun Sep 27 21:06:47 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.17/0.48 Running first-order model finding
% 0.17/0.48 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
% 0.23/0.51 % (161906)Will run a generic schedule for satisfiability detection.
% 0.23/0.51 % (161916)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1088020696:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.23/0.51 % (161916) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-161906-161916"...
% 0.23/0.51 % (161911)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2051305877_3000 on theBenchmark for (3000ds/0Mi)
% 0.23/0.51 % (161916)...printing done.
% 0.23/0.51 % (161916)Refutation found. Thanks to Tanya!
% 0.23/0.51 % SZS status Theorem for theBenchmark
% 0.23/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.51 % (161916)------------------------------
% 0.23/0.51 % (161916)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.51 % (161916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.51 % (161916)CaDiCaL version: 2.1.3
% 0.23/0.51 % (161916)Termination reason: Refutation
% 0.23/0.51 % (161916)Time elapsed: 0.001 s
% 0.23/0.51 % (161916)Peak memory usage: 12 MB
% 0.23/0.51 % (161916)Instructions burned: 1 (million)
% 0.23/0.51 % (161906)Success in time 0.023 s
% 0.23/0.51 % Vampire exiting
%------------------------------------------------------------------------------