%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM693_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 12:16:32 PM UTC 2026
% Result : Theorem 3.68s 1.49s
% Output : Refutation 3.68s
% 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/sandbox/benchmark/theBenchmark.p',satz3) ).
tff(f3,axiom,
! [X0: nat,X1: nat] : more(pl(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz18) ).
tff(f4,axiom,
! [X0: nat] : ( suc(X0) = pl(n_1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz4g) ).
tff(f5,conjecture,
( ~ more(x,n_1)
=> ( x = n_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz24) ).
tff(f6,negated_conjecture,
~ ( ~ more(x,n_1)
=> ( x = n_1 ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
tff(f9,plain,
( ( n_1 != x )
& ~ more(x,n_1) ),
inference(ennf_transformation,[],[f6]) ).
tff(f10,plain,
! [X0: nat] :
( ? [X1: nat] : ( suc(X1) = X0 )
| ( n_1 = X0 ) ),
inference(ennf_transformation,[],[f2]) ).
tff(f11,plain,
! [X0: nat] :
( ( suc(sK0(X0)) = X0 )
| ( n_1 = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f10]) ).
tff(f12,plain,
~ more(x,n_1),
inference(cnf_transformation,[],[f9]) ).
tff(f13,plain,
n_1 != x,
inference(cnf_transformation,[],[f9]) ).
tff(f14,plain,
! [X0: nat,X1: nat] : more(pl(X0,X1),X0),
inference(cnf_transformation,[],[f3]) ).
tff(f15,plain,
! [X0: nat] : ( suc(X0) = pl(n_1,X0) ),
inference(cnf_transformation,[],[f4]) ).
tff(f16,plain,
! [X0: nat] :
( ( suc(sK0(X0)) = X0 )
| ( n_1 = X0 ) ),
inference(cnf_transformation,[],[f11]) ).
tff(f17,plain,
! [X0: nat] :
( ( pl(n_1,sK0(X0)) = X0 )
| ( n_1 = X0 ) ),
inference(definition_unfolding,[],[f16,f15]) ).
tff(f18,plain,
! [X0: nat] :
( more(X0,n_1)
| ( n_1 = X0 ) ),
inference(superposition,[],[f14,f17]) ).
tff(f19,plain,
n_1 = x,
inference(resolution,[],[f18,f12]) ).
tff(f20,plain,
$false,
inference(forward_subsumption_resolution,[],[f19,f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM693_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n004.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 21:06:52 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.68/1.49 % (3878194)Detected formulas, will run a generic FOF schedule.
% 3.68/1.49 % (3878202)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3410614133:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.68/1.49 % (3878202)Refutation not found, incomplete strategy
% 3.68/1.49 % (3878202)------------------------------
% 3.68/1.49 % (3878202)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.49 % (3878202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.49 % (3878202)CaDiCaL version: 2.1.3
% 3.68/1.49 % (3878202)Termination reason: Refutation not found, incomplete strategy
% 3.68/1.49 % (3878202)Time elapsed: 0.001 s
% 3.68/1.49 % (3878202)Peak memory usage: 87 MB
% 3.68/1.49 % (3878200)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=3942254171:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.68/1.49 % (3878204)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1568186629:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.68/1.49 % (3878203)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3480960411:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.68/1.49 % (3878199)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=2915020456:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.68/1.49 % (3878205)dis-21_1_sil=8000:lcm=predicate:random_seed=89506790: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)
% 3.68/1.49 % (3878201)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=3680762343:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.68/1.49 % (3878205)Refutation not found, incomplete strategy
% 3.68/1.49 % (3878205)------------------------------
% 3.68/1.49 % (3878205)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.49 % (3878203)First to succeed.
% 3.68/1.49 % (3878205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.49 % (3878205)CaDiCaL version: 2.1.3
% 3.68/1.49 % (3878205)Termination reason: Refutation not found, incomplete strategy
% 3.68/1.49 % (3878205)Time elapsed: 0.001 s
% 3.68/1.49 % (3878205)Peak memory usage: 88 MB
% 3.68/1.49 % (3878204)Also succeeded, but the first one will report.
% 3.68/1.49 % (3878203)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3878194"
% 3.68/1.49 % (3878202)------------------------------
% 3.68/1.49 % (3878202)------------------------------
% 3.68/1.49 % (3878205)------------------------------
% 3.68/1.49 % (3878205)------------------------------
% 3.68/1.49 % (3878203)Refutation found. Thanks to Tanya!
% 3.68/1.49 % SZS status Theorem for theBenchmark
% 3.68/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.68/1.49 % (3878203)------------------------------
% 3.68/1.49 % (3878203)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.49 % (3878203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.49 % (3878203)CaDiCaL version: 2.1.3
% 3.68/1.49 % (3878203)Termination reason: Refutation
% 3.68/1.49 % (3878203)Time elapsed: 0.002 s
% 3.68/1.49 % (3878203)Peak memory usage: 88 MB
% 3.68/1.49 % (3878203)Instructions burned: 1 (million)
% 3.68/1.49 % (3878203)------------------------------
% 3.68/1.49 % (3878203)------------------------------
% 3.68/1.49 % (3878194)Success in time 0.436 s
% 3.68/1.49 % Vampire exiting
%------------------------------------------------------------------------------