%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM670^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 : Wed Sep 30 08:18:29 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 21 unt; 0 typ; 1 def)
% Number of atoms : 35 ( 21 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 140 ( 21 ~; 6 |; 0 &; 112 @)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 27 !; 1 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
x: nat ).
thf(func_def_1,type,
y: nat ).
thf(func_def_2,type,
z: nat ).
thf(func_def_3,type,
pl: nat > nat > nat ).
thf(func_def_7,type,
sK0: nat ).
thf(f1,axiom,
~ ! [X0: nat] :
( x
!= ( pl @ y @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(f3,axiom,
! [X1: nat,X0: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz6) ).
thf(f4,axiom,
! [X2: nat,X1: nat,X0: nat] :
( ( pl @ ( pl @ X0 @ X1 ) @ X2 )
= ( pl @ X0 @ ( pl @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz5) ).
thf(f5,conjecture,
~ ! [X0: nat] :
( ( pl @ x @ z )
!= ( pl @ ( pl @ y @ z ) @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19a) ).
thf(f6,negated_conjecture,
~ ~ ! [X0: nat] :
( ( pl @ x @ z )
!= ( pl @ ( pl @ y @ z ) @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f9,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( pl @ X2 @ ( pl @ X1 @ X0 ) )
= ( pl @ ( pl @ X2 @ X1 ) @ X0 ) ),
inference(rectify,[],[f4]) ).
thf(f11,plain,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
inference(rectify,[],[f3]) ).
thf(f12,plain,
! [X0: nat] :
( ( pl @ x @ z )
!= ( pl @ ( pl @ y @ z ) @ X0 ) ),
inference(flattening,[],[f6]) ).
thf(f14,plain,
? [X0: nat] :
( x
= ( pl @ y @ X0 ) ),
inference(ennf_transformation,[],[f1]) ).
thf(f15,plain,
( x
= ( pl @ y @ sK0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f14]) ).
thf(f16,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( pl @ ( pl @ X0 @ X2 ) @ X1 )
= ( pl @ X0 @ ( pl @ X2 @ X1 ) ) ),
inference(rectify,[],[f9]) ).
thf(f18,plain,
! [X0: nat] :
( ( pl @ x @ z )
!= ( pl @ ( pl @ y @ z ) @ X0 ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f19,plain,
( x
= ( pl @ y @ sK0 ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f20,plain,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f21,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( pl @ ( pl @ X0 @ X2 ) @ X1 )
= ( pl @ X0 @ ( pl @ X2 @ X1 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f25,definition,
( spl1_1
<=> ( x
= ( pl @ y @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f27,plain,
( ( x
= ( pl @ y @ sK0 ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f25]) ).
thf(f28,plain,
spl1_1,
inference(avatar_split_clause,[],[f19,f25]) ).
thf(f29,plain,
( ! [X0: nat] :
( ( pl @ ( pl @ y @ z ) @ X0 )
!= ( pl @ ( pl @ y @ sK0 ) @ z ) )
| ~ spl1_1 ),
inference(forward_demodulation,[],[f18,f27]) ).
thf(f59,plain,
( ! [X0: nat] :
( ( pl @ ( pl @ y @ z ) @ X0 )
!= ( pl @ y @ ( pl @ sK0 @ z ) ) )
| ~ spl1_1 ),
inference(forward_demodulation,[],[f29,f21]) ).
thf(f60,plain,
( ! [X0: nat] :
( ( pl @ y @ ( pl @ z @ X0 ) )
!= ( pl @ y @ ( pl @ sK0 @ z ) ) )
| ~ spl1_1 ),
inference(forward_demodulation,[],[f59,f21]) ).
thf(f116,plain,
( ! [X0: nat] :
( ( pl @ y @ ( pl @ X0 @ z ) )
!= ( pl @ y @ ( pl @ sK0 @ z ) ) )
| ~ spl1_1 ),
inference(superposition,[],[f60,f20]) ).
thf(f127,plain,
( $false
| ~ spl1_1 ),
inference(equality_resolution,[],[f116]) ).
thf(f128,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f127]) ).
cnf(s1,plain,
spl1_1,
inference(sat_conversion,[],[f28]) ).
cnf(s2,plain,
~ spl1_1,
inference(sat_conversion,[],[f128]) ).
cnf(s3,plain,
$false,
inference(rat,[],[s1,s2]) ).
thf(f129,plain,
$false,
inference(avatar_sat_refutation,[],[s3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM670^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n006.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 12:34:09 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.27 % (649816)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (649824)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1889116770:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.27 % (649824) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-649816-649824"...
% 0.20/0.27 % (649824)...printing done.
% 0.20/0.27 % (649824)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (649824)------------------------------
% 0.20/0.27 % (649824)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (649824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (649824)CaDiCaL version: 2.1.3
% 0.20/0.27 % (649824)Termination reason: Refutation
% 0.20/0.27 % (649824)Time elapsed: 0.004 s
% 0.20/0.27 % (649824)Peak memory usage: 13 MB
% 0.20/0.27 % (649824)Instructions burned: 11 (million)
% 0.20/0.27 % (649816)Success in time 0.034 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------