%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM662^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 08:18:26 AM UTC 2026
% Result : Theorem 0.26s 0.32s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 18 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 69 ( 13 ~; 0 |; 0 &; 56 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 19 ( 0 ^; 17 !; 2 ?; 19 :)
% 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(func_def_8,type,
sK1: nat ).
thf(func_def_9,type,
vNOT: $o > $o ).
thf(f1,axiom,
~ ! [X0: nat] :
( y
!= ( pl @ x @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
thf(f2,axiom,
~ ! [X0: nat] :
( z
!= ( pl @ y @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k) ).
thf(f4,axiom,
! [X1: nat,X0: nat,X2: nat] :
( ( pl @ ( pl @ X0 @ X1 ) @ X2 )
= ( pl @ X0 @ ( pl @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz5) ).
thf(f5,conjecture,
~ ! [X0: nat] :
( z
!= ( pl @ x @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz15) ).
thf(f6,negated_conjecture,
~ ~ ! [X0: nat] :
( z
!= ( pl @ x @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f10,plain,
! [X0: nat] :
( z
!= ( pl @ x @ X0 ) ),
inference(flattening,[],[f6]) ).
thf(f11,plain,
? [X0: nat] :
( y
= ( pl @ x @ X0 ) ),
inference(ennf_transformation,[],[f1]) ).
thf(f12,plain,
? [X0: nat] :
( z
= ( pl @ y @ X0 ) ),
inference(ennf_transformation,[],[f2]) ).
thf(f14,plain,
( z
= ( pl @ y @ sK0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f12]) ).
thf(f15,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( pl @ ( pl @ X1 @ X0 ) @ X2 )
= ( pl @ X1 @ ( pl @ X0 @ X2 ) ) ),
inference(rectify,[],[f4]) ).
thf(f16,plain,
( y
= ( pl @ x @ sK1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f11]) ).
thf(f17,plain,
( z
= ( pl @ y @ sK0 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f18,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( pl @ ( pl @ X1 @ X0 ) @ X2 )
= ( pl @ X1 @ ( pl @ X0 @ X2 ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f19,plain,
! [X0: nat] :
( ( pl @ x @ X0 )
!= z ),
inference(cnf_transformation,[],[f10]) ).
thf(f21,plain,
( y
= ( pl @ x @ sK1 ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f27,plain,
! [X0: nat] :
( ( pl @ y @ X0 )
= ( pl @ x @ ( pl @ sK1 @ X0 ) ) ),
inference(constrained_superposition,[],[f18,f21]) ).
thf(f42,plain,
! [X0: nat] :
( z
!= ( pl @ y @ X0 ) ),
inference(constrained_superposition,[],[f19,f27]) ).
thf(f45,plain,
z != z,
inference(constrained_superposition,[],[f42,f17]) ).
thf(f47,plain,
$false,
inference(trivial_inequality_removal,[],[f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM662^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.23 % Computer : n013.cluster.edu
% 0.11/0.23 % Model : x86_64 x86_64
% 0.11/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.23 % Memory : 8046.5625MB
% 0.11/0.23 % OS : Linux 6.8.0-71-generic
% 0.11/0.23 % CPULimit : 300
% 0.11/0.23 % WCLimit : 300
% 0.11/0.23 % DateTime : Tue Sep 29 12:32:22 UTC 2026
% 0.11/0.23 % CPUTime :
% 0.11/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.27 Running higher-order theorem proving
% 0.11/0.28 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.26/0.32 % (2034605)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.26/0.32 % (2034615)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3974487800:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_3000 on theBenchmark for (3000ds/75Mi)
% 0.26/0.32 % (2034613)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=2076817944: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_3000 on theBenchmark for (3000ds/634Mi)
% 0.26/0.32 % (2034615) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2034605-2034615"...
% 0.26/0.32 % (2034615)...printing done.
% 0.26/0.32 % (2034615)Refutation found. Thanks to Tanya!
% 0.26/0.32 % SZS status Theorem for theBenchmark
% 0.26/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.32 % (2034615)------------------------------
% 0.26/0.32 % (2034615)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.32 % (2034615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.32 % (2034615)CaDiCaL version: 2.1.3
% 0.26/0.32 % (2034615)Termination reason: Refutation
% 0.26/0.32 % (2034615)Time elapsed: 0.002 s
% 0.26/0.32 % (2034615)Peak memory usage: 13 MB
% 0.26/0.32 % (2034615)Instructions burned: 3 (million)
% 0.26/0.32 % (2034605)Success in time 0.027 s
% 0.26/0.32 % Vampire exiting
%------------------------------------------------------------------------------