%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG280^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 07:45:20 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 42 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 192 ( 9 ~; 0 |; 20 &; 159 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 60 ( 0 ^; 57 !; 3 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cE: a ).
thf(func_def_1,type,
cP: a > a > a ).
thf(func_def_2,type,
cJ: a > a ).
thf(func_def_4,type,
sK0: a ).
thf(f1,conjecture,
( ( ! [X1: a,X0: a,X2: a] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) )
& ! [X1: a] :
( ( cP @ ( cJ @ X1 ) @ X1 )
= cE )
& ! [X0: a] :
( ( cP @ cE @ X0 )
= X0 ) )
=> ! [X3: a] :
( ( cP @ X3 @ cE )
= X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM17_pme) ).
thf(f2,negated_conjecture,
~ ( ( ! [X1: a,X0: a,X2: a] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) )
& ! [X1: a] :
( ( cP @ ( cJ @ X1 ) @ X1 )
= cE )
& ! [X0: a] :
( ( cP @ cE @ X0 )
= X0 ) )
=> ! [X3: a] :
( ( cP @ X3 @ cE )
= X3 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: a,X1: a,X2: a] :
( ( cP @ X1 @ ( cP @ X0 @ X2 ) )
= ( cP @ ( cP @ X1 @ X0 ) @ X2 ) )
& ! [X3: a] :
( cE
= ( cP @ ( cJ @ X3 ) @ X3 ) )
& ! [X4: a] :
( ( cP @ cE @ X4 )
= X4 ) )
=> ! [X5: a] :
( ( cP @ X5 @ cE )
= X5 ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X2: a,X1: a,X0: a] :
( ( cP @ X1 @ ( cP @ X0 @ X2 ) )
= ( cP @ ( cP @ X1 @ X0 ) @ X2 ) )
& ! [X3: a] :
( cE
= ( cP @ ( cJ @ X3 ) @ X3 ) )
& ! [X4: a] :
( ( cP @ cE @ X4 )
= X4 ) )
=> ! [X5: a] :
( ( cP @ X5 @ cE )
= X5 ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ? [X5: a] :
( ( cP @ X5 @ cE )
!= X5 )
& ! [X2: a,X1: a,X0: a] :
( ( cP @ X1 @ ( cP @ X0 @ X2 ) )
= ( cP @ ( cP @ X1 @ X0 ) @ X2 ) )
& ! [X3: a] :
( cE
= ( cP @ ( cJ @ X3 ) @ X3 ) )
& ! [X4: a] :
( ( cP @ cE @ X4 )
= X4 ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ? [X5: a] :
( ( cP @ X5 @ cE )
!= X5 )
& ! [X4: a] :
( ( cP @ cE @ X4 )
= X4 )
& ! [X2: a,X1: a,X0: a] :
( ( cP @ X1 @ ( cP @ X0 @ X2 ) )
= ( cP @ ( cP @ X1 @ X0 ) @ X2 ) )
& ! [X3: a] :
( cE
= ( cP @ ( cJ @ X3 ) @ X3 ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ? [X0: a] :
( ( cP @ X0 @ cE )
!= X0 )
& ! [X1: a] :
( ( cP @ cE @ X1 )
= X1 )
& ! [X2: a,X3: a,X4: a] :
( ( cP @ ( cP @ X3 @ X4 ) @ X2 )
= ( cP @ X3 @ ( cP @ X4 @ X2 ) ) )
& ! [X5: a] :
( cE
= ( cP @ ( cJ @ X5 ) @ X5 ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( ( cP @ sK0 @ cE )
!= sK0 )
& ! [X1: a] :
( ( cP @ cE @ X1 )
= X1 )
& ! [X2: a,X3: a,X4: a] :
( ( cP @ ( cP @ X3 @ X4 ) @ X2 )
= ( cP @ X3 @ ( cP @ X4 @ X2 ) ) )
& ! [X5: a] :
( cE
= ( cP @ ( cJ @ X5 ) @ X5 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f7]) ).
thf(f9,plain,
! [X5: a] :
( cE
= ( cP @ ( cJ @ X5 ) @ X5 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
! [X2: a,X3: a,X4: a] :
( ( cP @ ( cP @ X3 @ X4 ) @ X2 )
= ( cP @ X3 @ ( cP @ X4 @ X2 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
! [X1: a] :
( ( cP @ cE @ X1 )
= X1 ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
( ( cP @ sK0 @ cE )
!= sK0 ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
! [X0: a,X1: a] :
( ( cP @ cE @ X1 )
= ( cP @ ( cJ @ X0 ) @ ( cP @ X0 @ X1 ) ) ),
inference(constrained_superposition,[],[f10,f9]) ).
thf(f16,plain,
! [X0: a,X1: a] :
( ( cP @ ( cJ @ X0 ) @ ( cP @ X0 @ X1 ) )
= X1 ),
inference(forward_demodulation,[],[f14,f11]) ).
thf(f20,plain,
! [X0: a] :
( ( cP @ ( cJ @ ( cJ @ X0 ) ) @ cE )
= X0 ),
inference(constrained_superposition,[],[f16,f9]) ).
thf(f22,plain,
! [X0: a,X1: a] :
( ( cP @ X1 @ X0 )
= ( cP @ ( cJ @ ( cJ @ X1 ) ) @ X0 ) ),
inference(constrained_superposition,[],[f16,f16]) ).
thf(f35,plain,
! [X0: a] :
( ( cP @ X0 @ cE )
= X0 ),
inference(constrained_superposition,[],[f22,f20]) ).
thf(f56,plain,
sK0 != sK0,
inference(constrained_superposition,[],[f12,f35]) ).
thf(f57,plain,
$false,
inference(trivial_inequality_removal,[],[f56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG280^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n011.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
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 17:36:31 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.20/0.27 % (411047)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (411054)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=409033176:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.27 % (411054) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-411047-411054"...
% 0.20/0.27 % (411054)...printing done.
% 0.20/0.27 % (411054)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 % (411054)------------------------------
% 0.20/0.27 % (411054)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (411054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (411054)CaDiCaL version: 2.1.3
% 0.20/0.27 % (411054)Termination reason: Refutation
% 0.20/0.27 % (411054)Time elapsed: 0.002 s
% 0.20/0.27 % (411054)Peak memory usage: 12 MB
% 0.20/0.27 % (411054)Instructions burned: 5 (million)
% 0.20/0.27 % (411047)Success in time 0.03 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------