%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG282^5 : 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 : n017.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 0.23s 0.27s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 40 ( 39 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 174 ( 11 ~; 0 |; 18 &; 142 @)
% ( 0 <=>; 3 =>; 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 : 8 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 69 ( 0 ^; 60 !; 9 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cP: a > a > a ).
thf(func_def_1,type,
cE: a ).
thf(func_def_2,type,
cJ: a > a ).
thf(func_def_4,type,
sK0: a ).
thf(func_def_5,type,
sK1: a ).
thf(f1,conjecture,
( ( ! [X2: a,X0: a,X1: 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,X4: a] :
? [X5: a] :
( ( cP @ X5 @ X3 )
= X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM21_pme) ).
thf(f2,negated_conjecture,
~ ( ( ! [X2: a,X0: a,X1: 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,X4: a] :
? [X5: a] :
( ( cP @ X5 @ X3 )
= X4 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X3: a] :
( cE
= ( cP @ ( cJ @ X3 ) @ X3 ) )
& ! [X2: a,X0: a,X1: a] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) )
& ! [X4: a] :
( ( cP @ cE @ X4 )
= X4 ) )
=> ! [X5: a,X6: a] :
? [X7: a] :
( ( cP @ X7 @ X5 )
= X6 ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( ? [X6: a,X5: a] :
! [X7: a] :
( ( cP @ X7 @ X5 )
!= X6 )
& ! [X3: a] :
( cE
= ( cP @ ( cJ @ X3 ) @ X3 ) )
& ! [X2: a,X0: a,X1: a] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) )
& ! [X4: a] :
( ( cP @ cE @ X4 )
= X4 ) ),
inference(ennf_transformation,[],[f3]) ).
thf(f5,plain,
( ! [X4: a] :
( ( cP @ cE @ X4 )
= X4 )
& ! [X3: a] :
( cE
= ( cP @ ( cJ @ X3 ) @ X3 ) )
& ! [X2: a,X0: a,X1: a] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) )
& ? [X6: a,X5: a] :
! [X7: a] :
( ( cP @ X7 @ X5 )
!= X6 ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ! [X0: a] :
( ( cP @ cE @ X0 )
= X0 )
& ! [X1: a] :
( cE
= ( cP @ ( cJ @ X1 ) @ X1 ) )
& ! [X2: a,X3: a,X4: a] :
( ( cP @ ( cP @ X3 @ X4 ) @ X2 )
= ( cP @ X3 @ ( cP @ X4 @ X2 ) ) )
& ? [X5: a,X6: a] :
! [X7: a] :
( ( cP @ X7 @ X6 )
!= X5 ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ! [X0: a] :
( ( cP @ cE @ X0 )
= X0 )
& ! [X1: a] :
( cE
= ( cP @ ( cJ @ X1 ) @ X1 ) )
& ! [X2: a,X3: a,X4: a] :
( ( cP @ ( cP @ X3 @ X4 ) @ X2 )
= ( cP @ X3 @ ( cP @ X4 @ X2 ) ) )
& ! [X7: a] :
( ( cP @ X7 @ sK1 )
!= sK0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X5,sK0),skolemize(X6,sK1)],[f6]) ).
thf(f8,plain,
! [X7: a] :
( ( cP @ X7 @ sK1 )
!= sK0 ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
! [X2: a,X3: a,X4: a] :
( ( cP @ ( cP @ X3 @ X4 ) @ X2 )
= ( cP @ X3 @ ( cP @ X4 @ X2 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
! [X1: a] :
( cE
= ( cP @ ( cJ @ X1 ) @ X1 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
! [X0: a] :
( ( cP @ cE @ X0 )
= X0 ),
inference(cnf_transformation,[],[f7]) ).
thf(f15,plain,
! [X0: a,X1: a] :
( ( cP @ cE @ X1 )
= ( cP @ ( cJ @ X0 ) @ ( cP @ X0 @ X1 ) ) ),
inference(superposition,[],[f9,f10]) ).
thf(f17,plain,
! [X0: a,X1: a] :
( ( cP @ X0 @ ( cP @ X1 @ sK1 ) )
!= sK0 ),
inference(superposition,[],[f8,f9]) ).
thf(f18,plain,
! [X0: a,X1: a] :
( ( cP @ ( cJ @ X0 ) @ ( cP @ X0 @ X1 ) )
= X1 ),
inference(forward_demodulation,[],[f15,f11]) ).
thf(f22,plain,
! [X0: a] :
( ( cP @ X0 @ cE )
!= sK0 ),
inference(superposition,[],[f17,f10]) ).
thf(f37,plain,
! [X0: a] :
( ( cP @ ( cJ @ ( cJ @ X0 ) ) @ cE )
= X0 ),
inference(superposition,[],[f18,f10]) ).
thf(f55,plain,
! [X0: a] : ( sK0 != X0 ),
inference(superposition,[],[f22,f37]) ).
thf(f59,plain,
sK0 != sK0,
inference(imitation,[],[f55]) ).
thf(f61,plain,
$false,
inference(trivial_inequality_removal,[],[f59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG282^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n017.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 17:31:53 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.23/0.27 % (648977)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.27 % (648990)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2551900538:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.27 % (648990) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-648977-648990"...
% 0.23/0.27 % (648990)...printing done.
% 0.23/0.27 % (648990)Refutation found. Thanks to Tanya!
% 0.23/0.27 % SZS status Theorem for theBenchmark
% 0.23/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.28 % (648990)------------------------------
% 0.23/0.28 % (648990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.28 % (648990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.28 % (648990)CaDiCaL version: 2.1.3
% 0.23/0.28 % (648990)Termination reason: Refutation
% 0.23/0.28 % (648990)Time elapsed: 0.002 s
% 0.23/0.28 % (648990)Peak memory usage: 12 MB
% 0.23/0.28 % (648990)Instructions burned: 5 (million)
% 0.23/0.28 % (648977)Success in time 0.019 s
% 0.23/0.28 % Vampire exiting
%------------------------------------------------------------------------------