%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG001^5 : 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 : n005.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 07:45:09 AM UTC 2026
% Result : Theorem 0.26s 0.36s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 27 ( 26 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 232 ( 9 ~; 0 |; 11 &; 209 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 3 ( 3 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 74 ( 0 ^; 53 !; 21 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
g: $tType ).
thf(type_def_6,type,
b: $tType ).
thf(type_def_7,type,
a: $tType ).
thf(type_def_8,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
sK0: b > b > b ).
thf(func_def_2,type,
sK1: b > a ).
thf(func_def_3,type,
sK2: a > a > a ).
thf(func_def_4,type,
sK3: g > g > g ).
thf(func_def_5,type,
sK4: g > b ).
thf(func_def_6,type,
sK5: g ).
thf(func_def_7,type,
sK6: g ).
thf(f1,conjecture,
! [X0: g > b,X3: b > b > b,X2: g > g > g,X1: b > a,X4: a > a > a] :
( ( ! [X6: g,X5: g] :
( ( X0 @ ( X2 @ X5 @ X6 ) )
= ( X3 @ ( X0 @ X5 ) @ ( X0 @ X6 ) ) )
& ! [X5: b,X6: b] :
( ( X1 @ ( X3 @ X5 @ X6 ) )
= ( X4 @ ( X1 @ X5 ) @ ( X1 @ X6 ) ) ) )
=> ! [X5: g,X6: g] :
( ( X1 @ ( X0 @ ( X2 @ X5 @ X6 ) ) )
= ( X4 @ ( X1 @ ( X0 @ X5 ) ) @ ( X1 @ ( X0 @ X6 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM133_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: g > b,X3: b > b > b,X2: g > g > g,X1: b > a,X4: a > a > a] :
( ( ! [X6: g,X5: g] :
( ( X0 @ ( X2 @ X5 @ X6 ) )
= ( X3 @ ( X0 @ X5 ) @ ( X0 @ X6 ) ) )
& ! [X5: b,X6: b] :
( ( X1 @ ( X3 @ X5 @ X6 ) )
= ( X4 @ ( X1 @ X5 ) @ ( X1 @ X6 ) ) ) )
=> ! [X5: g,X6: g] :
( ( X1 @ ( X0 @ ( X2 @ X5 @ X6 ) ) )
= ( X4 @ ( X1 @ ( X0 @ X5 ) ) @ ( X1 @ ( X0 @ X6 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: g > b,X1: b > b > b,X3: b > a,X2: g > g > g,X4: a > a > a] :
( ( ! [X6: g,X5: g] :
( ( X0 @ ( X2 @ X6 @ X5 ) )
= ( X1 @ ( X0 @ X6 ) @ ( X0 @ X5 ) ) )
& ! [X8: b,X7: b] :
( ( X4 @ ( X3 @ X7 ) @ ( X3 @ X8 ) )
= ( X3 @ ( X1 @ X7 @ X8 ) ) ) )
=> ! [X9: g,X10: g] :
( ( X4 @ ( X3 @ ( X0 @ X9 ) ) @ ( X3 @ ( X0 @ X10 ) ) )
= ( X3 @ ( X0 @ ( X2 @ X9 @ X10 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
? [X0: g > b,X1: b > b > b,X3: b > a,X2: g > g > g,X4: a > a > a] :
( ? [X10: g,X9: g] :
( ( X4 @ ( X3 @ ( X0 @ X9 ) ) @ ( X3 @ ( X0 @ X10 ) ) )
!= ( X3 @ ( X0 @ ( X2 @ X9 @ X10 ) ) ) )
& ! [X6: g,X5: g] :
( ( X0 @ ( X2 @ X6 @ X5 ) )
= ( X1 @ ( X0 @ X6 ) @ ( X0 @ X5 ) ) )
& ! [X8: b,X7: b] :
( ( X4 @ ( X3 @ X7 ) @ ( X3 @ X8 ) )
= ( X3 @ ( X1 @ X7 @ X8 ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
thf(f5,plain,
? [X1: b > b > b,X3: b > a,X4: a > a > a,X2: g > g > g,X0: g > b] :
( ? [X10: g,X9: g] :
( ( X4 @ ( X3 @ ( X0 @ X9 ) ) @ ( X3 @ ( X0 @ X10 ) ) )
!= ( X3 @ ( X0 @ ( X2 @ X9 @ X10 ) ) ) )
& ! [X8: b,X7: b] :
( ( X4 @ ( X3 @ X7 ) @ ( X3 @ X8 ) )
= ( X3 @ ( X1 @ X7 @ X8 ) ) )
& ! [X6: g,X5: g] :
( ( X0 @ ( X2 @ X6 @ X5 ) )
= ( X1 @ ( X0 @ X6 ) @ ( X0 @ X5 ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
? [X0: b > b > b,X1: b > a,X2: a > a > a,X3: g > g > g,X4: g > b] :
( ? [X5: g,X6: g] :
( ( X2 @ ( X1 @ ( X4 @ X6 ) ) @ ( X1 @ ( X4 @ X5 ) ) )
!= ( X1 @ ( X4 @ ( X3 @ X6 @ X5 ) ) ) )
& ! [X7: b,X8: b] :
( ( X1 @ ( X0 @ X8 @ X7 ) )
= ( X2 @ ( X1 @ X8 ) @ ( X1 @ X7 ) ) )
& ! [X9: g,X10: g] :
( ( X0 @ ( X4 @ X9 ) @ ( X4 @ X10 ) )
= ( X4 @ ( X3 @ X9 @ X10 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( ( sK1 @ ( sK4 @ ( sK3 @ sK6 @ sK5 ) ) )
!= ( sK2 @ ( sK1 @ ( sK4 @ sK6 ) ) @ ( sK1 @ ( sK4 @ sK5 ) ) ) )
& ! [X7: b,X8: b] :
( ( sK1 @ ( sK0 @ X8 @ X7 ) )
= ( sK2 @ ( sK1 @ X8 ) @ ( sK1 @ X7 ) ) )
& ! [X9: g,X10: g] :
( ( sK4 @ ( sK3 @ X9 @ X10 ) )
= ( sK0 @ ( sK4 @ X9 ) @ ( sK4 @ X10 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6)],[f6]) ).
thf(f8,plain,
! [X10: g,X9: g] :
( ( sK4 @ ( sK3 @ X9 @ X10 ) )
= ( sK0 @ ( sK4 @ X9 ) @ ( sK4 @ X10 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
! [X8: b,X7: b] :
( ( sK1 @ ( sK0 @ X8 @ X7 ) )
= ( sK2 @ ( sK1 @ X8 ) @ ( sK1 @ X7 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
( ( sK1 @ ( sK4 @ ( sK3 @ sK6 @ sK5 ) ) )
!= ( sK2 @ ( sK1 @ ( sK4 @ sK6 ) ) @ ( sK1 @ ( sK4 @ sK5 ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
( ( sK1 @ ( sK4 @ ( sK3 @ sK6 @ sK5 ) ) )
!= ( sK1 @ ( sK0 @ ( sK4 @ sK6 ) @ ( sK4 @ sK5 ) ) ) ),
inference(forward_demodulation,[],[f10,f9]) ).
thf(f12,plain,
( ( sK1 @ ( sK4 @ ( sK3 @ sK6 @ sK5 ) ) )
!= ( sK1 @ ( sK4 @ ( sK3 @ sK6 @ sK5 ) ) ) ),
inference(forward_demodulation,[],[f11,f8]) ).
thf(f13,plain,
$false,
inference(trivial_inequality_removal,[],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG001^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.25 % Computer : n005.cluster.edu
% 0.11/0.25 % Model : x86_64 x86_64
% 0.11/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.25 % Memory : 8046.5625MB
% 0.11/0.25 % OS : Linux 6.8.0-71-generic
% 0.11/0.25 % CPULimit : 300
% 0.11/0.25 % WCLimit : 300
% 0.11/0.25 % DateTime : Tue Sep 29 17:30:47 UTC 2026
% 0.11/0.25 % CPUTime :
% 0.11/0.25 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.30 Running higher-order theorem proving
% 0.26/0.32 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
% 0.26/0.36 % (1968446)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.26/0.36 % (1968457)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2091304966:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.26/0.36 % (1968457) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1968446-1968457"...
% 0.26/0.36 % (1968457)...printing done.
% 0.26/0.36 % (1968457)Refutation found. Thanks to Tanya!
% 0.26/0.36 % SZS status Theorem for theBenchmark
% 0.26/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.36 % (1968457)------------------------------
% 0.26/0.36 % (1968457)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.36 % (1968457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.36 % (1968457)CaDiCaL version: 2.1.3
% 0.26/0.36 % (1968457)Termination reason: Refutation
% 0.26/0.36 % (1968457)Time elapsed: 0.002 s
% 0.26/0.36 % (1968457)Peak memory usage: 12 MB
% 0.26/0.36 % (1968457)Instructions burned: 2 (million)
% 0.26/0.36 % (1968446)Success in time 0.029 s
% 0.26/0.36 % Vampire exiting
%------------------------------------------------------------------------------