%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG270^5 : 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 : n001.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 07:45:18 AM UTC 2026
% Result : Theorem 0.24s 0.35s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 10 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 15 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 165 ( 7 ~; 0 |; 3 &; 152 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 41 ( 0 ^; 33 !; 8 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
c_star: a > a > a ).
thf(func_def_2,type,
sK0: a ).
thf(func_def_3,type,
sK1: a ).
thf(func_def_4,type,
sK2: a ).
thf(func_def_5,type,
sK3: a ).
thf(f1,conjecture,
( ! [X1: a,X2: a,X0: a] :
( ( c_star @ ( c_star @ X0 @ X1 ) @ X2 )
= ( c_star @ X0 @ ( c_star @ X1 @ X2 ) ) )
=> ! [X4: a,X3: a,X5: a,X6: a] :
( ( c_star @ ( c_star @ ( c_star @ X3 @ X4 ) @ X5 ) @ X6 )
= ( c_star @ X3 @ ( c_star @ X4 @ ( c_star @ X5 @ X6 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM23_pme) ).
thf(f2,negated_conjecture,
~ ( ! [X1: a,X2: a,X0: a] :
( ( c_star @ ( c_star @ X0 @ X1 ) @ X2 )
= ( c_star @ X0 @ ( c_star @ X1 @ X2 ) ) )
=> ! [X4: a,X3: a,X5: a,X6: a] :
( ( c_star @ ( c_star @ ( c_star @ X3 @ X4 ) @ X5 ) @ X6 )
= ( c_star @ X3 @ ( c_star @ X4 @ ( c_star @ X5 @ X6 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X1: a,X2: a,X0: a] :
( ( c_star @ ( c_star @ X0 @ X1 ) @ X2 )
= ( c_star @ X0 @ ( c_star @ X1 @ X2 ) ) )
=> ! [X6: a,X3: a,X4: a,X5: a] :
( ( c_star @ ( c_star @ ( c_star @ X4 @ X3 ) @ X5 ) @ X6 )
= ( c_star @ X4 @ ( c_star @ X3 @ ( c_star @ X5 @ X6 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( ! [X1: a,X2: a,X0: a] :
( ( c_star @ ( c_star @ X0 @ X1 ) @ X2 )
= ( c_star @ X0 @ ( c_star @ X1 @ X2 ) ) )
& ? [X3: a,X5: a,X6: a,X4: a] :
( ( c_star @ ( c_star @ ( c_star @ X4 @ X3 ) @ X5 ) @ X6 )
!= ( c_star @ X4 @ ( c_star @ X3 @ ( c_star @ X5 @ X6 ) ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
thf(f5,plain,
( ! [X0: a,X1: a,X2: a] :
( ( c_star @ X2 @ ( c_star @ X0 @ X1 ) )
= ( c_star @ ( c_star @ X2 @ X0 ) @ X1 ) )
& ? [X3: a,X4: a,X5: a,X6: a] :
( ( c_star @ X6 @ ( c_star @ X3 @ ( c_star @ X4 @ X5 ) ) )
!= ( c_star @ ( c_star @ ( c_star @ X6 @ X3 ) @ X4 ) @ X5 ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
( ! [X0: a,X1: a,X2: a] :
( ( c_star @ X2 @ ( c_star @ X0 @ X1 ) )
= ( c_star @ ( c_star @ X2 @ X0 ) @ X1 ) )
& ( ( c_star @ sK3 @ ( c_star @ sK0 @ ( c_star @ sK1 @ sK2 ) ) )
!= ( c_star @ ( c_star @ ( c_star @ sK3 @ sK0 ) @ sK1 ) @ sK2 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X3,sK0),skolemize(X4,sK1),skolemize(X5,sK2),skolemize(X6,sK3)],[f5]) ).
thf(f7,plain,
( ( c_star @ sK3 @ ( c_star @ sK0 @ ( c_star @ sK1 @ sK2 ) ) )
!= ( c_star @ ( c_star @ ( c_star @ sK3 @ sK0 ) @ sK1 ) @ sK2 ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
! [X2: a,X0: a,X1: a] :
( ( c_star @ X2 @ ( c_star @ X0 @ X1 ) )
= ( c_star @ ( c_star @ X2 @ X0 ) @ X1 ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f12,plain,
( ( c_star @ sK3 @ ( c_star @ sK0 @ ( c_star @ sK1 @ sK2 ) ) )
!= ( c_star @ ( c_star @ sK3 @ sK0 ) @ ( c_star @ sK1 @ sK2 ) ) ),
inference(forward_demodulation,[],[f7,f8]) ).
thf(f13,plain,
$false,
inference(forward_subsumption_resolution,[],[f12,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG270^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 % Computer : n001.cluster.edu
% 0.11/0.24 % Model : x86_64 x86_64
% 0.11/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.24 % Memory : 8046.5625MB
% 0.11/0.24 % OS : Linux 6.8.0-71-generic
% 0.11/0.24 % CPULimit : 300
% 0.11/0.24 % WCLimit : 300
% 0.11/0.24 % DateTime : Tue Sep 29 17:41:36 UTC 2026
% 0.11/0.25 % CPUTime :
% 0.11/0.25 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.30 Running higher-order theorem proving
% 0.24/0.32 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
% 0.24/0.35 % (1576255)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.35 % (1576264)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3094196694:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.24/0.35 % (1576264) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1576255-1576264"...
% 0.24/0.35 % (1576264)...printing done.
% 0.24/0.35 % (1576264)Refutation found. Thanks to Tanya!
% 0.24/0.35 % SZS status Theorem for theBenchmark
% 0.24/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.35 % (1576264)------------------------------
% 0.24/0.35 % (1576264)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.35 % (1576264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.35 % (1576264)CaDiCaL version: 2.1.3
% 0.24/0.35 % (1576264)Termination reason: Refutation
% 0.24/0.35 % (1576264)Time elapsed: 0.002 s
% 0.24/0.35 % (1576264)Peak memory usage: 12 MB
% 0.24/0.35 % (1576264)Instructions burned: 2 (million)
% 0.24/0.35 % (1576255)Success in time 0.026 s
% 0.24/0.35 % Vampire exiting
%------------------------------------------------------------------------------