%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU928^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:31:58 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 51 ( 34 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 83 ( 12 ~; 6 |; 6 &; 50 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 31 ( 0 ^; 25 !; 6 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
sK0: $i > $i ).
thf(f1,conjecture,
! [X0: $i > $i] :
( ! [X2: $i,X1: $i] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: $i,X2: $i] :
( ( ( X0 @ ( X0 @ X1 ) )
= ( X0 @ ( X0 @ X2 ) ) )
=> ( X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM48A_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: $i > $i] :
( ! [X2: $i,X1: $i] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: $i,X2: $i] :
( ( ( X0 @ ( X0 @ X1 ) )
= ( X0 @ ( X0 @ X2 ) ) )
=> ( X1 = X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: $i > $i] :
( ! [X2: $i,X1: $i] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X4: $i,X3: $i] :
( ( ( X0 @ ( X0 @ X4 ) )
= ( X0 @ ( X0 @ X3 ) ) )
=> ( X3 = X4 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
? [X0: $i > $i] :
( ! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ( ( X0 @ X1 )
!= ( X0 @ X2 ) ) )
& ? [X4: $i,X3: $i] :
( ( X3 != X4 )
& ( ( X0 @ ( X0 @ X4 ) )
= ( X0 @ ( X0 @ X3 ) ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
thf(f5,plain,
? [X0: $i > $i] :
( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ( ( X0 @ X1 )
!= ( X0 @ X2 ) ) )
& ? [X3: $i,X4: $i] :
( ( X3 != X4 )
& ( ( X0 @ ( X0 @ X4 ) )
= ( X0 @ ( X0 @ X3 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ( ( sK0 @ X2 )
!= ( sK0 @ X1 ) ) )
& ( sK2 != sK1 )
& ( ( sK0 @ ( sK0 @ sK2 ) )
= ( sK0 @ ( sK0 @ sK1 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X3,sK1),skolemize(X4,sK2)],[f5]) ).
thf(f7,plain,
( ( sK0 @ ( sK0 @ sK2 ) )
= ( sK0 @ ( sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
sK2 != sK1,
inference(cnf_transformation,[],[f6]) ).
thf(f9,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ X2 )
!= ( sK0 @ X1 ) )
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f11,plain,
! [X0: $i] :
( ( ( sK0 @ ( sK0 @ sK1 ) )
!= ( sK0 @ X0 ) )
| ( ( sK0 @ sK2 )
= X0 ) ),
inference(constrained_superposition,[],[f9,f7]) ).
thf(f13,plain,
( ( sK0 @ sK1 )
= ( sK0 @ sK2 ) ),
inference(equality_resolution,[],[f11]) ).
thf(f14,plain,
! [X0: $i] :
( ( ( sK0 @ sK1 )
!= ( sK0 @ X0 ) )
| ( sK2 = X0 ) ),
inference(constrained_superposition,[],[f9,f13]) ).
thf(f17,plain,
sK2 = sK1,
inference(equality_resolution,[],[f14]) ).
thf(f19,plain,
$false,
inference(forward_subsumption_resolution,[],[f17,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU928^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n018.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:48:57 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.28 % (182364)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (182370)lrs+10_16_si=on:nwc=1.5:random_seed=1886267435:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.28 % (182370) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-182364-182370"...
% 0.20/0.28 % (182370)...printing done.
% 0.20/0.28 % (182370)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (182370)------------------------------
% 0.20/0.28 % (182370)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (182370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (182370)CaDiCaL version: 2.1.3
% 0.20/0.28 % (182370)Termination reason: Refutation
% 0.20/0.28 % (182370)Time elapsed: 0.001 s
% 0.20/0.28 % (182370)Peak memory usage: 12 MB
% 0.20/0.28 % (182370)Instructions burned: 1 (million)
% 0.20/0.28 % (182364)Success in time 0.033 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------