%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU930^5 : 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 : n019.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 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 18 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 70 ( 51 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 127 ( 13 ~; 5 |; 14 &; 80 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 2 con; 0-4 aty)
% Number of variables : 38 ( 20 ^; 16 !; 2 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
f: $i > $i ).
thf(func_def_1,type,
g: $i > $i ).
thf(func_def_3,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_4,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,conjecture,
( ( ( ^ [X0: $i] : ( g @ ( f @ X0 ) ) )
= ( ^ [X0: $i] : ( f @ ( g @ X0 ) ) ) )
=> ! [X0: $i] :
( ( ! [X1: $i] :
( ( ( g @ X1 )
= X1 )
=> ( X1 = X0 ) )
& ( ( g @ X0 )
= X0 ) )
=> ( ( f @ X0 )
= X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM171A_pme) ).
thf(f2,negated_conjecture,
~ ( ( ( ^ [X0: $i] : ( g @ ( f @ X0 ) ) )
= ( ^ [X0: $i] : ( f @ ( g @ X0 ) ) ) )
=> ! [X0: $i] :
( ( ! [X1: $i] :
( ( ( g @ X1 )
= X1 )
=> ( X1 = X0 ) )
& ( ( g @ X0 )
= X0 ) )
=> ( ( f @ X0 )
= X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ( ^ [X0: $i] : ( g @ ( f @ X0 ) ) )
= ( ^ [X1: $i] : ( f @ ( g @ X1 ) ) ) )
=> ! [X2: $i] :
( ( ! [X3: $i] :
( ( ( g @ X3 )
= X3 )
=> ( X2 = X3 ) )
& ( ( g @ X2 )
= X2 ) )
=> ( ( f @ X2 )
= X2 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ( ^ [Y0: $i] : ( g @ ( f @ Y0 ) ) )
= ( ^ [Y0: $i] : ( f @ ( g @ Y0 ) ) ) )
=> ! [X2: $i] :
( ( ! [X3: $i] :
( ( ( g @ X3 )
= X3 )
=> ( X2 = X3 ) )
& ( ( g @ X2 )
= X2 ) )
=> ( ( f @ X2 )
= X2 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ( ( ( ^ [Y0: $i] : ( g @ ( f @ Y0 ) ) )
= ( ^ [Y0: $i] : ( f @ ( g @ Y0 ) ) ) )
=> ! [X0: $i] :
( ( ! [X1: $i] :
( ( ( g @ X1 )
= X1 )
=> ( X0 = X1 ) )
& ( ( g @ X0 )
= X0 ) )
=> ( ( f @ X0 )
= X0 ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
( ? [X0: $i] :
( ( ( f @ X0 )
!= X0 )
& ! [X1: $i] :
( ( X0 = X1 )
| ( ( g @ X1 )
!= X1 ) )
& ( ( g @ X0 )
= X0 ) )
& ( ( ^ [Y0: $i] : ( g @ ( f @ Y0 ) ) )
= ( ^ [Y0: $i] : ( f @ ( g @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
( ( ( ^ [Y0: $i] : ( g @ ( f @ Y0 ) ) )
= ( ^ [Y0: $i] : ( f @ ( g @ Y0 ) ) ) )
& ? [X0: $i] :
( ( ( f @ X0 )
!= X0 )
& ( ( g @ X0 )
= X0 )
& ! [X1: $i] :
( ( X0 = X1 )
| ( ( g @ X1 )
!= X1 ) ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
( ( ( ^ [Y0: $i] : ( g @ ( f @ Y0 ) ) )
= ( ^ [Y0: $i] : ( f @ ( g @ Y0 ) ) ) )
& ( sK0
!= ( f @ sK0 ) )
& ( sK0
= ( g @ sK0 ) )
& ! [X1: $i] :
( ( sK0 = X1 )
| ( ( g @ X1 )
!= X1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f7]) ).
thf(f9,plain,
! [X1: $i] :
( ( ( g @ X1 )
!= X1 )
| ( sK0 = X1 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( sK0
= ( g @ sK0 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( sK0
!= ( f @ sK0 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
( ( ^ [Y0: $i] : ( g @ ( f @ Y0 ) ) )
= ( ^ [Y0: $i] : ( f @ ( g @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( g @ ( f @ Y0 ) )
@ X1 )
= ( ^ [Y0: $i] : ( f @ ( g @ Y0 ) )
@ X1 ) ),
inference(argument_congruence,[],[f12]) ).
thf(f15,plain,
! [X1: $i] :
( ( g @ ( f @ X1 ) )
= ( f @ ( g @ X1 ) ) ),
inference(beta-eta_normalization,[],[f14]) ).
thf(f16,plain,
( ( f @ sK0 )
= ( g @ ( f @ sK0 ) ) ),
inference(constrained_superposition,[],[f15,f10]) ).
thf(f18,plain,
( ( sK0
= ( f @ sK0 ) )
| ( ( f @ sK0 )
!= ( f @ sK0 ) ) ),
inference(constrained_superposition,[],[f9,f16]) ).
thf(f19,plain,
( sK0
= ( f @ sK0 ) ),
inference(trivial_inequality_removal,[],[f18]) ).
thf(f20,plain,
$false,
inference(forward_subsumption_resolution,[],[f19,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU930^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n019.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
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:47:03 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 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
% 0.20/0.27 % (880393)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (880400)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=912819796:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.27 % (880400) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-880393-880400"...
% 0.20/0.27 % (880400)...printing done.
% 0.20/0.27 % (880400)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 % (880400)------------------------------
% 0.20/0.27 % (880400)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (880400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (880400)CaDiCaL version: 2.1.3
% 0.20/0.27 % (880400)Termination reason: Refutation
% 0.20/0.27 % (880400)Time elapsed: 0.002 s
% 0.20/0.27 % (880400)Peak memory usage: 12 MB
% 0.20/0.27 % (880400)Instructions burned: 2 (million)
% 0.20/0.27 % (880393)Success in time 0.034 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------