%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU953^5 : 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 : n008.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 08:32:01 AM UTC 2026
% Result : Theorem 0.24s 0.37s
% Output : Refutation 0.24s
% 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 : 26 ( 25 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 67 ( 12 ~; 3 |; 2 &; 42 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 1 con; 0-4 aty)
% Number of variables : 40 ( 16 ^; 20 !; 4 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
g: $i > $i ).
thf(func_def_2,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_3,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_4,type,
inv_g_0: $i > $i ).
thf(func_def_5,type,
sK1: ( $i > $i ) > $i ).
thf(f1,conjecture,
( ! [X0: $i,X1: $i] :
( ( ( g @ X0 )
= ( g @ X1 ) )
=> ( X0 = X1 ) )
=> ? [X2: $i > $i] :
( ( ^ [X0: $i] : X0 )
= ( ^ [X0: $i] : ( X2 @ ( g @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM591_pme) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i,X1: $i] :
( ( ( g @ X0 )
= ( g @ X1 ) )
=> ( X0 = X1 ) )
=> ? [X2: $i > $i] :
( ( ^ [X0: $i] : X0 )
= ( ^ [X0: $i] : ( X2 @ ( g @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: $i,X1: $i] :
( ( ( g @ X0 )
= ( g @ X1 ) )
=> ( X0 = X1 ) )
=> ? [X2: $i > $i] :
( ( ^ [X3: $i] : X3 )
= ( ^ [X4: $i] : ( X2 @ ( g @ X4 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X1: $i,X0: $i] :
( ( ( g @ X0 )
= ( g @ X1 ) )
=> ( X0 = X1 ) )
=> ? [X2: $i > $i] :
( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] : ( X2 @ ( g @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X1: $i,X0: $i] :
( ( ( g @ X0 )
!= ( g @ X1 ) )
| ( X0 = X1 ) )
& ! [X2: $i > $i] :
( ( ^ [Y0: $i] : Y0 )
!= ( ^ [Y0: $i] : ( X2 @ ( g @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ! [X0: $i,X1: $i] :
( ( ( g @ X0 )
!= ( g @ X1 ) )
| ( X0 = X1 ) )
& ! [X2: $i > $i] :
( ( ^ [Y0: $i] : Y0 )
!= ( ^ [Y0: $i] : ( X2 @ ( g @ Y0 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
! [X2: $i > $i] :
( ( ^ [Y0: $i] : Y0 )
!= ( ^ [Y0: $i] : ( X2 @ ( g @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
! [X0: $i,X1: $i] :
( ( ( g @ X0 )
!= ( g @ X1 ) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f9,plain,
! [X0: $i] :
( ( inv_g_0 @ ( g @ X0 ) )
= X0 ),
inference(injectivity,[],[f8]) ).
thf(f11,plain,
! [X2: $i > $i] :
( ( ^ [Y0: $i] : ( X2 @ ( g @ Y0 ) )
@ ( sK1 @ X2 ) )
!= ( ^ [Y0: $i] : Y0
@ ( sK1 @ X2 ) ) ),
inference(negative_extensionality,[],[f7]) ).
thf(f12,plain,
! [X2: $i > $i] :
( ( X2 @ ( g @ ( sK1 @ X2 ) ) )
!= ( sK1 @ X2 ) ),
inference(beta-eta_normalization,[],[f11]) ).
thf(f14,plain,
( ( sK1 @ inv_g_0 )
!= ( sK1 @ inv_g_0 ) ),
inference(constrained_superposition,[],[f12,f9]) ).
thf(f15,plain,
$false,
inference(trivial_inequality_removal,[],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU953^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.25 % Computer : n008.cluster.edu
% 0.12/0.25 % Model : x86_64 x86_64
% 0.12/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.25 % Memory : 8046.5625MB
% 0.12/0.25 % OS : Linux 6.8.0-71-generic
% 0.12/0.25 % CPULimit : 300
% 0.12/0.25 % WCLimit : 300
% 0.12/0.25 % DateTime : Tue Sep 29 14:51:25 UTC 2026
% 0.12/0.26 % CPUTime :
% 0.12/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.31 Running higher-order theorem proving
% 0.24/0.33 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
% 0.24/0.37 % (3264299)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.37 % (3264310)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1188515437:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.37 % (3264310) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3264299-3264310"...
% 0.24/0.37 % (3264310)...printing done.
% 0.24/0.37 % (3264314)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.37 % (3264310)Refutation found. Thanks to Tanya!
% 0.24/0.37 % SZS status Theorem for theBenchmark
% 0.24/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.37 % (3264310)------------------------------
% 0.24/0.37 % (3264310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.37 % (3264310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.37 % (3264310)CaDiCaL version: 2.1.3
% 0.24/0.37 % (3264310)Termination reason: Refutation
% 0.24/0.37 % (3264310)Time elapsed: 0.002 s
% 0.24/0.37 % (3264310)Peak memory usage: 12 MB
% 0.24/0.37 % (3264310)Instructions burned: 1 (million)
% 0.24/0.37 % (3264299)Success in time 0.031 s
% 0.29/0.37 % Vampire exiting
%------------------------------------------------------------------------------