%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU844^5 : 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 : n017.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 08:31:47 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 52 ( 8 unt; 0 typ; 4 def)
% Number of atoms : 211 ( 57 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 171 ( 42 ~; 44 |; 13 &; 56 @)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 8 con; 0-4 aty)
% Number of variables : 50 ( 0 sgn 46 !; 4 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cS: a > $o ).
thf(func_def_1,type,
cT: a > $o ).
thf(func_def_5,type,
sK0: a ).
thf(func_def_6,type,
sK1: a ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,conjecture,
( ! [X1: a > $o,X0: a > $o] : ( X0 = X1 )
=> ( ! [X2: a] :
( ( cT @ X2 )
=> ( cS @ X2 ) )
& ! [X2: a] :
( ( cS @ X2 )
=> ( cT @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGAZING_THM8_pme) ).
thf(f2,negated_conjecture,
~ ( ! [X1: a > $o,X0: a > $o] : ( X0 = X1 )
=> ( ! [X2: a] :
( ( cT @ X2 )
=> ( cS @ X2 ) )
& ! [X2: a] :
( ( cS @ X2 )
=> ( cT @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: a > $o,X1: a > $o] : ( X0 = X1 )
=> ( ! [X2: a] :
( ( cT @ X2 )
=> ( cS @ X2 ) )
& ! [X3: a] :
( ( cS @ X3 )
=> ( cT @ X3 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X1: a > $o,X0: a > $o] : ( X0 = X1 )
=> ( ! [X2: a] :
( ( ( cT @ X2 )
= $true )
=> ( ( cS @ X2 )
= $true ) )
& ! [X3: a] :
( ( ( cS @ X3 )
= $true )
=> ( $true
= ( cT @ X3 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ? [X2: a] :
( ( ( cT @ X2 )
= $true )
& ( ( cS @ X2 )
!= $true ) )
| ? [X3: a] :
( ( ( cS @ X3 )
= $true )
& ( $true
!= ( cT @ X3 ) ) ) )
& ! [X1: a > $o,X0: a > $o] : ( X0 = X1 ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ? [X0: a] :
( ( ( cT @ X0 )
= $true )
& ( ( cS @ X0 )
!= $true ) )
| ? [X1: a] :
( ( ( cS @ X1 )
= $true )
& ( ( cT @ X1 )
!= $true ) ) )
& ! [X2: a > $o,X3: a > $o] : ( X2 = X3 ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( ( ( $true
= ( cT @ sK0 ) )
& ( ( cS @ sK0 )
!= $true ) )
| ( ( ( cS @ sK1 )
= $true )
& ( ( cT @ sK1 )
!= $true ) ) )
& ! [X2: a > $o,X3: a > $o] : ( X2 = X3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f6]) ).
thf(f8,plain,
! [X2: a > $o,X3: a > $o] : ( X2 = X3 ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
( ( ( cT @ sK1 )
!= $true )
| ( ( cS @ sK0 )
!= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
( ( ( cS @ sK0 )
!= $true )
| ( ( cS @ sK1 )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
( ( ( cT @ sK1 )
!= $true )
| ( $true
= ( cT @ sK0 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f12,plain,
( ( $true
= ( cT @ sK0 ) )
| ( ( cS @ sK1 )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f16,definition,
( spl2_1
<=> ( ( cS @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f17,plain,
( ( ( cS @ sK1 )
= $true )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f16]) ).
thf(f19,definition,
( spl2_2
<=> ( $true
= ( cT @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f20,plain,
( ( $true
= ( cT @ sK0 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f21,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f12,f19,f16]) ).
thf(f23,definition,
( spl2_3
<=> ( ( cT @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f24,plain,
( ( ( cT @ sK1 )
!= $true )
| spl2_3 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f26,definition,
( spl2_4
<=> ( ( cS @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f27,plain,
( ( ( cS @ sK0 )
!= $true )
| spl2_4 ),
inference(avatar_component_clause,[],[f26]) ).
thf(f28,plain,
( ~ spl2_3
| ~ spl2_4 ),
inference(avatar_split_clause,[],[f9,f26,f23]) ).
thf(f29,plain,
( spl2_1
| ~ spl2_4 ),
inference(avatar_split_clause,[],[f10,f26,f16]) ).
thf(f30,plain,
( spl2_2
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f11,f23,f19]) ).
thf(f31,plain,
! [X2: a > $o,X3: a > $o,X4: a] :
( ( X3 @ X4 )
= ( X2 @ X4 ) ),
inference(argument_congruence,[],[f8]) ).
thf(f33,plain,
! [X2: a > $o,X3: a > $o,X4: a] :
( ( $true
= ( X2 @ X4 ) )
| ( $false
= ( X3 @ X4 ) ) ),
inference(iff_proxy_clausification,[],[f31]) ).
thf(f39,plain,
( ! [X0: a,X1: a > $o] :
( ( $false = $true )
| ( ( X1 @ X0 )
= $true ) )
| ~ spl2_2 ),
inference(constrained_superposition,[],[f20,f33]) ).
thf(f52,plain,
( ! [X0: a,X1: a > $o] :
( ( X1 @ X0 )
= $true )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f39]) ).
thf(f68,plain,
( ( $true != $true )
| ~ spl2_2
| spl2_4 ),
inference(backward_demodulation,[],[f27,f52]) ).
thf(f71,plain,
( $false
| ~ spl2_2
| spl2_4 ),
inference(trivial_inequality_removal,[],[f68]) ).
thf(f72,plain,
( ~ spl2_2
| spl2_4 ),
inference(avatar_contradiction_clause,[],[f71]) ).
thf(f95,plain,
( ! [X0: a,X1: a > $o] :
( ( $false = $true )
| ( ( X1 @ X0 )
= $true ) )
| ~ spl2_1 ),
inference(constrained_superposition,[],[f33,f17]) ).
thf(f98,plain,
( ! [X0: a,X1: a > $o] :
( ( $true != $true )
| ( $false
= ( X1 @ X0 ) ) )
| spl2_3 ),
inference(constrained_superposition,[],[f24,f33]) ).
thf(f107,plain,
( ! [X0: a,X1: a > $o] :
( ( X1 @ X0 )
= $true )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f95]) ).
thf(f108,plain,
( ! [X0: a,X1: a > $o] :
( $false
= ( X1 @ X0 ) )
| spl2_3 ),
inference(trivial_inequality_removal,[],[f98]) ).
thf(f129,plain,
( ! [X2: a > $o,X4: a] :
( ( $false = $true )
| ( $true
= ( X2 @ X4 ) ) )
| ~ spl2_1 ),
inference(backward_demodulation,[],[f33,f107]) ).
thf(f134,plain,
( ! [X2: a > $o,X4: a] :
( $true
= ( X2 @ X4 ) )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f129]) ).
thf(f150,plain,
( ( $false = $true )
| ~ spl2_1
| spl2_3 ),
inference(forward_demodulation,[],[f134,f108]) ).
thf(f151,plain,
( $false
| ~ spl2_1
| spl2_3 ),
inference(trivial_inequality_removal,[],[f150]) ).
thf(f152,plain,
( ~ spl2_1
| spl2_3 ),
inference(avatar_contradiction_clause,[],[f151]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f21]) ).
cnf(s2,plain,
( ~ spl2_3
| ~ spl2_4 ),
inference(sat_conversion,[],[f28]) ).
cnf(s3,plain,
( spl2_1
| ~ spl2_4 ),
inference(sat_conversion,[],[f29]) ).
cnf(s4,plain,
( spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f30]) ).
cnf(s5,plain,
( ~ spl2_2
| spl2_4 ),
inference(sat_conversion,[],[f72]) ).
cnf(s14,plain,
( ~ spl2_1
| spl2_3 ),
inference(sat_conversion,[],[f152]) ).
cnf(s15,plain,
spl2_1,
inference(rat,[],[s5,s1,s3]) ).
cnf(s16,plain,
spl2_3,
inference(rat,[],[s14,s15]) ).
cnf(s17,plain,
spl2_2,
inference(rat,[],[s4,s16]) ).
cnf(s18,plain,
~ spl2_4,
inference(rat,[],[s2,s16]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s5,s18,s17]) ).
thf(f154,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU844^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n017.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:35:07 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.22/0.29 % (420631)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (420641)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2614500603:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.29 % (420641) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-420631-420641"...
% 0.22/0.29 % (420642)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.29 % (420642)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.29 % (420641)...printing done.
% 0.22/0.29 % (420641)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (420641)------------------------------
% 0.22/0.29 % (420641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (420641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (420641)CaDiCaL version: 2.1.3
% 0.22/0.29 % (420641)Termination reason: Refutation
% 0.22/0.29 % (420641)Time elapsed: 0.003 s
% 0.22/0.29 % (420641)Peak memory usage: 13 MB
% 0.22/0.29 % (420641)Instructions burned: 7 (million)
% 0.22/0.29 % (420631)Success in time 0.038 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------