%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV412^5 : 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 08:38:36 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 54 ( 7 unt; 0 typ; 4 def)
% Number of atoms : 409 ( 98 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 263 ( 58 ~; 71 |; 16 &; 86 @)
% ( 4 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 17 !; 6 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cG: $o ).
thf(func_def_1,type,
cB: $i > $o ).
thf(func_def_2,type,
cA: $i > $o ).
thf(f1,conjecture,
( ( ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> cG )
| ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> cG ) )
=> ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> cG ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cDUAL_EG2_pme) ).
thf(f2,negated_conjecture,
~ ( ( ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> cG )
| ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> cG ) )
=> ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> cG ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> cG )
| ( ! [X1: $i] :
( ( cA @ X1 )
=> ( cB @ X1 ) )
=> cG ) )
=> ( ! [X2: $i] :
( ( cA @ X2 )
=> ( cB @ X2 ) )
=> cG ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ( ! [X1: $i] :
( ( $true
= ( cA @ X1 ) )
=> ( $true
= ( cB @ X1 ) ) )
=> ( cG = $true ) )
| ( ! [X0: $i] :
( ( ( cA @ X0 )
= $true )
=> ( ( cB @ X0 )
= $true ) )
=> ( cG = $true ) ) )
=> ( ! [X2: $i] :
( ( $true
= ( cA @ X2 ) )
=> ( $true
= ( cB @ X2 ) ) )
=> ( cG = $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( cG != $true )
& ! [X2: $i] :
( ( $true
!= ( cA @ X2 ) )
| ( $true
= ( cB @ X2 ) ) )
& ( ( cG = $true )
| ? [X1: $i] :
( ( $true
!= ( cB @ X1 ) )
& ( $true
= ( cA @ X1 ) ) )
| ( cG = $true )
| ? [X0: $i] :
( ( ( cB @ X0 )
!= $true )
& ( ( cA @ X0 )
= $true ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ? [X1: $i] :
( ( $true
!= ( cB @ X1 ) )
& ( $true
= ( cA @ X1 ) ) )
| ( cG = $true )
| ( cG = $true )
| ? [X0: $i] :
( ( ( cB @ X0 )
!= $true )
& ( ( cA @ X0 )
= $true ) ) )
& ( cG != $true )
& ! [X2: $i] :
( ( $true
!= ( cA @ X2 ) )
| ( $true
= ( cB @ X2 ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ( ? [X0: $i] :
( ( ( cB @ X0 )
!= $true )
& ( ( cA @ X0 )
= $true ) )
| ( cG = $true )
| ( cG = $true )
| ? [X1: $i] :
( ( $true
!= ( cB @ X1 ) )
& ( $true
= ( cA @ X1 ) ) ) )
& ( cG != $true )
& ! [X2: $i] :
( ( $true
!= ( cA @ X2 ) )
| ( $true
= ( cB @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( ( ( $true
!= ( cB @ sK0 ) )
& ( $true
= ( cA @ sK0 ) ) )
| ( cG = $true )
| ( cG = $true )
| ( ( $true
!= ( cB @ sK1 ) )
& ( $true
= ( cA @ sK1 ) ) ) )
& ( cG != $true )
& ! [X2: $i] :
( ( $true
!= ( cA @ X2 ) )
| ( $true
= ( cB @ X2 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f7]) ).
thf(f9,plain,
! [X2: $i] :
( ( $true
!= ( cA @ X2 ) )
| ( $true
= ( cB @ X2 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
cG != $true,
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( ( $true
= ( cA @ sK1 ) )
| ( cG = $true )
| ( cG = $true )
| ( $true
= ( cA @ sK0 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
( ( $true
= ( cA @ sK0 ) )
| ( $true
!= ( cB @ sK1 ) )
| ( cG = $true )
| ( cG = $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f13,plain,
( ( $true
!= ( cB @ sK0 ) )
| ( cG = $true )
| ( cG = $true )
| ( $true
= ( cA @ sK1 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
( ( $true
!= ( cB @ sK0 ) )
| ( cG = $true )
| ( $true
!= ( cB @ sK1 ) )
| ( cG = $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f17,plain,
( ( cG = $true )
| ( $true
!= ( cB @ sK0 ) )
| ( $true
!= ( cB @ sK1 ) ) ),
inference(duplicate_literal_removal,[],[f14]) ).
thf(f18,plain,
( ( $true
= ( cA @ sK0 ) )
| ( $true
= ( cA @ sK1 ) )
| ( cG = $true ) ),
inference(duplicate_literal_removal,[],[f11]) ).
thf(f19,plain,
( ( $true
!= ( cB @ sK0 ) )
| ( $true
= ( cA @ sK1 ) )
| ( cG = $true ) ),
inference(duplicate_literal_removal,[],[f13]) ).
thf(f20,plain,
( ( $true
!= ( cB @ sK1 ) )
| ( $true
= ( cA @ sK0 ) )
| ( cG = $true ) ),
inference(duplicate_literal_removal,[],[f12]) ).
thf(f21,plain,
( ( $true
!= ( cB @ sK1 ) )
| ( $true
!= ( cB @ sK0 ) ) ),
inference(forward_subsumption_resolution,[],[f17,f10]) ).
thf(f22,plain,
( ( $true
= ( cA @ sK0 ) )
| ( $true
= ( cA @ sK1 ) ) ),
inference(forward_subsumption_resolution,[],[f18,f10]) ).
thf(f23,plain,
( ( $true
= ( cA @ sK1 ) )
| ( $true
!= ( cB @ sK0 ) ) ),
inference(forward_subsumption_resolution,[],[f19,f10]) ).
thf(f24,plain,
( ( $true
= ( cA @ sK0 ) )
| ( $true
!= ( cB @ sK1 ) ) ),
inference(forward_subsumption_resolution,[],[f20,f10]) ).
thf(f26,definition,
( spl2_1
<=> ( $true
= ( cB @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f28,plain,
( ( $true
!= ( cB @ sK0 ) )
| spl2_1 ),
inference(avatar_component_clause,[],[f26]) ).
thf(f30,definition,
( spl2_2
<=> ( $true
= ( cB @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f32,plain,
( ( $true
!= ( cB @ sK1 ) )
| spl2_2 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f33,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f21,f30,f26]) ).
thf(f35,definition,
( spl2_3
<=> ( $true
= ( cA @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f37,plain,
( ( $true
= ( cA @ sK0 ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f39,definition,
( spl2_4
<=> ( $true
= ( cA @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f41,plain,
( ( $true
= ( cA @ sK1 ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f39]) ).
thf(f42,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f22,f39,f35]) ).
thf(f43,plain,
( ~ spl2_1
| spl2_4 ),
inference(avatar_split_clause,[],[f23,f39,f26]) ).
thf(f44,plain,
( ~ spl2_2
| spl2_3 ),
inference(avatar_split_clause,[],[f24,f35,f30]) ).
thf(f45,plain,
( ( $true
= ( cB @ sK0 ) )
| ( $true != $true )
| ~ spl2_3 ),
inference(constrained_superposition,[],[f9,f37]) ).
thf(f46,plain,
( ( $true
= ( cB @ sK0 ) )
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f45]) ).
thf(f47,plain,
( $false
| spl2_1
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f46,f28]) ).
thf(f48,plain,
( spl2_1
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f47]) ).
thf(f49,plain,
( ( $true
= ( cB @ sK1 ) )
| ( $true != $true )
| ~ spl2_4 ),
inference(constrained_superposition,[],[f9,f41]) ).
thf(f50,plain,
( ( $true
= ( cB @ sK1 ) )
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f49]) ).
thf(f51,plain,
( $false
| spl2_2
| ~ spl2_4 ),
inference(forward_subsumption_resolution,[],[f50,f32]) ).
thf(f52,plain,
( spl2_2
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f51]) ).
cnf(s1,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f33]) ).
cnf(s2,plain,
( spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f42]) ).
cnf(s3,plain,
( ~ spl2_1
| spl2_4 ),
inference(sat_conversion,[],[f43]) ).
cnf(s4,plain,
( ~ spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f44]) ).
cnf(s5,plain,
( spl2_1
| ~ spl2_3 ),
inference(sat_conversion,[],[f48]) ).
cnf(s6,plain,
( spl2_2
| ~ spl2_4 ),
inference(sat_conversion,[],[f52]) ).
cnf(s7,plain,
spl2_3,
inference(rat,[],[s6,s2,s4]) ).
cnf(s8,plain,
spl2_1,
inference(rat,[],[s5,s7]) ).
cnf(s9,plain,
spl2_4,
inference(rat,[],[s3,s8]) ).
cnf(s10,plain,
~ spl2_2,
inference(rat,[],[s1,s8]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s6,s9,s10]) ).
thf(f53,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV412^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n017.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 15:40:37 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.22/0.28 % (488056)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (488064)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2788372384:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.28 % (488064) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-488056-488064"...
% 0.22/0.28 % (488064)...printing done.
% 0.22/0.28 % (488064)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.28 % (488064)------------------------------
% 0.22/0.28 % (488064)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (488064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (488064)CaDiCaL version: 2.1.3
% 0.22/0.28 % (488064)Termination reason: Refutation
% 0.22/0.28 % (488064)Time elapsed: 0.002 s
% 0.22/0.28 % (488064)Peak memory usage: 13 MB
% 0.22/0.28 % (488064)Instructions burned: 2 (million)
% 0.22/0.28 % (488056)Success in time 0.027 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------