%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO235^5 : 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 : 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 08:47:15 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 56 ( 6 unt; 0 typ; 5 def)
% Number of atoms : 288 ( 64 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 201 ( 69 ~; 81 |; 5 &; 28 @)
% ( 9 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 9 con; 0-4 aty)
% Number of variables : 14 ( 0 sgn 14 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cB: $o ).
thf(func_def_1,type,
cA: $o ).
thf(func_def_5,type,
vNOT: $o > $o ).
thf(func_def_7,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
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,
( ( ! [X0: $o > $o] :
( ( X0 @ cA )
=> ( X0 @ cB ) )
| ( cA
<=> cB ) )
=> ( cA = cB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM505) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $o > $o] :
( ( X0 @ cA )
=> ( X0 @ cB ) )
| ( cA
<=> cB ) )
=> ( cA = cB ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: $o > $o] :
( ( X0 @ cA )
=> ( X0 @ cB ) )
| ( cA
<=> cB ) )
=> ( cA = cB ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X0: $o > $o] :
( ( ( X0 @ cA )
= $true )
=> ( ( X0 @ cB )
= $true ) )
| ( cA = cB ) )
=> ( ( cA = $true )
<=> ( cB = $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ! [X0: $o > $o] :
( ( ( X0 @ cA )
!= $true )
| ( ( X0 @ cB )
= $true ) )
| ( cA = cB ) )
& ( ( cB = $true )
<~> ( cA = $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ! [X0: $o > $o] :
( ( ( X0 @ cA )
!= $true )
| ( ( X0 @ cB )
= $true ) )
| ( cA = cB ) )
& ( ( cA != $true )
| ( cB != $true ) )
& ( ( cA = $true )
| ( cB = $true ) ) ),
inference(nnf_transformation,[],[f5]) ).
thf(f7,plain,
( ( ! [X0: $o > $o] :
( ( ( X0 @ cA )
!= $true )
| ( ( X0 @ cB )
= $true ) )
| ( cA = cB ) )
& ( ( cA != $true )
| ( cB != $true ) )
& ( ( cA = $true )
| ( cB = $true ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
( ( cB = $true )
| ( cA = $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
( ( cA != $true )
| ( cB != $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
! [X0: $o > $o] :
( ( ( X0 @ cB )
= $true )
| ( ( X0 @ cA )
!= $true )
| ( cA = cB ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,plain,
! [X0: $o > $o] :
( ( cA = $true )
| ( ( X0 @ cB )
= $true )
| ( cB = $false )
| ( ( X0 @ cA )
!= $true ) ),
inference(iff_proxy_clausification,[],[f10]) ).
thf(f14,plain,
! [X0: $o > $o] :
( ( cB = $true )
| ( cA = $false )
| ( ( X0 @ cA )
!= $true )
| ( ( X0 @ cB )
= $true ) ),
inference(iff_proxy_clausification,[],[f10]) ).
thf(f16,definition,
( spl0_1
<=> ( cB = $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f17,plain,
( ( cB != $true )
| spl0_1 ),
inference(avatar_component_clause,[],[f16]) ).
thf(f19,definition,
( spl0_2
<=> ( cA = $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f20,plain,
( ( cA != $true )
| spl0_2 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f21,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f9,f19,f16]) ).
thf(f22,plain,
( ( cB = $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f16]) ).
thf(f23,plain,
( ( cA = $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f24,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f8,f19,f16]) ).
thf(f26,definition,
( spl0_3
<=> ! [X0: $o > $o] :
( ( ( X0 @ cA )
!= $true )
| ( ( X0 @ cB )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f27,plain,
( ! [X0: $o > $o] :
( ( ( X0 @ cB )
= $true )
| ( ( X0 @ cA )
!= $true ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f26]) ).
thf(f29,definition,
( spl0_4
<=> ( cA = $false ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
thf(f30,plain,
( ( cA = $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f29]) ).
thf(f31,plain,
( spl0_3
| spl0_4
| spl0_1 ),
inference(avatar_split_clause,[],[f14,f16,f29,f26]) ).
thf(f33,definition,
( spl0_5
<=> ( cB = $false ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
thf(f34,plain,
( ( cB = $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f33]) ).
thf(f35,plain,
( spl0_5
| spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f13,f19,f26,f33]) ).
thf(f36,plain,
( ! [X0: $o > $o] :
( ( ( X0 @ $true )
!= $true )
| ( ( X0 @ cB )
= $true ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f27,f23]) ).
thf(f38,plain,
( ( cB = $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(leibniz_equality_elimination,[],[f36]) ).
thf(f63,plain,
( $false
| spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f38,f17]) ).
thf(f64,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f63]) ).
thf(f65,plain,
( ! [X0: $o > $o] :
( ( ( X0 @ cA )
!= $true )
| ( ( X0 @ $true )
= $true ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(backward_demodulation,[],[f27,f22]) ).
thf(f66,plain,
( ( cA = $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(leibniz_equality_elimination,[],[f65]) ).
thf(f85,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f66,f20]) ).
thf(f86,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f85]) ).
thf(f87,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_5 ),
inference(backward_demodulation,[],[f22,f34]) ).
thf(f88,plain,
( $false
| ~ spl0_1
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f87]) ).
thf(f89,plain,
( ~ spl0_1
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f88]) ).
thf(f90,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(backward_demodulation,[],[f23,f30]) ).
thf(f91,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f90]) ).
thf(f92,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f91]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f21]) ).
cnf(s2,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f24]) ).
cnf(s3,plain,
( spl0_1
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f31]) ).
cnf(s4,plain,
( spl0_2
| spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f35]) ).
cnf(s8,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f64]) ).
cnf(s10,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f86]) ).
cnf(s11,plain,
( ~ spl0_1
| ~ spl0_5 ),
inference(sat_conversion,[],[f89]) ).
cnf(s12,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f92]) ).
cnf(s13,plain,
spl0_1,
inference(rat,[],[s3,s8,s12,s2]) ).
cnf(s14,plain,
~ spl0_5,
inference(rat,[],[s11,s13]) ).
cnf(s15,plain,
~ spl0_2,
inference(rat,[],[s1,s13]) ).
cnf(s16,plain,
~ spl0_3,
inference(rat,[],[s10,s15,s13]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s4,s15,s14,s16]) ).
thf(f94,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO235^5 : 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 : n008.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 16:41:10 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 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
% 0.21/0.27 % (3397292)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (3397308)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4146784377:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.27 % (3397308) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3397292-3397308"...
% 0.21/0.27 % (3397308)...printing done.
% 0.21/0.27 % (3397308)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.27 % (3397308)------------------------------
% 0.21/0.27 % (3397308)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (3397308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (3397308)CaDiCaL version: 2.1.3
% 0.21/0.27 % (3397308)Termination reason: Refutation
% 0.21/0.27 % (3397308)Time elapsed: 0.002 s
% 0.21/0.27 % (3397308)Peak memory usage: 13 MB
% 0.21/0.27 % (3397308)Instructions burned: 3 (million)
% 0.21/0.27 % (3397292)Success in time 0.017 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------