%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n006.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 08:49:35 AM UTC 2026
% Result : Theorem 0.18s 0.26s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of formulae : 44 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 267 ( 70 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 167 ( 46 ~; 69 |; 1 &; 38 @)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 6 con; 0-4 aty)
% Number of variables : 19 ( 0 sgn 19 !; 0 ?; 19 :)
% 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,
( ( ( cA
<=> cB )
| ! [X0: $o > $o] :
( ( X0 @ cA )
=> ( X0 @ cB ) ) )
=> ( cA = cB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM505) ).
thf(f2,negated_conjecture,
~ ( ( ( cA
<=> cB )
| ! [X0: $o > $o] :
( ( X0 @ cA )
=> ( X0 @ cB ) ) )
=> ( cA = cB ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ( cA
<=> cB )
| ! [X0: $o > $o] :
( ( X0 @ cA )
=> ( X0 @ cB ) ) )
=> ( cA = cB ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ( cA = cB )
| ! [X0: $o > $o] :
( ( ( X0 @ cA )
= $true )
=> ( ( X0 @ cB )
= $true ) ) )
=> ( cA = cB ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( cA != cB )
& ( ( cA = cB )
| ! [X0: $o > $o] :
( ( ( X0 @ cB )
= $true )
| ( ( X0 @ cA )
!= $true ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
! [X0: $o > $o] :
( ( cA = cB )
| ( ( X0 @ cB )
= $true )
| ( ( X0 @ cA )
!= $true ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f7,plain,
cA != cB,
inference(cnf_transformation,[],[f5]) ).
thf(f10,plain,
! [X0: $o > $o] :
( ( cA = $true )
| ( ( X0 @ cB )
= $true )
| ( ( X0 @ cA )
!= $true )
| ( cB = $false ) ),
inference(iff_proxy_clausification,[],[f6]) ).
thf(f11,plain,
! [X0: $o > $o] :
( ( cA = $false )
| ( ( X0 @ cB )
= $true )
| ( ( X0 @ cA )
!= $true )
| ( cB = $true ) ),
inference(iff_proxy_clausification,[],[f6]) ).
thf(f12,plain,
( ( cA = $true )
| ( cB = $true ) ),
inference(xor_proxy_clausification,[],[f7]) ).
thf(f13,plain,
( ( cA = $false )
| ( cB = $false ) ),
inference(xor_proxy_clausification,[],[f7]) ).
thf(f15,definition,
( spl0_1
<=> ( cB = $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f16,plain,
( ( cB != $true )
| spl0_1 ),
inference(avatar_component_clause,[],[f15]) ).
thf(f17,plain,
( ( cB = $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f15]) ).
thf(f19,definition,
( spl0_2
<=> ( cA = $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f21,plain,
( ( cA = $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f22,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f12,f19,f15]) ).
thf(f23,plain,
( ( $true = $false )
| ( cA = $false )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f13,f17]) ).
thf(f24,plain,
( ( cA = $false )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f23]) ).
thf(f25,plain,
( ! [X0: $o > $o] :
( ( $true = $false )
| ( ( X0 @ cB )
= $true )
| ( ( X0 @ cA )
!= $true )
| ( cB = $false ) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f10,f24]) ).
thf(f26,plain,
( ! [X0: $o > $o] :
( ( ( X0 @ cB )
= $true )
| ( ( X0 @ cA )
!= $true )
| ( cB = $false ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f25]) ).
thf(f27,plain,
( ! [X0: $o > $o] :
( ( $true
= ( X0 @ $true ) )
| ( ( X0 @ cA )
!= $true )
| ( cB = $false ) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f26,f17]) ).
thf(f28,plain,
( ! [X0: $o > $o] :
( ( $true
!= ( X0 @ $false ) )
| ( $true
= ( X0 @ $true ) )
| ( cB = $false ) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f27,f24]) ).
thf(f29,plain,
( ! [X0: $o > $o] :
( ( $true = $false )
| ( $true
!= ( X0 @ $false ) )
| ( $true
= ( X0 @ $true ) ) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f28,f17]) ).
thf(f30,plain,
( ! [X0: $o > $o] :
( ( $true
!= ( X0 @ $false ) )
| ( $true
= ( X0 @ $true ) ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f29]) ).
thf(f37,plain,
( ( $true = $false )
| ~ spl0_1 ),
inference(leibniz_equality_elimination,[],[f30]) ).
thf(f58,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f37]) ).
thf(f59,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f58]) ).
thf(f75,plain,
( ( $true = $false )
| ( cB = $false )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f13,f21]) ).
thf(f76,plain,
( ( cB = $false )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f75]) ).
thf(f98,plain,
( ! [X0: $o > $o] :
( ( cA = $false )
| ( ( X0 @ cB )
= $true )
| ( ( X0 @ cA )
!= $true ) )
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f11,f16]) ).
thf(f99,plain,
( ! [X0: $o > $o] :
( ( $true = $false )
| ( ( X0 @ cB )
= $true )
| ( ( X0 @ cA )
!= $true ) )
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f98,f21]) ).
thf(f100,plain,
( ! [X0: $o > $o] :
( ( ( X0 @ cB )
= $true )
| ( ( X0 @ cA )
!= $true ) )
| spl0_1
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f99]) ).
thf(f101,plain,
( ! [X0: $o > $o] :
( ( $true
= ( X0 @ $false ) )
| ( ( X0 @ cA )
!= $true ) )
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f100,f76]) ).
thf(f102,plain,
( ! [X0: $o > $o] :
( ( $true
!= ( X0 @ $true ) )
| ( $true
= ( X0 @ $false ) ) )
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f101,f21]) ).
thf(f109,plain,
( ( $true = $false )
| spl0_1
| ~ spl0_2 ),
inference(leibniz_equality_elimination,[],[f102]) ).
thf(f136,plain,
( $false
| spl0_1
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f109]) ).
thf(f137,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_contradiction_clause,[],[f136]) ).
cnf(s9,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f22]) ).
cnf(s17,plain,
~ spl0_1,
inference(sat_conversion,[],[f59]) ).
cnf(s44,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f137]) ).
cnf(s46,plain,
~ spl0_2,
inference(rat,[],[s44,s17]) ).
cnf(s47,plain,
$false,
inference(rat,[],[s9,s46,s17]) ).
thf(f138,plain,
$false,
inference(avatar_sat_refutation,[],[s47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO235^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n006.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 16:40:10 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.26 % (991457)Will run a generic schedule for satisfiability detection.
% 0.18/0.26 % (991464)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3875751150:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.26 % (991464) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-991457-991464"...
% 0.18/0.26 % (991464)...printing done.
% 0.18/0.26 % (991464)Refutation found. Thanks to Tanya!
% 0.18/0.26 % SZS status Theorem for theBenchmark
% 0.18/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.26 % (991464)------------------------------
% 0.18/0.26 % (991464)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.26 % (991464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.26 % (991464)CaDiCaL version: 2.1.3
% 0.18/0.26 % (991464)Termination reason: Refutation
% 0.18/0.26 % (991464)Time elapsed: 0.002 s
% 0.18/0.26 % (991464)Peak memory usage: 12 MB
% 0.18/0.26 % (991464)Instructions burned: 4 (million)
% 0.18/0.26 % (991457)Success in time 0.033 s
% 0.18/0.26 % Vampire exiting
%------------------------------------------------------------------------------