%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO371^5 : 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 : n003.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 08:47:32 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 47 ( 7 unt; 0 typ; 4 def)
% Number of atoms : 175 ( 33 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 138 ( 56 ~; 46 |; 1 &; 20 @)
% ( 7 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 8 con; 0-4 aty)
% Number of variables : 10 ( 0 sgn 10 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cQ: $o ).
thf(func_def_1,type,
cP: $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 @ cP )
=> ( X0 @ cQ ) )
=> ( cP
<=> cQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEXT_O_LEIB) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $o > $o] :
( ( X0 @ cP )
=> ( X0 @ cQ ) )
=> ( cP
<=> cQ ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: $o > $o] :
( ( X0 @ cP )
=> ( X0 @ cQ ) )
=> ( cP
<=> cQ ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X0: $o > $o] :
( ( ( X0 @ cP )
= $true )
=> ( ( X0 @ cQ )
= $true ) )
=> ( cP = cQ ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( cP != cQ )
& ! [X0: $o > $o] :
( ( ( X0 @ cQ )
= $true )
| ( ( X0 @ cP )
!= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
! [X0: $o > $o] :
( ( ( X0 @ cQ )
= $true )
| ( ( X0 @ cP )
!= $true ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f7,plain,
cP != cQ,
inference(cnf_transformation,[],[f5]) ).
thf(f9,plain,
( ( cP = $true )
| ( cQ = $true ) ),
inference(xor_proxy_clausification,[],[f7]) ).
thf(f10,plain,
( ( cP = $false )
| ( cQ = $false ) ),
inference(xor_proxy_clausification,[],[f7]) ).
thf(f12,definition,
( spl0_1
<=> ( cQ = $false ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f14,plain,
( ( cQ = $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f12]) ).
thf(f16,definition,
( spl0_2
<=> ( cP = $false ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f18,plain,
( ( cP = $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f16]) ).
thf(f19,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f10,f16,f12]) ).
thf(f21,definition,
( spl0_3
<=> ( cP = $true ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f23,plain,
( ( cP = $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f21]) ).
thf(f25,definition,
( spl0_4
<=> ( cQ = $true ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
thf(f27,plain,
( ( cQ = $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f25]) ).
thf(f28,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f9,f25,f21]) ).
thf(f29,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f23,f18]) ).
thf(f30,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f29]) ).
thf(f31,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f30]) ).
thf(f35,plain,
( ! [X0: $o > $o] :
( ( $true
!= ( X0 @ $true ) )
| ( ( X0 @ cQ )
= $true ) )
| ~ spl0_3 ),
inference(forward_demodulation,[],[f6,f23]) ).
thf(f36,plain,
( ! [X0: $o > $o] :
( ( $true
= ( X0 @ $false ) )
| ( $true
!= ( X0 @ $true ) ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_demodulation,[],[f35,f14]) ).
thf(f37,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_3 ),
inference(leibniz_equality_elimination,[],[f36]) ).
thf(f53,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f37]) ).
thf(f54,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f53]) ).
thf(f57,plain,
( ! [X0: $o > $o] :
( ( $true
= ( X0 @ $true ) )
| ( ( X0 @ cP )
!= $true ) )
| ~ spl0_4 ),
inference(forward_demodulation,[],[f6,f27]) ).
thf(f58,plain,
( ! [X0: $o > $o] :
( ( $true
= ( X0 @ $true ) )
| ( $true
!= ( X0 @ $false ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f57,f18]) ).
thf(f59,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(leibniz_equality_elimination,[],[f58]) ).
thf(f71,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f59]) ).
thf(f72,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f71]) ).
thf(f77,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(superposition,[],[f27,f14]) ).
thf(f80,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f77]) ).
thf(f81,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f80]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f19]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f28]) ).
cnf(s3,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f31]) ).
cnf(s6,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(sat_conversion,[],[f54]) ).
cnf(s8,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f72]) ).
cnf(s10,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f81]) ).
cnf(s11,plain,
~ spl0_2,
inference(rat,[],[s2,s3,s8]) ).
cnf(s12,plain,
spl0_1,
inference(rat,[],[s1,s11]) ).
cnf(s13,plain,
~ spl0_4,
inference(rat,[],[s10,s12]) ).
cnf(s14,plain,
~ spl0_3,
inference(rat,[],[s6,s12]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s2,s13,s14]) ).
thf(f82,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO371^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n003.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 16:51:14 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.19/0.27 % (2745384)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.27 % (2745392)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3005146190:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.19/0.27 % (2745392) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2745384-2745392"...
% 0.19/0.27 % (2745392)...printing done.
% 0.19/0.27 % (2745392)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (2745392)------------------------------
% 0.19/0.27 % (2745392)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (2745392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (2745392)CaDiCaL version: 2.1.3
% 0.19/0.27 % (2745392)Termination reason: Refutation
% 0.19/0.27 % (2745392)Time elapsed: 0.002 s
% 0.19/0.27 % (2745392)Peak memory usage: 13 MB
% 0.19/0.27 % (2745392)Instructions burned: 3 (million)
% 0.19/0.27 % (2745384)Success in time 0.031 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------