%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV121^5 : 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 : n014.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 08:39:01 AM UTC 2026
% Result : Theorem 0.28s 0.37s
% Output : Refutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 60 ( 15 unt; 0 typ; 4 def)
% Number of atoms : 325 ( 94 equ; 9 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 377 ( 50 ~; 58 |; 0 &; 213 @)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 76 ( 76 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 17 usr; 10 con; 0-4 aty)
% ( 32 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 95 ( 0 sgn 17 !; 0 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_2,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_3,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_4,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_5,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
vIMP: $o > $o > $o ).
thf(func_def_7,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vNOT: $o > $o ).
thf(func_def_13,type,
sK2: $i > $i > $o ).
thf(func_def_14,type,
sK3: ( $i > $i > $o ) > $i ).
thf(f1,conjecture,
( ( ^ [X0: $i,X1: $i] : ( X0 = X1 ) )
= ( ^ [X2: $i,X3: $i] :
! [X4: $i > $i > $o] :
( ! [X5: $i] : ( X4 @ X5 @ X5 )
=> ( X4 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM47C_pme) ).
thf(f2,negated_conjecture,
( ( ^ [X0: $i,X1: $i] : ( X0 = X1 ) )
!= ( ^ [X2: $i,X3: $i] :
! [X4: $i > $i > $o] :
( ! [X5: $i] : ( X4 @ X5 @ X5 )
=> ( X4 @ X2 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
( ( ^ [X0: $i,X1: $i] : ( X0 = X1 ) )
!= ( ^ [X2: $i,X3: $i] :
! [X4: $i > $i > $o] :
( ! [X5: $i] : ( X4 @ X5 @ X5 )
=> ( X4 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) )
!= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] : ( Y2 @ Y3 @ Y3 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) )
!= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] : ( Y2 @ Y3 @ Y3 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) )
!= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] : ( Y2 @ Y3 @ Y3 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f9,plain,
( (=)
!= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] : ( Y2 @ Y3 @ Y3 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f6]) ).
thf(f17,plain,
( ( (=) @ sK0 )
!= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] : ( Y2 @ Y3 @ Y3 ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK0 ) ),
inference(negative_extensionality,[],[f9]) ).
thf(f18,plain,
( ( (=) @ sK0 )
!= ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 @ Y2 ) )
=> ( Y1 @ sK0 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f19,plain,
( ( sK0 = sK1 )
!= ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 @ Y2 ) )
=> ( Y1 @ sK0 @ Y0 ) ) )
@ sK1 ) ),
inference(negative_extensionality,[],[f18]) ).
thf(f20,plain,
( ( $true
= ( sK0 = sK1 ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 @ Y2 ) )
=> ( Y1 @ sK0 @ Y0 ) ) )
@ sK1 ) ) ),
inference(xor_proxy_clausification,[],[f19]) ).
thf(f21,plain,
( ( $false
= ( sK0 = sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 @ Y2 ) )
=> ( Y1 @ sK0 @ Y0 ) ) )
@ sK1 ) ) ),
inference(xor_proxy_clausification,[],[f19]) ).
thf(f22,plain,
( ( sK0 != sK1 )
| ( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 @ Y2 ) )
=> ( Y1 @ sK0 @ Y0 ) ) )
@ sK1 ) ) ),
inference(equality_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( ( sK0 != sK1 )
| ( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
=> ( Y0 @ sK0 @ sK1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
( ( sK0 != sK1 )
| ( $false
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
=> ( Y0 @ sK0 @ sK1 ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( ( sK0 != sK1 )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] : ( sK2 @ Y0 @ Y0 ) )
=> ( sK2 @ sK0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f26,plain,
( ( sK0 != sK1 )
| ( $false
= ( sK2 @ sK0 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f25]) ).
thf(f27,plain,
( ( sK0 != sK1 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( sK2 @ Y0 @ Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f25]) ).
thf(f28,plain,
! [X1: $i] :
( ( sK0 != sK1 )
| ( $true
= ( ^ [Y0: $i] : ( sK2 @ Y0 @ Y0 )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f27]) ).
thf(f29,plain,
! [X1: $i] :
( ( sK0 != sK1 )
| ( $true
= ( sK2 @ X1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,plain,
( ( sK0 = sK1 )
| ( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 @ Y2 ) )
=> ( Y1 @ sK0 @ Y0 ) ) )
@ sK1 ) ) ),
inference(equality_proxy_clausification,[],[f20]) ).
thf(f31,plain,
( ( sK0 = sK1 )
| ( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
=> ( Y0 @ sK0 @ sK1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f32,plain,
! [X1: $i > $i > $o] :
( ( sK0 = sK1 )
| ( $true
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
=> ( Y0 @ sK0 @ sK1 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f31]) ).
thf(f33,plain,
! [X1: $i > $i > $o] :
( ( sK0 = sK1 )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] : ( X1 @ Y0 @ Y0 ) )
=> ( X1 @ sK0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f32]) ).
thf(f34,plain,
! [X1: $i > $i > $o] :
( ( sK0 = sK1 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] : ( X1 @ Y0 @ Y0 ) ) )
| ( $true
= ( X1 @ sK0 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f33]) ).
thf(f35,plain,
! [X1: $i > $i > $o] :
( ( sK0 = sK1 )
| ( $false
= ( ^ [Y0: $i] : ( X1 @ Y0 @ Y0 )
@ ( sK3 @ X1 ) ) )
| ( $true
= ( X1 @ sK0 @ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f34]) ).
thf(f36,plain,
! [X1: $i > $i > $o] :
( ( sK0 = sK1 )
| ( $false
= ( X1 @ ( sK3 @ X1 ) @ ( sK3 @ X1 ) ) )
| ( $true
= ( X1 @ sK0 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f35]) ).
thf(f38,definition,
( spl4_1
<=> ! [X1: $i] :
( $true
= ( sK2 @ X1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f39,plain,
( ! [X1: $i] :
( $true
= ( sK2 @ X1 @ X1 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f38]) ).
thf(f41,definition,
( spl4_2
<=> ( sK0 = sK1 ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f42,plain,
( ( sK0 = sK1 )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f41]) ).
thf(f43,plain,
( ( sK0 != sK1 )
| spl4_2 ),
inference(avatar_component_clause,[],[f41]) ).
thf(f44,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f29,f41,f38]) ).
thf(f46,definition,
( spl4_3
<=> ( $false
= ( sK2 @ sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f48,plain,
( ( $false
= ( sK2 @ sK0 @ sK1 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f46]) ).
thf(f49,plain,
( spl4_3
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f26,f41,f46]) ).
thf(f51,definition,
( spl4_4
<=> ! [X1: $i > $i > $o] :
( ( $false
= ( X1 @ ( sK3 @ X1 ) @ ( sK3 @ X1 ) ) )
| ( $true
= ( X1 @ sK0 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f52,plain,
( ! [X1: $i > $i > $o] :
( ( $false
= ( X1 @ ( sK3 @ X1 ) @ ( sK3 @ X1 ) ) )
| ( $true
= ( X1 @ sK0 @ sK1 ) ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f51]) ).
thf(f53,plain,
( spl4_4
| spl4_2 ),
inference(avatar_split_clause,[],[f36,f41,f51]) ).
thf(f54,plain,
( ( $false
= ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 )
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) )
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) ) ) )
| ( $true
= ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 )
@ sK0
@ sK1 ) )
| ~ spl4_4 ),
inference(primitive_instantiation,[],[f52]) ).
thf(f85,plain,
( ( $false
= ( ( sK3 @ (=) )
= ( sK3 @ (=) ) ) )
| ( $true
= ( sK0 = sK1 ) )
| ~ spl4_4 ),
inference(beta-eta_normalization,[],[f54]) ).
thf(f86,plain,
( ( ( sK3 @ (=) )
!= ( sK3 @ (=) ) )
| ( $true
= ( sK0 = sK1 ) )
| ~ spl4_4 ),
inference(equality_proxy_clausification,[],[f85]) ).
thf(f87,plain,
( ( ( sK3 @ (=) )
!= ( sK3 @ (=) ) )
| ( sK0 = sK1 )
| ~ spl4_4 ),
inference(equality_proxy_clausification,[],[f86]) ).
thf(f88,plain,
( ( sK0 = sK1 )
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f87]) ).
thf(f90,plain,
( $false
| spl4_2
| ~ spl4_4 ),
inference(forward_subsumption_resolution,[],[f88,f43]) ).
thf(f91,plain,
( spl4_2
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f90]) ).
thf(f92,plain,
( ( $false
= ( sK2 @ sK0 @ sK0 ) )
| ~ spl4_2
| ~ spl4_3 ),
inference(forward_demodulation,[],[f48,f42]) ).
thf(f93,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_2
| ~ spl4_3 ),
inference(forward_demodulation,[],[f92,f39]) ).
thf(f94,plain,
( $false
| ~ spl4_1
| ~ spl4_2
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f93]) ).
thf(f95,plain,
( ~ spl4_1
| ~ spl4_2
| ~ spl4_3 ),
inference(avatar_contradiction_clause,[],[f94]) ).
cnf(s1,plain,
( spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f44]) ).
cnf(s2,plain,
( ~ spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f49]) ).
cnf(s3,plain,
( spl4_2
| spl4_4 ),
inference(sat_conversion,[],[f53]) ).
cnf(s4,plain,
( spl4_2
| ~ spl4_4 ),
inference(sat_conversion,[],[f91]) ).
cnf(s5,plain,
( ~ spl4_1
| ~ spl4_2
| ~ spl4_3 ),
inference(sat_conversion,[],[f95]) ).
cnf(s6,plain,
spl4_2,
inference(rat,[],[s3,s4]) ).
cnf(s7,plain,
spl4_3,
inference(rat,[],[s2,s6]) ).
cnf(s8,plain,
spl4_1,
inference(rat,[],[s1,s6]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s5,s6,s8,s7]) ).
thf(f96,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV121^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.28 % Computer : n014.cluster.edu
% 0.11/0.28 % Model : x86_64 x86_64
% 0.11/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.28 % Memory : 8046.5625MB
% 0.11/0.28 % OS : Linux 6.8.0-71-generic
% 0.11/0.28 % CPULimit : 300
% 0.11/0.28 % WCLimit : 300
% 0.11/0.28 % DateTime : Tue Sep 29 15:11:45 UTC 2026
% 0.11/0.28 % CPUTime :
% 0.11/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.28/0.32 Running first-order model finding
% 0.28/0.32 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
% 0.28/0.37 % (2785760)Will run a generic schedule for satisfiability detection.
% 0.28/0.37 % (2785770)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1125670524:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.28/0.37 % (2785770) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2785760-2785770"...
% 0.28/0.37 % (2785770)...printing done.
% 0.28/0.37 % (2785770)Refutation found. Thanks to Tanya!
% 0.28/0.37 % SZS status Theorem for theBenchmark
% 0.28/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.28/0.37 % (2785770)------------------------------
% 0.28/0.37 % (2785770)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.37 % (2785770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.37 % (2785770)CaDiCaL version: 2.1.3
% 0.28/0.37 % (2785770)Termination reason: Refutation
% 0.28/0.37 % (2785770)Time elapsed: 0.004 s
% 0.28/0.37 % (2785770)Peak memory usage: 12 MB
% 0.28/0.37 % (2785770)Instructions burned: 5 (million)
% 0.28/0.37 % (2785760)Success in time 0.037 s
% 0.28/0.37 % Vampire exiting
%------------------------------------------------------------------------------