%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV417^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 08:39:29 AM UTC 2026
% Result : Theorem 0.30s 0.39s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of formulae : 44 ( 10 unt; 0 typ; 2 def)
% Number of atoms : 281 ( 85 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 257 ( 29 ~; 39 |; 53 &; 119 @)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 100 ( 36 sgn 38 !; 6 ?; 100 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cP: ( a > $o ) > $o ).
thf(func_def_4,type,
vAND: $o > $o > $o ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_7,type,
sK0: a > $o ).
thf(func_def_8,type,
sK1: a > $o ).
thf(func_def_9,type,
sK2: a > $o ).
thf(func_def_11,type,
sK4: a ).
thf(func_def_12,type,
sK5: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( cP
@ ^ [X3: a] :
( ( X2 @ X3 )
& ( X1 @ X3 ) ) )
& ( ( ^ [X3: a] :
( ( X2 @ X3 )
& ( X1 @ X3 ) ) )
= ( ^ [X3: a] : $false ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) )
=> ( ( cP
@ ^ [X3: a] : $false )
& ( X0
= ( ^ [X3: a] : $false ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM502_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( cP
@ ^ [X3: a] :
( ( X2 @ X3 )
& ( X1 @ X3 ) ) )
& ( ( ^ [X3: a] :
( ( X2 @ X3 )
& ( X1 @ X3 ) ) )
= ( ^ [X3: a] : $false ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) )
=> ( ( cP
@ ^ [X3: a] : $false )
& ( X0
= ( ^ [X3: a] : $false ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( cP
@ ^ [X3: a] :
( ( X2 @ X3 )
& ( X1 @ X3 ) ) )
& ( ( ^ [X4: a] :
( ( X2 @ X4 )
& ( X1 @ X4 ) ) )
= ( ^ [X5: a] : $false ) )
& ! [X6: a] :
( ( X0 @ X6 )
=> ( X2 @ X6 ) )
& ! [X7: a] :
( ( X0 @ X7 )
=> ( X1 @ X7 ) ) )
=> ( ( cP
@ ^ [X8: a] : $false )
& ( X0
= ( ^ [X9: a] : $false ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( $true
= ( cP
@ ^ [Y0: a] :
( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) )
& ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ! [X6: a] :
( ( ( X0 @ X6 )
= $true )
=> ( ( X2 @ X6 )
= $true ) )
& ! [X7: a] :
( ( ( X0 @ X7 )
= $true )
=> ( ( X1 @ X7 )
= $true ) ) )
=> ( ( $true
= ( cP
@ ^ [Y0: a] : $false ) )
& ( ( ^ [Y0: a] : $false )
= X0 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( $true
= ( cP
@ ^ [Y0: a] :
( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) )
& ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
=> ( ( X2 @ X3 )
= $true ) )
& ! [X4: a] :
( ( $true
= ( X0 @ X4 ) )
=> ( ( X1 @ X4 )
= $true ) ) )
=> ( ( $true
= ( cP
@ ^ [Y0: a] : $false ) )
& ( ( ^ [Y0: a] : $false )
= X0 ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( $true
!= ( cP
@ ^ [Y0: a] : $false ) )
| ( ( ^ [Y0: a] : $false )
!= X0 ) )
& ( $true
= ( cP
@ ^ [Y0: a] :
( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) )
& ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
| ( ( X0 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( ( X1 @ X4 )
= $true )
| ( $true
!= ( X0 @ X4 ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( $true
!= ( cP
@ ^ [Y0: a] : $false ) )
| ( ( ^ [Y0: a] : $false )
!= X0 ) )
& ( $true
= ( cP
@ ^ [Y0: a] :
( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) )
& ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
| ( ( X0 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( ( X1 @ X4 )
= $true )
| ( $true
!= ( X0 @ X4 ) ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
( ( ( $true
!= ( cP
@ ^ [Y0: a] : $false ) )
| ( ( ^ [Y0: a] : $false )
!= sK0 ) )
& ( $true
= ( cP
@ ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
& ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
& ! [X3: a] :
( ( $true
= ( sK2 @ X3 ) )
| ( $true
!= ( sK0 @ X3 ) ) )
& ! [X4: a] :
( ( $true
= ( sK1 @ X4 ) )
| ( $true
!= ( sK0 @ X4 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f7]) ).
thf(f9,plain,
! [X4: a] :
( ( $true
!= ( sK0 @ X4 ) )
| ( $true
= ( sK1 @ X4 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
! [X3: a] :
( ( $true
!= ( sK0 @ X3 ) )
| ( $true
= ( sK2 @ X3 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
( $true
= ( cP
@ ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f13,plain,
( ( $true
!= ( cP
@ ^ [Y0: a] : $false ) )
| ( ( ^ [Y0: a] : $false )
!= sK0 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f17,definition,
( spl3_1
<=> ( ( ^ [Y0: a] : $false )
= sK0 ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f19,plain,
( ( ( ^ [Y0: a] : $false )
!= sK0 )
| spl3_1 ),
inference(avatar_component_clause,[],[f17]) ).
thf(f21,definition,
( spl3_2
<=> ( $true
= ( cP
@ ^ [Y0: a] : $false ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f23,plain,
( ( $true
!= ( cP
@ ^ [Y0: a] : $false ) )
| spl3_2 ),
inference(avatar_component_clause,[],[f21]) ).
thf(f24,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f13,f21,f17]) ).
thf(f47,plain,
! [X1: a] :
( ( ^ [Y0: a] : $false
@ X1 )
= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
@ X1 ) ),
inference(argument_congruence,[],[f11]) ).
thf(f48,plain,
! [X1: a] :
( ( $true
= ( ^ [Y0: a] : $false
@ X1 ) )
| ( $false
= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
@ X1 ) ) ),
inference(iff_proxy_clausification,[],[f47]) ).
thf(f53,plain,
! [X1: a] :
( ( $true = $false )
| ( $false
= ( ( sK1 @ X1 )
& ( sK2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f48]) ).
thf(f54,plain,
! [X1: a] :
( ( $true = $false )
| ( $false
= ( sK2 @ X1 ) )
| ( $false
= ( sK1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f53]) ).
thf(f55,plain,
! [X1: a] :
( ( $false
= ( sK2 @ X1 ) )
| ( $false
= ( sK1 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f54]) ).
thf(f78,plain,
( $true
= ( cP
@ ^ [Y0: a] : $false ) ),
inference(forward_demodulation,[],[f12,f11]) ).
thf(f79,plain,
( $false
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f78,f23]) ).
thf(f80,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f79]) ).
thf(f81,plain,
( ( ( ^ [Y0: a] : $false
@ sK5 )
!= ( sK0 @ sK5 ) )
| spl3_1 ),
inference(negative_extensionality,[],[f19]) ).
thf(f82,plain,
( ( $true
= ( ^ [Y0: a] : $false
@ sK5 ) )
| ( $true
= ( sK0 @ sK5 ) )
| spl3_1 ),
inference(xor_proxy_clausification,[],[f81]) ).
thf(f85,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK5 ) )
| spl3_1 ),
inference(beta-eta_normalization,[],[f82]) ).
thf(f86,plain,
( ( $true
= ( sK0 @ sK5 ) )
| spl3_1 ),
inference(trivial_inequality_removal,[],[f85]) ).
thf(f87,plain,
( ( $true != $true )
| ( $true
= ( sK2 @ sK5 ) )
| spl3_1 ),
inference(constrained_superposition,[],[f10,f86]) ).
thf(f88,plain,
( ( $true != $true )
| ( $true
= ( sK1 @ sK5 ) )
| spl3_1 ),
inference(constrained_superposition,[],[f9,f86]) ).
thf(f89,plain,
( ( $true
= ( sK1 @ sK5 ) )
| spl3_1 ),
inference(trivial_inequality_removal,[],[f88]) ).
thf(f90,plain,
( ( $true
= ( sK2 @ sK5 ) )
| spl3_1 ),
inference(trivial_inequality_removal,[],[f87]) ).
thf(f98,plain,
( ( $true = $false )
| ( $false
= ( sK1 @ sK5 ) )
| spl3_1 ),
inference(constrained_superposition,[],[f90,f55]) ).
thf(f99,plain,
( ( $false
= ( sK1 @ sK5 ) )
| spl3_1 ),
inference(trivial_inequality_removal,[],[f98]) ).
thf(f113,plain,
( ( $true = $false )
| spl3_1 ),
inference(constrained_superposition,[],[f99,f89]) ).
thf(f117,plain,
( $false
| spl3_1 ),
inference(trivial_inequality_removal,[],[f113]) ).
thf(f118,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f117]) ).
cnf(s9,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f24]) ).
cnf(s43,plain,
spl3_2,
inference(sat_conversion,[],[f80]) ).
cnf(s69,plain,
spl3_1,
inference(sat_conversion,[],[f118]) ).
cnf(s70,plain,
$false,
inference(rat,[],[s9,s43,s69]) ).
thf(f119,plain,
$false,
inference(avatar_sat_refutation,[],[s70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEV417^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.29 % Computer : n018.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8046.5625MB
% 0.12/0.29 % OS : Linux 6.8.0-71-generic
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Sep 29 15:47:56 UTC 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.30/0.33 Running first-order model finding
% 0.30/0.33 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.30/0.39 % (250828)Will run a generic schedule for satisfiability detection.
% 0.30/0.39 % (250835)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=126511114:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.30/0.39 % (250835) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-250828-250835"...
% 0.30/0.39 % (250835)...printing done.
% 0.30/0.39 % (250834)% WARNING: option uhcvi not known.
% 0.30/0.39 % (250835)Refutation found. Thanks to Tanya!
% 0.30/0.39 % SZS status Theorem for theBenchmark
% 0.30/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.30/0.39 % (250835)------------------------------
% 0.30/0.39 % (250835)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.39 % (250835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.39 % (250835)CaDiCaL version: 2.1.3
% 0.30/0.39 % (250835)Termination reason: Refutation
% 0.30/0.39 % (250835)Time elapsed: 0.006 s
% 0.30/0.39 % (250835)Peak memory usage: 13 MB
% 0.30/0.39 % (250835)Instructions burned: 7 (million)
% 0.30/0.39 % (250828)Success in time 0.037 s
% 0.30/0.39 % Vampire exiting
%------------------------------------------------------------------------------