%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU615^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 08:32:41 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 4
% Syntax : Number of formulae : 49 ( 21 unt; 0 typ; 2 def)
% Number of atoms : 357 ( 74 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 630 ( 72 ~; 33 |; 9 &; 368 @)
% ( 2 <=>; 121 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 17 usr; 9 con; 0-4 aty)
% ( 25 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 109 ( 0 sgn 74 !; 6 ?; 109 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
symdiff: $i > $i > $i ).
thf(func_def_2,type,
symdiffE: $o ).
thf(func_def_4,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
vIMP: $o > $o > $o ).
thf(func_def_6,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vNOT: $o > $o ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,axiom,
( symdiffE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
=> ! [X3: $o] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> X3 ) )
=> ( ( ~ ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> X3 ) )
=> X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffE) ).
thf(f2,conjecture,
( symdiffE
=> ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( symdiff @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(f3,negated_conjecture,
~ ( symdiffE
=> ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( symdiff @ X0 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( symdiffE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
=> ! [X3: $o] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> X3 ) )
=> ( ( ~ ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> X3 ) )
=> X3 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( symdiffE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( symdiff @ Y2 @ Y1 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( symdiffE
=> ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( symdiff @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( symdiffE = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
=> ( ( ( in @ X2 @ X1 )
!= $true )
=> ( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
!= $true ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
~ ( ( symdiffE = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
=> ( ( ( in @ X2 @ X1 )
!= $true )
=> ( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
!= $true ) ) ) ),
inference(flattening,[],[f7]) ).
thf(f9,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
= $true )
& ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
!= $true ) )
& ( symdiffE = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
= $true )
& ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
!= $true ) )
& ( symdiffE = $true ) ),
inference(flattening,[],[f9]) ).
thf(f11,plain,
( ( $true
= ( in @ sK2 @ ( symdiff @ sK0 @ sK1 ) ) )
& ( $true
!= ( in @ sK2 @ sK1 ) )
& ( $true
!= ( in @ sK2 @ sK0 ) )
& ( symdiffE = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f10]) ).
thf(f12,plain,
( symdiffE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( symdiff @ Y2 @ Y1 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f13,plain,
symdiffE = $true,
inference(cnf_transformation,[],[f11]) ).
thf(f14,plain,
( $true
!= ( in @ sK2 @ sK0 ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f15,plain,
( $true
!= ( in @ sK2 @ sK1 ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f16,plain,
( $true
= ( in @ sK2 @ ( symdiff @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f19,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( symdiff @ Y2 @ Y1 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f12,f13]) ).
thf(f20,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( symdiff @ Y2 @ Y1 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f19]) ).
thf(f21,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( symdiff @ Y1 @ Y0 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( ( in @ X1 @ Y1 )
=> ( ~ ( in @ X1 @ Y0 )
=> Y2 ) )
=> ( ( ~ ( in @ X1 @ Y1 )
=> ( ( in @ X1 @ Y0 )
=> Y2 ) )
=> Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f22,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( symdiff @ Y1 @ Y0 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( ( in @ X1 @ Y1 )
=> ( ~ ( in @ X1 @ Y0 )
=> Y2 ) )
=> ( ( ~ ( in @ X1 @ Y1 )
=> ( ( in @ X1 @ Y0 )
=> Y2 ) )
=> Y2 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f21]) ).
thf(f23,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( symdiff @ Y0 @ X2 ) )
=> ( !! @ $o
@ ^ [Y1: $o] :
( ( ( in @ X1 @ Y0 )
=> ( ~ ( in @ X1 @ X2 )
=> Y1 ) )
=> ( ( ~ ( in @ X1 @ Y0 )
=> ( ( in @ X1 @ X2 )
=> Y1 ) )
=> Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( symdiff @ Y0 @ X2 ) )
=> ( !! @ $o
@ ^ [Y1: $o] :
( ( ( in @ X1 @ Y0 )
=> ( ~ ( in @ X1 @ X2 )
=> Y1 ) )
=> ( ( ~ ( in @ X1 @ Y0 )
=> ( ( in @ X1 @ X2 )
=> Y1 ) )
=> Y1 ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f23]) ).
thf(f25,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( symdiff @ X3 @ X2 ) )
=> ( !! @ $o
@ ^ [Y0: $o] :
( ( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X2 )
=> Y0 ) )
=> ( ( ~ ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X2 )
=> Y0 ) )
=> Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f26,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( symdiff @ X3 @ X2 ) ) )
| ( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( ( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X2 )
=> Y0 ) )
=> ( ( ~ ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X2 )
=> Y0 ) )
=> Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f25]) ).
thf(f27,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false
= ( in @ X1 @ ( symdiff @ X3 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $o] :
( ( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X2 )
=> Y0 ) )
=> ( ( ~ ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X2 )
=> Y0 ) )
=> Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f26]) ).
thf(f28,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false
= ( in @ X1 @ ( symdiff @ X3 @ X2 ) ) )
| ( $true
= ( ( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X2 )
=> X4 ) )
=> ( ( ~ ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X2 )
=> X4 ) )
=> X4 ) ) ) ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f29,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false
= ( in @ X1 @ ( symdiff @ X3 @ X2 ) ) )
| ( $false
= ( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X2 )
=> X4 ) ) )
| ( $true
= ( ( ~ ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X2 )
=> X4 ) )
=> X4 ) ) ),
inference(imp_proxy_clausification,[],[f28]) ).
thf(f31,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false
= ( in @ X1 @ ( symdiff @ X3 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X3 ) )
| ( $true
= ( ( ~ ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X2 )
=> X4 ) )
=> X4 ) ) ),
inference(imp_proxy_clausification,[],[f29]) ).
thf(f32,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false
= ( in @ X1 @ ( symdiff @ X3 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X3 ) )
| ( $false
= ( ~ ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X2 )
=> X4 ) ) )
| ( $true = X4 ) ),
inference(imp_proxy_clausification,[],[f31]) ).
thf(f33,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false
= ( in @ X1 @ ( symdiff @ X3 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X3 ) )
| ( $false
= ( ( in @ X1 @ X2 )
=> X4 ) )
| ( $true = X4 ) ),
inference(imp_proxy_clausification,[],[f32]) ).
thf(f37,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false
= ( in @ X1 @ ( symdiff @ X3 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X3 ) )
| ( $true
= ( in @ X1 @ X2 ) )
| ( $true = X4 ) ),
inference(imp_proxy_clausification,[],[f33]) ).
thf(f55,definition,
( spl3_1
<=> ! [X4: $o] : ( $true = X4 ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f56,plain,
( ! [X4: $o] : ( $true = X4 )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f55]) ).
thf(f62,definition,
( spl3_3
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $false
= ( in @ X1 @ ( symdiff @ X3 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X2 ) )
| ( $true
= ( in @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f63,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( symdiff @ X3 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X2 ) )
| ( $true
= ( in @ X1 @ X3 ) ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f62]) ).
thf(f64,plain,
( spl3_1
| spl3_3 ),
inference(avatar_split_clause,[],[f37,f62,f55]) ).
thf(f123,plain,
( ( $true = $false )
| ( $true
= ( in @ sK2 @ sK1 ) )
| ( $true
= ( in @ sK2 @ sK0 ) )
| ~ spl3_3 ),
inference(constrained_superposition,[],[f63,f16]) ).
thf(f126,plain,
( ( $true
= ( in @ sK2 @ sK1 ) )
| ( $true
= ( in @ sK2 @ sK0 ) )
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f123]) ).
thf(f129,plain,
( ( $true
= ( in @ sK2 @ sK0 ) )
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f126,f15]) ).
thf(f132,plain,
( $false
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f129,f14]) ).
thf(f133,plain,
~ spl3_3,
inference(avatar_contradiction_clause,[],[f132]) ).
thf(f139,plain,
( ( $true != $true )
| ~ spl3_1 ),
inference(constrained_superposition,[],[f14,f56]) ).
thf(f146,plain,
( $false
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f139]) ).
thf(f147,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f146]) ).
cnf(s2,plain,
( spl3_1
| spl3_3 ),
inference(sat_conversion,[],[f64]) ).
cnf(s13,plain,
~ spl3_3,
inference(sat_conversion,[],[f133]) ).
cnf(s16,plain,
~ spl3_1,
inference(sat_conversion,[],[f147]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s2,s13,s16]) ).
thf(f158,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU615^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n015.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 14:01:48 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 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
% 0.09/0.25 % (3567661)Will run a generic schedule for satisfiability detection.
% 0.09/0.25 % (3567669)dis+10_1_sil=32000:sp=arity:random_seed=2178051739:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.25 % (3567669) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3567661-3567669"...
% 0.09/0.25 % (3567667)% WARNING: option uhcvi not known.
% 0.09/0.25 % (3567669)...printing done.
% 0.09/0.25 % (3567669)Refutation found. Thanks to Tanya!
% 0.09/0.25 % SZS status Theorem for theBenchmark
% 0.09/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.25 % (3567669)------------------------------
% 0.09/0.25 % (3567669)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (3567669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (3567669)CaDiCaL version: 2.1.3
% 0.09/0.25 % (3567669)Termination reason: Refutation
% 0.09/0.25 % (3567669)Time elapsed: 0.003 s
% 0.09/0.25 % (3567669)Peak memory usage: 12 MB
% 0.09/0.25 % (3567669)Instructions burned: 8 (million)
% 0.09/0.25 % (3567661)Success in time 0.028 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------