%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n007.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 08:30:20 AM UTC 2026
% Result : Theorem 0.23s 0.26s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 41 ( 10 unt; 0 typ; 1 def)
% Number of atoms : 557 ( 178 equ; 0 cnn)
% Maximal formula atoms : 14 ( 13 avg)
% Number of connectives : 617 ( 97 ~; 64 |; 51 &; 356 @)
% ( 6 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 10 con; 0-4 aty)
% Number of variables : 117 ( 0 ^; 100 !; 17 ?; 117 :)
% 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_6,type,
sP0: $i > $i > $i > $o > $o ).
thf(func_def_13,type,
sK7: $o ).
thf(func_def_14,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
=> ! [X3: $o] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> X3 ) )
=> ( ( ~ ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> X3 ) )
=> X3 ) ) )
= symdiffE ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffE) ).
thf(f2,conjecture,
( symdiffE
=> ! [X1: $i,X2: $i,X0: $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
=> ! [X1: $i,X2: $i,X0: $i] :
( ~ ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( symdiff @ X0 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( symdiff @ X2 @ X1 ) )
=> ! [X3: $o] :
( ( ( in @ X0 @ X2 )
=> ( ~ ( in @ X0 @ X1 )
=> X3 ) )
=> ( ( ~ ( in @ X0 @ X2 )
=> ( ( in @ X0 @ X1 )
=> X3 ) )
=> X3 ) ) )
= symdiffE ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( symdiff @ X2 @ X1 ) ) )
=> ! [X3: $o] :
( ( ( ( in @ X0 @ X2 )
= $true )
=> ( ( $true
!= ( in @ X0 @ X1 ) )
=> ( $true = X3 ) ) )
=> ( ( ( ( in @ X0 @ X2 )
!= $true )
=> ( ( $true
= ( in @ X0 @ X1 ) )
=> ( $true = X3 ) ) )
=> ( $true = X3 ) ) ) )
<=> ( symdiffE = $true ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( symdiffE
=> ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X1 @ X2 )
=> ( ~ ( in @ X1 @ X0 )
=> ~ ( in @ X1 @ ( symdiff @ X2 @ X0 ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( symdiffE = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
=> ( ( $true
!= ( in @ X1 @ X0 ) )
=> ( ( in @ X1 @ ( symdiff @ X2 @ X0 ) )
!= $true ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ( symdiffE = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( symdiff @ X2 @ X1 ) ) )
=> ! [X3: $o] :
( ( ( ( in @ X0 @ X2 )
= $true )
=> ( ( $true
!= ( in @ X0 @ X1 ) )
=> ( $true = X3 ) ) )
=> ( ( ( ( in @ X0 @ X2 )
!= $true )
=> ( ( $true
= ( in @ X0 @ X1 ) )
=> ( $true = X3 ) ) )
=> ( $true = X3 ) ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f9,plain,
~ ( ( symdiffE = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
=> ( ( $true
!= ( in @ X1 @ X0 ) )
=> ( ( in @ X1 @ ( symdiff @ X2 @ X0 ) )
!= $true ) ) ) ),
inference(flattening,[],[f7]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( symdiff @ X2 @ X0 ) )
= $true )
& ( $true
!= ( in @ X1 @ X0 ) )
& ( ( in @ X1 @ X2 )
!= $true ) )
& ( symdiffE = $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f11,plain,
( ? [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( symdiff @ X2 @ X0 ) )
= $true )
& ( ( in @ X1 @ X2 )
!= $true )
& ( $true
!= ( in @ X1 @ X0 ) ) )
& ( symdiffE = $true ) ),
inference(flattening,[],[f10]) ).
thf(f12,plain,
( ( symdiffE = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ! [X3: $o] :
( ( $true = X3 )
| ( ( $true != X3 )
& ( $true
= ( in @ X0 @ X1 ) )
& ( ( in @ X0 @ X2 )
!= $true ) )
| ( ( $true != X3 )
& ( $true
!= ( in @ X0 @ X1 ) )
& ( ( in @ X0 @ X2 )
= $true ) ) )
| ( $true
!= ( in @ X0 @ ( symdiff @ X2 @ X1 ) ) ) ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f13,plain,
( ( symdiffE = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( symdiff @ X2 @ X1 ) ) )
| ! [X3: $o] :
( ( ( $true
!= ( in @ X0 @ X1 ) )
& ( $true != X3 )
& ( ( in @ X0 @ X2 )
= $true ) )
| ( $true = X3 )
| ( ( $true != X3 )
& ( ( in @ X0 @ X2 )
!= $true )
& ( $true
= ( in @ X0 @ X1 ) ) ) ) ) ),
inference(flattening,[],[f12]) ).
thf(f14,definition,
! [X3: $o,X2: $i,X0: $i,X1: $i] :
( ( ( sP0 @ X1 @ X0 @ X2 @ X3 )
= $true )
<=> ( ( $true != X3 )
& ( ( in @ X0 @ X2 )
!= $true )
& ( $true
= ( in @ X0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction]) ).
thf(f15,plain,
( ( symdiffE = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( symdiff @ X2 @ X1 ) ) )
| ! [X3: $o] :
( ( ( $true
!= ( in @ X0 @ X1 ) )
& ( $true != X3 )
& ( ( in @ X0 @ X2 )
= $true ) )
| ( $true = X3 )
| ( ( sP0 @ X1 @ X0 @ X2 @ X3 )
= $true ) ) ) ),
inference(definition_folding,[],[f13,f14]) ).
thf(f16,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
= $true )
& ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ X1 )
!= $true ) )
& ( symdiffE = $true ) ),
inference(rectify,[],[f11]) ).
thf(f17,plain,
( ( ( in @ sK3 @ ( symdiff @ sK1 @ sK2 ) )
= $true )
& ( ( in @ sK3 @ sK1 )
!= $true )
& ( $true
!= ( in @ sK3 @ sK2 ) )
& ( symdiffE = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f16]) ).
thf(f18,plain,
! [X3: $o,X2: $i,X0: $i,X1: $i] :
( ( ( ( sP0 @ X1 @ X0 @ X2 @ X3 )
= $true )
| ( $true = X3 )
| ( ( in @ X0 @ X2 )
= $true )
| ( $true
!= ( in @ X0 @ X1 ) ) )
& ( ( ( $true != X3 )
& ( ( in @ X0 @ X2 )
!= $true )
& ( $true
= ( in @ X0 @ X1 ) ) )
| ( ( sP0 @ X1 @ X0 @ X2 @ X3 )
!= $true ) ) ),
inference(nnf_transformation,[],[f14]) ).
thf(f19,plain,
! [X3: $o,X2: $i,X0: $i,X1: $i] :
( ( ( ( sP0 @ X1 @ X0 @ X2 @ X3 )
= $true )
| ( $true = X3 )
| ( ( in @ X0 @ X2 )
= $true )
| ( $true
!= ( in @ X0 @ X1 ) ) )
& ( ( ( $true != X3 )
& ( ( in @ X0 @ X2 )
!= $true )
& ( $true
= ( in @ X0 @ X1 ) ) )
| ( ( sP0 @ X1 @ X0 @ X2 @ X3 )
!= $true ) ) ),
inference(flattening,[],[f18]) ).
thf(f20,plain,
! [X0: $o,X1: $i,X2: $i,X3: $i] :
( ( ( ( sP0 @ X3 @ X2 @ X1 @ X0 )
= $true )
| ( $true = X0 )
| ( ( in @ X2 @ X1 )
= $true )
| ( $true
!= ( in @ X2 @ X3 ) ) )
& ( ( ( $true != X0 )
& ( ( in @ X2 @ X1 )
!= $true )
& ( $true
= ( in @ X2 @ X3 ) ) )
| ( ( sP0 @ X3 @ X2 @ X1 @ X0 )
!= $true ) ) ),
inference(rectify,[],[f19]) ).
thf(f21,plain,
( ( ( symdiffE = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( symdiff @ X2 @ X1 ) ) )
& ? [X3: $o] :
( ( ( $true
= ( in @ X0 @ X1 ) )
| ( $true = X3 )
| ( ( in @ X0 @ X2 )
!= $true ) )
& ( $true != X3 )
& ( ( sP0 @ X1 @ X0 @ X2 @ X3 )
!= $true ) ) ) )
& ( ! [X1: $i,X2: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( symdiff @ X2 @ X1 ) ) )
| ! [X3: $o] :
( ( ( $true
!= ( in @ X0 @ X1 ) )
& ( $true != X3 )
& ( ( in @ X0 @ X2 )
= $true ) )
| ( $true = X3 )
| ( ( sP0 @ X1 @ X0 @ X2 @ X3 )
= $true ) ) )
| ( symdiffE != $true ) ) ),
inference(nnf_transformation,[],[f15]) ).
thf(f22,plain,
( ( ( symdiffE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( symdiff @ X1 @ X0 ) ) )
& ? [X3: $o] :
( ( ( ( in @ X2 @ X0 )
= $true )
| ( $true = X3 )
| ( ( in @ X2 @ X1 )
!= $true ) )
& ( $true != X3 )
& ( ( sP0 @ X0 @ X2 @ X1 @ X3 )
!= $true ) ) ) )
& ( ! [X4: $i,X5: $i,X6: $i] :
( ( ( in @ X6 @ ( symdiff @ X5 @ X4 ) )
!= $true )
| ! [X7: $o] :
( ( ( $true
!= ( in @ X6 @ X4 ) )
& ( $true != X7 )
& ( ( in @ X6 @ X5 )
= $true ) )
| ( $true = X7 )
| ( $true
= ( sP0 @ X4 @ X6 @ X5 @ X7 ) ) ) )
| ( symdiffE != $true ) ) ),
inference(rectify,[],[f21]) ).
thf(f23,plain,
( ( ( symdiffE = $true )
| ( ( ( in @ sK6 @ ( symdiff @ sK5 @ sK4 ) )
= $true )
& ( ( ( in @ sK6 @ sK4 )
= $true )
| ( $true = sK7 )
| ( $true
!= ( in @ sK6 @ sK5 ) ) )
& ( $true != sK7 )
& ( ( sP0 @ sK4 @ sK6 @ sK5 @ sK7 )
!= $true ) ) )
& ( ! [X4: $i,X5: $i,X6: $i] :
( ( ( in @ X6 @ ( symdiff @ X5 @ X4 ) )
!= $true )
| ! [X7: $o] :
( ( ( $true
!= ( in @ X6 @ X4 ) )
& ( $true != X7 )
& ( ( in @ X6 @ X5 )
= $true ) )
| ( $true = X7 )
| ( $true
= ( sP0 @ X4 @ X6 @ X5 @ X7 ) ) ) )
| ( symdiffE != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f22]) ).
thf(f24,plain,
symdiffE = $true,
inference(cnf_transformation,[],[f17]) ).
thf(f25,plain,
( $true
!= ( in @ sK3 @ sK2 ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f26,plain,
( ( in @ sK3 @ sK1 )
!= $true ),
inference(cnf_transformation,[],[f17]) ).
thf(f27,plain,
( ( in @ sK3 @ ( symdiff @ sK1 @ sK2 ) )
= $true ),
inference(cnf_transformation,[],[f17]) ).
thf(f28,plain,
! [X2: $i,X3: $i,X0: $o,X1: $i] :
( ( ( sP0 @ X3 @ X2 @ X1 @ X0 )
!= $true )
| ( $true
= ( in @ X2 @ X3 ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f30,plain,
! [X2: $i,X3: $i,X0: $o,X1: $i] :
( ( $true != X0 )
| ( ( sP0 @ X3 @ X2 @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f32,plain,
! [X6: $i,X7: $o,X4: $i,X5: $i] :
( ( ( in @ X6 @ ( symdiff @ X5 @ X4 ) )
!= $true )
| ( ( in @ X6 @ X5 )
= $true )
| ( $true = X7 )
| ( $true
= ( sP0 @ X4 @ X6 @ X5 @ X7 ) )
| ( symdiffE != $true ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f47,plain,
! [X6: $i,X7: $o,X4: $i,X5: $i] :
( ( $true = X7 )
| ( $true != $true )
| ( ( in @ X6 @ ( symdiff @ X5 @ X4 ) )
!= $true )
| ( $true
= ( sP0 @ X4 @ X6 @ X5 @ X7 ) )
| ( ( in @ X6 @ X5 )
= $true ) ),
inference(definition_unfolding,[],[f32,f24]) ).
thf(f48,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sP0 @ X3 @ X2 @ X1 @ $true )
!= $true ),
inference(equality_resolution,[],[f30]) ).
thf(f51,plain,
! [X6: $i,X7: $o,X4: $i,X5: $i] :
( ( ( in @ X6 @ ( symdiff @ X5 @ X4 ) )
!= $true )
| ( ( in @ X6 @ X5 )
= $true )
| ( $true
= ( sP0 @ X4 @ X6 @ X5 @ X7 ) )
| ( $true = X7 ) ),
inference(trivial_inequality_removal,[],[f47]) ).
thf(f54,plain,
! [X0: $o] :
( ( $true = X0 )
| ( ( in @ sK3 @ sK1 )
= $true )
| ( $true
= ( sP0 @ sK2 @ sK3 @ sK1 @ X0 ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f51,f27]) ).
thf(f55,plain,
! [X0: $o] :
( ( ( in @ sK3 @ sK1 )
= $true )
| ( $true
= ( sP0 @ sK2 @ sK3 @ sK1 @ X0 ) )
| ( $true = X0 ) ),
inference(trivial_inequality_removal,[],[f54]) ).
thf(f56,plain,
! [X0: $o] :
( ( $true
= ( sP0 @ sK2 @ sK3 @ sK1 @ X0 ) )
| ( $true = X0 ) ),
inference(forward_subsumption_resolution,[],[f55,f26]) ).
thf(f57,plain,
! [X0: $o] :
( ( $true
= ( in @ sK3 @ sK2 ) )
| ( $true != $true )
| ( $true = X0 ) ),
inference(constrained_superposition,[],[f28,f56]) ).
thf(f58,plain,
! [X0: $o] :
( ( $true
= ( in @ sK3 @ sK2 ) )
| ( $true = X0 ) ),
inference(trivial_inequality_removal,[],[f57]) ).
thf(f59,plain,
! [X0: $o] : ( $true = X0 ),
inference(forward_subsumption_resolution,[],[f58,f25]) ).
thf(f66,plain,
$true != $true,
inference(constrained_superposition,[],[f48,f59]) ).
thf(f70,plain,
$false,
inference(trivial_inequality_removal,[],[f66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU615^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n007.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 13:56:26 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 Running higher-order theorem proving
% 0.07/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.26 % (3406679)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.26 % (3406684)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2278327437:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.26 % (3406684) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3406679-3406684"...
% 0.23/0.26 % (3406684)...printing done.
% 0.23/0.26 % (3406684)Refutation found. Thanks to Tanya!
% 0.23/0.26 % SZS status Theorem for theBenchmark
% 0.23/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.26 % (3406684)------------------------------
% 0.23/0.26 % (3406684)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.26 % (3406684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.26 % (3406684)CaDiCaL version: 2.1.3
% 0.23/0.26 % (3406684)Termination reason: Refutation
% 0.23/0.26 % (3406684)Time elapsed: 0.002 s
% 0.23/0.26 % (3406684)Peak memory usage: 12 MB
% 0.23/0.26 % (3406684)Instructions burned: 7 (million)
% 0.23/0.26 % (3406679)Success in time 0.032 s
% 0.23/0.26 % Vampire exiting
%------------------------------------------------------------------------------