%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU769^2 : 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 : n026.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 08:31:16 AM UTC 2026
% Result : Theorem 0.24s 0.30s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 242 ( 71 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 316 ( 26 ~; 17 |; 12 &; 248 @)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 7 con; 0-4 aty)
% Number of variables : 114 ( 63 ^; 41 !; 10 ?; 114 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_3,type,
dsetconstrER: $o ).
thf(func_def_5,type,
subset: $i > $i > $o ).
thf(func_def_6,type,
cartprod: $i > $i > $i ).
thf(func_def_7,type,
breln: $i > $i > $i > $o ).
thf(func_def_8,type,
breln1: $i > $i > $o ).
thf(func_def_9,type,
breln1Set: $i > $i ).
thf(func_def_12,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_15,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK0: $i > $o ).
thf(func_def_21,type,
vNOT: $o > $o ).
thf(f1,axiom,
( dsetconstrER
= ( ! [X0: $i,X2: $i,X1: $i > $o] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(f2,axiom,
( ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) )
= breln ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln) ).
thf(f3,axiom,
( breln1
= ( ^ [X0: $i,X1: $i] : ( breln @ X0 @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1) ).
thf(f4,axiom,
( ( ^ [X0: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ X0 @ X0 ) )
@ ^ [X1: $i] : ( breln1 @ X0 @ X1 ) ) )
= breln1Set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1Set) ).
thf(f5,conjecture,
( dsetconstrER
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( breln1Set @ X0 ) )
=> ( breln1 @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1SetBreln1) ).
thf(f6,negated_conjecture,
~ ( dsetconstrER
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( breln1Set @ X0 ) )
=> ( breln1 @ X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
~ ( dsetconstrER
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( breln1Set @ X0 ) )
=> ( breln1 @ X0 @ X1 ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
~ ( ( dsetconstrER = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( breln1Set @ X0 ) )
= $true )
=> ( ( breln1 @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f10,plain,
( ( ^ [X0: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ X0 @ X0 ) )
@ ^ [X1: $i] : ( breln1 @ X0 @ X1 ) ) )
= breln1Set ),
inference(rectify,[],[f4]) ).
thf(f11,plain,
( breln1Set
= ( ^ [Y0: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y0 ) )
@ ^ [Y1: $i] : ( breln1 @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( dsetconstrER
= ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X2 @ X3 ) ) )
=> ( X2 @ X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f13,plain,
( ( dsetconstrER = $true )
<=> ! [X1: $i,X0: $i,X2: $i > $o] :
( ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
=> ( ( X2 @ X1 )
= $true ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f15,plain,
( ( dsetconstrER = $true )
<=> ! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( X2 @ X1 )
= $true )
| ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f16,plain,
( ? [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( breln1Set @ X0 ) )
= $true )
& ( ( breln1 @ X0 @ X1 )
!= $true ) )
& ( dsetconstrER = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f17,plain,
( ( ( dsetconstrER = $true )
| ? [X2: $i > $o,X0: $i,X1: $i] :
( ( ( X2 @ X1 )
!= $true )
& ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true ) ) )
& ( ! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( X2 @ X1 )
= $true )
| ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) ) ),
inference(nnf_transformation,[],[f15]) ).
thf(f18,plain,
( ( ( dsetconstrER = $true )
| ? [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X2 )
!= $true )
& ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) ) )
& ( ! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( X3 @ X5 )
= $true )
| ( $true
!= ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) ) ),
inference(rectify,[],[f17]) ).
thf(f19,plain,
( ( ( dsetconstrER = $true )
| ( ( ( sK0 @ sK2 )
!= $true )
& ( ( in @ sK2
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
= $true ) ) )
& ( ! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( X3 @ X5 )
= $true )
| ( $true
!= ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f18]) ).
thf(f20,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( breln1Set @ X1 ) ) )
& ( ( breln1 @ X1 @ X0 )
!= $true ) )
& ( dsetconstrER = $true ) ),
inference(rectify,[],[f16]) ).
thf(f21,plain,
( ( ( in @ sK3 @ ( breln1Set @ sK4 ) )
= $true )
& ( $true
!= ( breln1 @ sK4 @ sK3 ) )
& ( dsetconstrER = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f20]) ).
thf(f22,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( X3 @ X5 )
= $true )
| ( $true
!= ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) )
| ( dsetconstrER != $true ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f25,plain,
dsetconstrER = $true,
inference(cnf_transformation,[],[f21]) ).
thf(f26,plain,
( $true
!= ( breln1 @ sK4 @ sK3 ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f27,plain,
( ( in @ sK3 @ ( breln1Set @ sK4 ) )
= $true ),
inference(cnf_transformation,[],[f21]) ).
thf(f28,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f29,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f30,plain,
( breln1Set
= ( ^ [Y0: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y0 ) )
@ ^ [Y1: $i] : ( breln1 @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f33,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 ) ) ),
inference(definition_unfolding,[],[f29,f28]) ).
thf(f34,plain,
( breln1Set
= ( ^ [Y0: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y0 ) )
@ ^ [Y1: $i] :
( ^ [Y2: $i,Y3: $i] :
( ^ [Y4: $i,Y5: $i,Y6: $i] : ( subset @ Y6 @ ( cartprod @ Y4 @ Y5 ) )
@ Y2
@ Y2
@ Y3 )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f30,f33]) ).
thf(f37,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) )
| ( $true != $true )
| ( ( X3 @ X5 )
= $true ) ),
inference(definition_unfolding,[],[f22,f25]) ).
thf(f38,plain,
( ( in @ sK3
@ ( ^ [Y0: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y0 ) )
@ ^ [Y1: $i] :
( ^ [Y2: $i,Y3: $i] :
( ^ [Y4: $i,Y5: $i,Y6: $i] : ( subset @ Y6 @ ( cartprod @ Y4 @ Y5 ) )
@ Y2
@ Y2
@ Y3 )
@ Y0
@ Y1 ) )
@ sK4 ) )
= $true ),
inference(definition_unfolding,[],[f27,f34]) ).
thf(f39,plain,
( ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ sK4
@ sK3 )
!= $true ),
inference(definition_unfolding,[],[f26,f33]) ).
thf(f40,plain,
( $true
= ( in @ sK3
@ ( dsetconstr @ ( powerset @ ( cartprod @ sK4 @ sK4 ) )
@ ^ [Y0: $i] : ( subset @ Y0 @ ( cartprod @ sK4 @ sK4 ) ) ) ) ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f41,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( X3 @ X5 )
= $true )
| ( $true
!= ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f37]) ).
thf(f42,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( dsetconstr @ X4 @ X3 ) ) )
| ( ( X3 @ X5 )
= $true ) ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f43,plain,
( ( subset @ sK3 @ ( cartprod @ sK4 @ sK4 ) )
!= $true ),
inference(beta-eta_normalization,[],[f39]) ).
thf(f44,plain,
( ( $true != $true )
| ( ( ^ [Y0: $i] : ( subset @ Y0 @ ( cartprod @ sK4 @ sK4 ) )
@ sK3 )
= $true ) ),
inference(constrained_superposition,[],[f42,f40]) ).
thf(f45,plain,
( ( ^ [Y0: $i] : ( subset @ Y0 @ ( cartprod @ sK4 @ sK4 ) )
@ sK3 )
= $true ),
inference(trivial_inequality_removal,[],[f44]) ).
thf(f46,plain,
( ( subset @ sK3 @ ( cartprod @ sK4 @ sK4 ) )
= $true ),
inference(beta-eta_normalization,[],[f45]) ).
thf(f47,plain,
$false,
inference(forward_subsumption_resolution,[],[f46,f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU769^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n026.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 14:26:27 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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
% 0.24/0.30 % (672880)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.30 % (672886)lrs+10_16_si=on:nwc=1.5:random_seed=3416529531:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.30 % (672888)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=1863018670: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)
% 0.24/0.30 % (672887)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3320502203:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.30 % (672889)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=211842804:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.24/0.30 % (672885)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2312338446:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.30 % (672887)Refutation not found, incomplete strategy
% 0.24/0.30 % (672887)------------------------------
% 0.24/0.30 % (672887)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.30 % (672887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.30 % (672887)CaDiCaL version: 2.1.3
% 0.24/0.30 % (672887)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.30 % (672887)Time elapsed: 0.002 s
% 0.24/0.30 % (672887)Peak memory usage: 12 MB
% 0.24/0.30 % (672887)Instructions burned: 2 (million)
% 0.24/0.30 % (672885) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-672880-672885"...
% 0.24/0.30 % (672886) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-672880-672886"...
% 0.24/0.30 % (672887)------------------------------
% 0.24/0.30 % (672887)------------------------------
% 0.24/0.30 % (672889) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-672880-672889"...
% 0.24/0.30 % (672888) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-672880-672888"...
% 0.24/0.30 % (672885)...printing done.
% 0.24/0.30 % (672886)...printing done.
% 0.24/0.30 % (672889)...printing done.
% 0.24/0.30 % (672885)Refutation found. Thanks to Tanya!
% 0.24/0.30 % SZS status Theorem for theBenchmark
% 0.24/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.30 % (672885)------------------------------
% 0.24/0.30 % (672885)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.30 % (672885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.30 % (672885)CaDiCaL version: 2.1.3
% 0.24/0.30 % (672885)Termination reason: Refutation
% 0.24/0.30 % (672885)Time elapsed: 0.003 s
% 0.24/0.30 % (672885)Peak memory usage: 12 MB
% 0.24/0.30 % (672885)Instructions burned: 4 (million)
% 0.24/0.30 % (672880)Success in time 0.042 s
% 0.24/0.30 % Vampire exiting
%------------------------------------------------------------------------------