%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n013.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 08:33:20 AM UTC 2026
% Result : Theorem 0.07s 0.24s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 185 ( 45 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 307 ( 8 ~; 2 |; 4 &; 259 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 19 usr; 6 con; 0-4 aty)
% ( 15 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 105 ( 74 ^; 29 !; 2 ?; 105 :)
% 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_10,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_11,type,
vIMP: $o > $o > $o ).
thf(func_def_12,type,
db2:
!>[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,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vNOT: $o > $o ).
thf(f1,axiom,
( dsetconstrER
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(f2,axiom,
( breln
= ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) ) ),
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,
( breln1Set
= ( ^ [X0: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ X0 @ X0 ) )
@ ^ [X1: $i] : ( breln1 @ X0 @ X1 ) ) ) ),
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 > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f10,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f11,plain,
( breln1Set
= ( ^ [X0: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ X0 @ X0 ) )
@ ^ [X1: $i] : ( breln1 @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f12,plain,
( breln1Set
= ( ^ [Y0: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y0 ) )
@ ^ [Y1: $i] : ( breln1 @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
~ ( dsetconstrER
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( breln1Set @ X0 ) )
=> ( breln1 @ X0 @ X1 ) ) ),
inference(rectify,[],[f6]) ).
thf(f14,plain,
~ ( ( dsetconstrER = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( breln1Set @ X0 ) )
= $true )
=> ( ( breln1 @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
!= $true )
& ( ( in @ X1 @ ( breln1Set @ X0 ) )
= $true ) )
& ( dsetconstrER = $true ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f16,plain,
( ( $true
!= ( breln1 @ sK0 @ sK1 ) )
& ( $true
= ( in @ sK1 @ ( breln1Set @ sK0 ) ) )
& ( dsetconstrER = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f15]) ).
thf(f17,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f18,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f19,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f20,plain,
( breln1Set
= ( ^ [Y0: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y0 ) )
@ ^ [Y1: $i] : ( breln1 @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f21,plain,
dsetconstrER = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f22,plain,
( $true
= ( in @ sK1 @ ( breln1Set @ sK0 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f23,plain,
( $true
!= ( breln1 @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f26,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 ) ) ),
inference(definition_unfolding,[],[f19,f18]) ).
thf(f27,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,[],[f20,f26]) ).
thf(f28,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f17,f21]) ).
thf(f29,plain,
( $true
!= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ sK0
@ sK1 ) ),
inference(definition_unfolding,[],[f23,f26]) ).
thf(f30,plain,
( $true
= ( in @ sK1
@ ( ^ [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 ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f22,f27]) ).
thf(f31,plain,
( $true
= ( in @ sK1
@ ( dsetconstr @ ( powerset @ ( cartprod @ sK0 @ sK0 ) )
@ ^ [Y0: $i] : ( subset @ Y0 @ ( cartprod @ sK0 @ sK0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f32,plain,
( $true
!= ( subset @ sK1 @ ( cartprod @ sK0 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f29]) ).
thf(f33,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f28]) ).
thf(f34,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f35,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f34]) ).
thf(f36,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f35]) ).
thf(f37,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( X2 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f36]) ).
thf(f38,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
=> ( X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f37]) ).
thf(f39,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) )
| ( $true
= ( X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f38]) ).
thf(f56,plain,
( ( $true = $false )
| ( $true
= ( ^ [Y0: $i] : ( subset @ Y0 @ ( cartprod @ sK0 @ sK0 ) )
@ sK1 ) ) ),
inference(constrained_superposition,[],[f39,f31]) ).
thf(f57,plain,
( $true
= ( ^ [Y0: $i] : ( subset @ Y0 @ ( cartprod @ sK0 @ sK0 ) )
@ sK1 ) ),
inference(trivial_inequality_removal,[],[f56]) ).
thf(f58,plain,
( $true
= ( subset @ sK1 @ ( cartprod @ sK0 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f61,plain,
$false,
inference(forward_subsumption_resolution,[],[f58,f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU769^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n013.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 14:23:06 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 Running first-order model finding
% 0.07/0.20 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
% 0.07/0.24 % (2191859)Will run a generic schedule for satisfiability detection.
% 0.07/0.24 % (2191865)% WARNING: option uhcvi not known.
% 0.07/0.24 % (2191865)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=211604946:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.24 % (2191865)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.24 % (2191865)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.07/0.24 % (2191865) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2191859-2191865"...
% 0.07/0.24 % (2191865)...printing done.
% 0.07/0.24 % (2191865)Refutation found. Thanks to Tanya!
% 0.07/0.24 % SZS status Theorem for theBenchmark
% 0.07/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.24 % (2191865)------------------------------
% 0.07/0.24 % (2191865)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.25 % (2191865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.25 % (2191865)CaDiCaL version: 2.1.3
% 0.07/0.25 % (2191865)Termination reason: Refutation
% 0.07/0.25 % (2191865)Time elapsed: 0.002 s
% 0.07/0.25 % (2191865)Peak memory usage: 12 MB
% 0.07/0.25 % (2191865)Instructions burned: 5 (million)
% 0.07/0.25 % (2191859)Success in time 0.034 s
% 0.07/0.25 % Vampire exiting
%------------------------------------------------------------------------------