%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU798^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 08:31:28 AM UTC 2026
% Result : Theorem 0.04s 0.22s
% Output : Refutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of formulae : 36 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 233 ( 51 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 361 ( 10 ~; 7 |; 9 &; 285 @)
% ( 0 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 17 usr; 7 con; 0-4 aty)
% ( 15 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 81 ( 39 ^; 36 !; 6 ?; 81 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_2,type,
dsetconstrI: $o ).
thf(func_def_4,type,
funcSet: $i > $i > $i ).
thf(func_def_5,type,
injective: $i > $i > $i > $o ).
thf(func_def_6,type,
injFuncSet: $i > $i > $i ).
thf(func_def_7,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_8,type,
vIMP: $o > $o > $o ).
thf(func_def_9,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_18,type,
vNOT: $o > $o ).
thf(f1,axiom,
( dsetconstrI
= ( ! [X1: $i > $o,X0: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(f2,axiom,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( funcSet @ X0 @ X1 )
@ ^ [X2: $i] : ( injective @ X0 @ X1 @ X2 ) ) )
= injFuncSet ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injFuncSet) ).
thf(f3,conjecture,
( dsetconstrI
=> ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ( ( injective @ X0 @ X1 @ X2 )
=> ( in @ X2 @ ( injFuncSet @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injFuncInInjFuncSet) ).
thf(f4,negated_conjecture,
~ ( dsetconstrI
=> ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ( ( injective @ X0 @ X1 @ X2 )
=> ( in @ X2 @ ( injFuncSet @ X0 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( dsetconstrI
= ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( ( X0 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X0 @ X3 ) ) ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
~ ( dsetconstrI
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( funcSet @ X2 @ X1 ) )
=> ( ( injective @ X2 @ X1 @ X0 )
=> ( in @ X0 @ ( injFuncSet @ X2 @ X1 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f8,plain,
~ ( ( dsetconstrI = $true )
=> ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X0 @ ( funcSet @ X2 @ X1 ) )
= $true )
=> ( ( ( injective @ X2 @ X1 @ X0 )
= $true )
=> ( ( in @ X0 @ ( injFuncSet @ X2 @ X1 ) )
= $true ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( funcSet @ X0 @ X1 )
@ ^ [X2: $i] : ( injective @ X0 @ X1 @ X2 ) ) )
= injFuncSet ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
( injFuncSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] : ( injective @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ? [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X0 @ ( injFuncSet @ X2 @ X1 ) )
!= $true )
& ( ( injective @ X2 @ X1 @ X0 )
= $true )
& ( ( in @ X0 @ ( funcSet @ X2 @ X1 ) )
= $true ) )
& ( dsetconstrI = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( funcSet @ X2 @ X1 ) )
= $true )
& ( ( in @ X0 @ ( injFuncSet @ X2 @ X1 ) )
!= $true )
& ( ( injective @ X2 @ X1 @ X0 )
= $true ) )
& ( dsetconstrI = $true ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ( ( in @ sK0 @ ( funcSet @ sK2 @ sK1 ) )
= $true )
& ( ( in @ sK0 @ ( injFuncSet @ sK2 @ sK1 ) )
!= $true )
& ( $true
= ( injective @ sK2 @ sK1 @ sK0 ) )
& ( dsetconstrI = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f12]) ).
thf(f14,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f15,plain,
( injFuncSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] : ( injective @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f16,plain,
dsetconstrI = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f17,plain,
( $true
= ( injective @ sK2 @ sK1 @ sK0 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f18,plain,
( ( in @ sK0 @ ( injFuncSet @ sK2 @ sK1 ) )
!= $true ),
inference(cnf_transformation,[],[f13]) ).
thf(f19,plain,
( ( in @ sK0 @ ( funcSet @ sK2 @ sK1 ) )
= $true ),
inference(cnf_transformation,[],[f13]) ).
thf(f22,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f14,f16]) ).
thf(f23,plain,
( ( in @ sK0
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] : ( injective @ Y0 @ Y1 @ Y2 ) )
@ sK2
@ sK1 ) )
!= $true ),
inference(definition_unfolding,[],[f18,f15]) ).
thf(f24,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f22]) ).
thf(f25,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ X1 @ Y0 )
=> ( ( Y1 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f26,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ X1 @ Y0 )
=> ( ( Y1 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f25]) ).
thf(f27,plain,
! [X2: $i,X1: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X1 @ X2 )
=> ( ( Y0 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ X2 @ Y0 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f28,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( ( in @ X1 @ X2 )
=> ( ( Y0 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ X2 @ Y0 ) ) ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f27]) ).
thf(f29,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X1 @ X2 )
=> ( ( X3 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ X2 @ X3 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( $false
= ( in @ X1 @ X2 ) )
| ( ( ( X3 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ X2 @ X3 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f29]) ).
thf(f31,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( $true
= ( in @ X1 @ ( dsetconstr @ X2 @ X3 ) ) )
| ( ( X3 @ X1 )
= $false )
| ( $false
= ( in @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f30]) ).
thf(f32,plain,
( $true
!= ( in @ sK0 @ ( dsetconstr @ ( funcSet @ sK2 @ sK1 ) @ ( injective @ sK2 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f37,plain,
( ( $true != $true )
| ( ( in @ sK0 @ ( funcSet @ sK2 @ sK1 ) )
= $false )
| ( $false
= ( injective @ sK2 @ sK1 @ sK0 ) ) ),
inference(constrained_superposition,[],[f32,f31]) ).
thf(f38,plain,
( ( ( in @ sK0 @ ( funcSet @ sK2 @ sK1 ) )
= $false )
| ( $false
= ( injective @ sK2 @ sK1 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f37]) ).
thf(f39,plain,
( ( $false
= ( injective @ sK2 @ sK1 @ sK0 ) )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f38,f19]) ).
thf(f40,plain,
( $false
= ( injective @ sK2 @ sK1 @ sK0 ) ),
inference(trivial_inequality_removal,[],[f39]) ).
thf(f42,plain,
$true = $false,
inference(constrained_superposition,[],[f17,f40]) ).
thf(f43,plain,
$false,
inference(trivial_inequality_removal,[],[f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU798^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.15 % Computer : n012.cluster.edu
% 0.04/0.15 % Model : x86_64 x86_64
% 0.04/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.15 % Memory : 8046.5625MB
% 0.04/0.15 % OS : Linux 6.8.0-71-generic
% 0.04/0.15 % CPULimit : 300
% 0.04/0.15 % WCLimit : 300
% 0.04/0.15 % DateTime : Tue Sep 29 14:31:34 UTC 2026
% 0.04/0.15 % CPUTime :
% 0.04/0.15 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.18 Running higher-order theorem proving
% 0.04/0.18 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.21 % (183018)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.04/0.21 % (183029)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.04/0.21 % (183029)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.04/0.21 % (183026)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=2021659707: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)
% 0.04/0.21 % (183023)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3902185997:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.04/0.21 % (183025)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2220392939:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.04/0.22 % (183024)lrs+10_16_si=on:nwc=1.5:random_seed=1862045775:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.04/0.22 % (183029)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=604132367:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.04/0.22 % (183028)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2706577632:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.04/0.22 % (183027)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1660834628:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.04/0.22 % (183025)Refutation not found, incomplete strategy
% 0.04/0.22 % (183025)------------------------------
% 0.04/0.22 % (183025)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.04/0.22 % (183025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.04/0.22 % (183025)CaDiCaL version: 2.1.3
% 0.04/0.22 % (183025)Termination reason: Refutation not found, incomplete strategy
% 0.04/0.22 % (183025)Time elapsed: 0.002 s
% 0.04/0.22 % (183025)Peak memory usage: 12 MB
% 0.04/0.22 % (183025)Instructions burned: 2 (million)
% 0.04/0.22 % (183023) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-183018-183023"...
% 0.04/0.22 % (183024) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-183018-183024"...
% 0.04/0.22 % (183027) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-183018-183027"...
% 0.04/0.22 % (183025)------------------------------
% 0.04/0.22 % (183025)------------------------------
% 0.04/0.22 % (183026) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-183018-183026"...
% 0.04/0.22 % (183029) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-183018-183029"...
% 0.04/0.22 % (183023)...printing done.
% 0.04/0.22 % (183024)...printing done.
% 0.04/0.22 % (183027)...printing done.
% 0.04/0.22 % (183024)Refutation found. Thanks to Tanya!
% 0.04/0.22 % SZS status Theorem for theBenchmark
% 0.04/0.22 % SZS output start Proof for theBenchmark
% See solution above
% 0.04/0.22 % (183024)------------------------------
% 0.04/0.22 % (183024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.04/0.22 % (183024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.04/0.22 % (183024)CaDiCaL version: 2.1.3
% 0.04/0.22 % (183024)Termination reason: Refutation
% 0.04/0.22 % (183024)Time elapsed: 0.003 s
% 0.04/0.22 % (183024)Peak memory usage: 12 MB
% 0.04/0.22 % (183024)Instructions burned: 5 (million)
% 0.04/0.22 % (183018)Success in time 0.025 s
% 0.04/0.22 % Vampire exiting
%------------------------------------------------------------------------------