%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU784^2 : 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 : n019.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 08:31:21 AM UTC 2026
% Result : Theorem 0.27s 0.33s
% Output : Refutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 25 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 285 ( 76 equ; 0 cnn)
% Maximal formula atoms : 7 ( 11 avg)
% Number of connectives : 344 ( 25 ~; 16 |; 30 &; 244 @)
% ( 2 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 11 con; 0-2 aty)
% Number of variables : 73 ( 0 ^; 52 !; 21 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
binunion: $i > $i > $i ).
thf(func_def_2,type,
binunionIR: $o ).
thf(func_def_4,type,
kpair: $i > $i > $i ).
thf(func_def_5,type,
breln1: $i > $i > $o ).
thf(func_def_16,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) )
= binunionIR ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR) ).
thf(f2,conjecture,
( binunionIR
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionIR) ).
thf(f3,negated_conjecture,
~ ( binunionIR
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
~ ( binunionIR
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f5,plain,
~ ( ( binunionIR = $true )
=> ! [X1: $i,X0: $i] :
( ( ( breln1 @ X0 @ X1 )
= $true )
=> ! [X2: $i] :
( ( ( breln1 @ X0 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
=> ( in @ X1 @ ( binunion @ X0 @ X2 ) ) )
= binunionIR ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ X2 )
= $true )
=> ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
= $true ) )
<=> ( binunionIR = $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ( binunionIR = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
= $true ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
!= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
& ( ( in @ X4 @ X0 )
= $true ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( breln1 @ X0 @ X2 )
= $true ) )
& ( ( breln1 @ X0 @ X1 )
= $true ) )
& ( binunionIR = $true ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f10,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
& ( ( in @ X4 @ X0 )
= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
!= $true ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( breln1 @ X0 @ X2 )
= $true ) )
& ( ( breln1 @ X0 @ X1 )
= $true ) )
& ( binunionIR = $true ) ),
inference(flattening,[],[f9]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
& ( ( in @ X4 @ X1 )
= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X0 @ X2 ) )
!= $true ) )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( breln1 @ X1 @ X2 )
= $true ) )
& ( ( breln1 @ X1 @ X0 )
= $true ) )
& ( binunionIR = $true ) ),
inference(rectify,[],[f10]) ).
thf(f12,plain,
( ( ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 )
= $true )
& ( ( in @ sK4 @ sK1 )
= $true )
& ( ( in @ ( kpair @ sK3 @ sK4 ) @ ( binunion @ sK0 @ sK2 ) )
!= $true )
& ( ( in @ sK3 @ sK1 )
= $true )
& ( $true
= ( breln1 @ sK1 @ sK2 ) )
& ( ( breln1 @ sK1 @ sK0 )
= $true )
& ( binunionIR = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f11]) ).
thf(f13,plain,
( ( ( binunionIR = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
!= $true ) ) )
& ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
= $true ) )
| ( binunionIR != $true ) ) ),
inference(nnf_transformation,[],[f8]) ).
thf(f14,plain,
( ( ( binunionIR = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( $true
!= ( in @ X0 @ ( binunion @ X2 @ X1 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ X4 ) )
| ( $true
= ( in @ X3 @ ( binunion @ X5 @ X4 ) ) ) )
| ( binunionIR != $true ) ) ),
inference(rectify,[],[f13]) ).
thf(f15,plain,
( ( ( binunionIR = $true )
| ( ( $true
= ( in @ sK5 @ sK6 ) )
& ( ( in @ sK5 @ ( binunion @ sK7 @ sK6 ) )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ X4 ) )
| ( $true
= ( in @ X3 @ ( binunion @ X5 @ X4 ) ) ) )
| ( binunionIR != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7)],[f14]) ).
thf(f16,plain,
binunionIR = $true,
inference(cnf_transformation,[],[f12]) ).
thf(f20,plain,
( ( in @ ( kpair @ sK3 @ sK4 ) @ ( binunion @ sK0 @ sK2 ) )
!= $true ),
inference(cnf_transformation,[],[f12]) ).
thf(f22,plain,
( ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 )
= $true ),
inference(cnf_transformation,[],[f12]) ).
thf(f23,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ X4 ) )
| ( $true
= ( in @ X3 @ ( binunion @ X5 @ X4 ) ) )
| ( binunionIR != $true ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f30,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X3 @ ( binunion @ X5 @ X4 ) ) )
| ( $true
!= ( in @ X3 @ X4 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[],[f23,f16]) ).
thf(f31,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ X4 ) )
| ( $true
= ( in @ X3 @ ( binunion @ X5 @ X4 ) ) ) ),
inference(trivial_inequality_removal,[],[f30]) ).
thf(f34,plain,
! [X0: $i] :
( ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ ( binunion @ X0 @ sK2 ) ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f31,f22]) ).
thf(f35,plain,
! [X0: $i] :
( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ ( binunion @ X0 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f34]) ).
thf(f43,plain,
$true != $true,
inference(constrained_superposition,[],[f20,f35]) ).
thf(f44,plain,
$false,
inference(trivial_inequality_removal,[],[f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU784^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 % Computer : n019.cluster.edu
% 0.08/0.22 % Model : x86_64 x86_64
% 0.08/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.22 % Memory : 8046.5625MB
% 0.08/0.22 % OS : Linux 6.8.0-71-generic
% 0.08/0.22 % CPULimit : 300
% 0.08/0.22 % WCLimit : 300
% 0.08/0.22 % DateTime : Tue Sep 29 14:28:33 UTC 2026
% 0.08/0.23 % CPUTime :
% 0.08/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.27 Running higher-order theorem proving
% 0.08/0.28 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
% 0.27/0.33 % (855570)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.27/0.33 % (855578)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3024517213:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.27/0.33 % (855578)Refutation not found, incomplete strategy
% 0.27/0.33 % (855578)------------------------------
% 0.27/0.33 % (855578)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.33 % (855578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.33 % (855578)CaDiCaL version: 2.1.3
% 0.27/0.33 % (855578)Termination reason: Refutation not found, incomplete strategy
% 0.27/0.33 % (855578)Time elapsed: 0.002 s
% 0.27/0.33 % (855578)Peak memory usage: 12 MB
% 0.27/0.33 % (855578)Instructions burned: 2 (million)
% 0.27/0.33 % (855578)------------------------------
% 0.27/0.33 % (855578)------------------------------
% 0.27/0.33 % (855582)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.27/0.33 % (855582)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
% 0.27/0.33 % (855576)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3800790083:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.27/0.33 % (855576) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-855570-855576"...
% 0.27/0.33 % (855582)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=1243260473:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.27/0.33 % (855580)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3800278947:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.27/0.33 % (855581)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=168922404:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.27/0.33 % (855577)lrs+10_16_si=on:nwc=1.5:random_seed=408929411:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.27/0.33 % (855579)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=2141239599: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)
% 0.27/0.33 % (855576)...printing done.
% 0.27/0.33 % (855580) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-855570-855580"...
% 0.27/0.33 % (855577) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-855570-855577"...
% 0.27/0.33 % (855581) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-855570-855581"...
% 0.27/0.33 % (855576)Refutation found. Thanks to Tanya!
% 0.27/0.33 % SZS status Theorem for theBenchmark
% 0.27/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.27/0.34 % (855576)------------------------------
% 0.27/0.34 % (855576)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.34 % (855576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.34 % (855576)CaDiCaL version: 2.1.3
% 0.27/0.34 % (855576)Termination reason: Refutation
% 0.27/0.34 % (855576)Time elapsed: 0.006 s
% 0.27/0.34 % (855576)Peak memory usage: 12 MB
% 0.27/0.34 % (855576)Instructions burned: 5 (million)
% 0.27/0.34 % (855570)Success in time 0.041 s
% 0.27/0.34 % Vampire exiting
%------------------------------------------------------------------------------