%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU650^2 : 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 : n014.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 08:30:31 AM UTC 2026
% Result : Theorem 0.23s 0.29s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 68 ( 27 unt; 0 typ; 9 def)
% Number of atoms : 373 ( 107 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 412 ( 46 ~; 44 |; 4 &; 282 @)
% ( 3 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 21 usr; 16 con; 0-4 aty)
% ( 14 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 47 ( 0 sgn 29 !; 2 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
setadjoin: $i > $i > $i ).
thf(func_def_2,type,
setukpairinjR11: $o ).
thf(func_def_4,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
vIMP: $o > $o > $o ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_19,type,
sF7: $o ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( ( X0 = X1 )
=> ( ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X0 @ emptyset ) ) )
= setukpairinjR11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR11) ).
thf(f2,conjecture,
( setukpairinjR11
=> ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR12) ).
thf(f3,negated_conjecture,
~ ( setukpairinjR11
=> ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ emptyset ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( setukpairinjR11
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f5,plain,
~ ( setukpairinjR11
=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f6,plain,
~ ( ( setukpairinjR11 = $true )
=> ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( ( setukpairinjR11 = $true )
& ? [X0: $i,X1: $i] :
( ( X0 = X1 )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset )
!= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f8,plain,
( ( setukpairinjR11 = $true )
& ( sK1 = sK0 )
& ( ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ emptyset )
!= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f7]) ).
thf(f9,plain,
( ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ emptyset )
!= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
sK1 = sK0,
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
setukpairinjR11 = $true,
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
( setukpairinjR11
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(cnf_transformation,[],[f4]) ).
thf(f15,plain,
( ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ emptyset ) ),
inference(definition_unfolding,[],[f9,f10,f10,f10]) ).
thf(f16,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f12,f11]) ).
thf(f17,definition,
( sF2
= ( setadjoin @ sK0 @ emptyset ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f18,definition,
( sF3
= ( setadjoin @ sK0 @ sF2 ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f19,plain,
( ( setadjoin @ sK0 @ sF2 )
= sF3 ),
inference(reorient_equations,[],[f18]) ).
thf(f20,definition,
( sF4
= ( setadjoin @ sF3 @ emptyset ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f21,plain,
( ( setadjoin @ sF3 @ emptyset )
= sF4 ),
inference(reorient_equations,[],[f20]) ).
thf(f22,definition,
( sF5
= ( setadjoin @ sF2 @ sF4 ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f23,plain,
( ( setadjoin @ sF2 @ sF4 )
= sF5 ),
inference(reorient_equations,[],[f22]) ).
thf(f24,definition,
( sF6
= ( setadjoin @ sF2 @ emptyset ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f25,plain,
sF6 != sF5,
inference(definition_folding,[],[f15,f24,f17,f23,f21,f19,f17,f17]) ).
thf(f26,definition,
( sF7
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
thf(f27,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) )
= sF7 ),
inference(reorient_equations,[],[f26]) ).
thf(f28,plain,
$true = sF7,
inference(definition_folding,[],[f16,f27]) ).
thf(f29,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) )
= $true )
| ( $false = sF7 ) ),
inference(iff_proxy_clausification,[],[f27]) ).
thf(f39,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) )
@ X1 ) )
| ( $false = sF7 ) ),
inference(pi_proxy_clausification,[],[f29]) ).
thf(f40,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( Y0 = X1 )
=> ( ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) )
= $true )
| ( $false = sF7 ) ),
inference(beta-eta_normalization,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( Y0 = X1 )
=> ( ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ Y0 @ emptyset ) ) )
@ X2 ) )
| ( $false = sF7 ) ),
inference(pi_proxy_clausification,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( ( $false = sF7 )
| ( $true
= ( ( X2 = X1 )
=> ( ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f43,plain,
! [X2: $i,X1: $i] :
( ( $false = sF7 )
| ( ( X2 = X1 )
= $false )
| ( $true
= ( ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ),
inference(imp_proxy_clausification,[],[f42]) ).
thf(f44,plain,
! [X2: $i,X1: $i] :
( ( X1 != X2 )
| ( $false = sF7 )
| ( $true
= ( ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ),
inference(equality_proxy_clausification,[],[f43]) ).
thf(f45,plain,
! [X2: $i,X1: $i] :
( ( X1 != X2 )
| ( $false = sF7 )
| ( ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ),
inference(equality_proxy_clausification,[],[f44]) ).
thf(f51,definition,
( spl10_2
<=> ( $true = sF7 ) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
thf(f53,plain,
( ( $true = sF7 )
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f51]) ).
thf(f61,definition,
( spl10_4
<=> ! [X2: $i,X1: $i] :
( ( X1 != X2 )
| ( ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
thf(f62,plain,
( ! [X2: $i,X1: $i] :
( ( ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) )
| ( X1 != X2 ) )
| ~ spl10_4 ),
inference(avatar_component_clause,[],[f61]) ).
thf(f64,definition,
( spl10_5
<=> ( $false = sF7 ) ),
introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition]) ).
thf(f66,plain,
( ( $false = sF7 )
| ~ spl10_5 ),
inference(avatar_component_clause,[],[f64]) ).
thf(f67,plain,
( spl10_4
| spl10_5 ),
inference(avatar_split_clause,[],[f45,f64,f61]) ).
thf(f68,plain,
spl10_2,
inference(avatar_split_clause,[],[f28,f51]) ).
thf(f76,plain,
( ! [X0: $i] :
( ( ( setadjoin @ X0 @ emptyset )
= ( setadjoin @ X0 @ sF2 ) )
| ( sK0 != X0 ) )
| ~ spl10_4 ),
inference(constrained_superposition,[],[f62,f17]) ).
thf(f77,plain,
( ! [X0: $i] :
( ( sF2 != X0 )
| ( ( setadjoin @ X0 @ emptyset )
= ( setadjoin @ X0 @ sF6 ) ) )
| ~ spl10_4 ),
inference(constrained_superposition,[],[f62,f24]) ).
thf(f79,plain,
( ( sK0 != sK0 )
| ( sF2
= ( setadjoin @ sK0 @ sF2 ) )
| ~ spl10_4 ),
inference(constrained_superposition,[],[f76,f17]) ).
thf(f86,plain,
( ( sF2
= ( setadjoin @ sK0 @ sF2 ) )
| ~ spl10_4 ),
inference(trivial_inequality_removal,[],[f79]) ).
thf(f107,plain,
( ( sF2 = sF3 )
| ~ spl10_4 ),
inference(forward_demodulation,[],[f86,f19]) ).
thf(f111,plain,
( ( sF6
= ( setadjoin @ sF3 @ emptyset ) )
| ~ spl10_4 ),
inference(constrained_superposition,[],[f24,f107]) ).
thf(f112,plain,
( ( ( setadjoin @ sF3 @ sF4 )
= sF5 )
| ~ spl10_4 ),
inference(constrained_superposition,[],[f23,f107]) ).
thf(f114,plain,
( ( sF6 = sF4 )
| ~ spl10_4 ),
inference(forward_demodulation,[],[f111,f21]) ).
thf(f117,plain,
( ( sF5
= ( setadjoin @ sF3 @ sF6 ) )
| ~ spl10_4 ),
inference(forward_demodulation,[],[f112,f114]) ).
thf(f118,plain,
( ! [X0: $i] :
( ( ( setadjoin @ X0 @ emptyset )
= ( setadjoin @ X0 @ sF6 ) )
| ( sF3 != X0 ) )
| ~ spl10_4 ),
inference(forward_demodulation,[],[f77,f107]) ).
thf(f122,plain,
( ( sF2 != sF3 )
| ( ( setadjoin @ sF2 @ sF6 )
= sF6 )
| ~ spl10_4 ),
inference(constrained_superposition,[],[f118,f24]) ).
thf(f135,plain,
( ( ( setadjoin @ sF2 @ sF6 )
= sF6 )
| ~ spl10_4 ),
inference(forward_subsumption_resolution,[],[f122,f107]) ).
thf(f140,plain,
( ( sF6
= ( setadjoin @ sF3 @ sF6 ) )
| ~ spl10_4 ),
inference(forward_demodulation,[],[f135,f107]) ).
thf(f146,plain,
( ( sF6 = sF5 )
| ~ spl10_4 ),
inference(forward_demodulation,[],[f140,f117]) ).
thf(f149,plain,
( $false
| ~ spl10_4 ),
inference(forward_subsumption_resolution,[],[f146,f25]) ).
thf(f150,plain,
~ spl10_4,
inference(avatar_contradiction_clause,[],[f149]) ).
thf(f151,plain,
( ( $true = $false )
| ~ spl10_2
| ~ spl10_5 ),
inference(forward_demodulation,[],[f66,f53]) ).
thf(f152,plain,
( $false
| ~ spl10_2
| ~ spl10_5 ),
inference(trivial_inequality_removal,[],[f151]) ).
thf(f153,plain,
( ~ spl10_2
| ~ spl10_5 ),
inference(avatar_contradiction_clause,[],[f152]) ).
cnf(s3,plain,
( spl10_4
| spl10_5 ),
inference(sat_conversion,[],[f67]) ).
cnf(s4,plain,
spl10_2,
inference(sat_conversion,[],[f68]) ).
cnf(s12,plain,
~ spl10_4,
inference(sat_conversion,[],[f150]) ).
cnf(s13,plain,
( ~ spl10_2
| ~ spl10_5 ),
inference(sat_conversion,[],[f153]) ).
cnf(s14,plain,
~ spl10_5,
inference(rat,[],[s13,s4]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s3,s14,s12]) ).
thf(f154,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU650^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n014.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:02:30 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.23/0.29 % (2711174)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.29 % (2711185)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.29 % (2711185)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
% 0.23/0.29 % (2711185)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=984407475:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.29 % (2711185) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2711174-2711185"...
% 0.23/0.29 % (2711179)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3769356429:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.29 % (2711181)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3840478597:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.29 % (2711185)...printing done.
% 0.23/0.29 % (2711183)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2133553582:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.29 % (2711180)lrs+10_16_si=on:nwc=1.5:random_seed=186422086:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.29 % (2711185)Refutation found. Thanks to Tanya!
% 0.23/0.29 % SZS status Theorem for theBenchmark
% 0.23/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.29 % (2711185)------------------------------
% 0.23/0.29 % (2711185)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (2711185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (2711185)CaDiCaL version: 2.1.3
% 0.23/0.29 % (2711185)Termination reason: Refutation
% 0.23/0.29 % (2711185)Time elapsed: 0.004 s
% 0.23/0.29 % (2711185)Peak memory usage: 13 MB
% 0.23/0.29 % (2711185)Instructions burned: 8 (million)
% 0.23/0.29 % (2711174)Success in time 0.036 s
% 0.23/0.29 % Vampire exiting
%------------------------------------------------------------------------------