%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU641^2 : 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 : n001.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 08:30:28 AM UTC 2026
% Result : Theorem 0.23s 0.29s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 267 ( 91 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 235 ( 32 ~; 24 |; 21 &; 140 @)
% ( 3 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 60 ( 0 ^; 46 !; 14 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
setadjoinIL: $o ).
thf(func_def_5,type,
uniqinunit: $o ).
thf(func_def_14,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= setadjoinIL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(f2,axiom,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(f3,conjecture,
( setadjoinIL
=> ( uniqinunit
=> ! [X0: $i,X1: $i] :
( ( ( setadjoin @ X0 @ emptyset )
= ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsuniq) ).
thf(f4,negated_conjecture,
~ ( setadjoinIL
=> ( uniqinunit
=> ! [X0: $i,X1: $i] :
( ( ( setadjoin @ X0 @ emptyset )
= ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X1 @ X0 ) )
= setadjoinIL ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
( ( setadjoinIL = $true )
<=> ! [X1: $i,X0: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
~ ( setadjoinIL
=> ( uniqinunit
=> ! [X0: $i,X1: $i] :
( ( ( setadjoin @ X0 @ emptyset )
= ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f8,plain,
~ ( ( setadjoinIL = $true )
=> ( ( uniqinunit = $true )
=> ! [X0: $i,X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
= ( setadjoin @ X0 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true )
=> ( X0 = X1 ) )
<=> ( uniqinunit = $true ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ? [X1: $i,X0: $i] :
( ( ( setadjoin @ X1 @ emptyset )
= ( setadjoin @ X0 @ emptyset ) )
& ( X0 != X1 ) )
& ( uniqinunit = $true )
& ( setadjoinIL = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f12,plain,
( ( setadjoinIL = $true )
& ( uniqinunit = $true )
& ? [X1: $i,X0: $i] :
( ( ( setadjoin @ X1 @ emptyset )
= ( setadjoin @ X0 @ emptyset ) )
& ( X0 != X1 ) ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ( uniqinunit = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f14,plain,
( ( ( setadjoinIL = $true )
| ? [X1: $i,X0: $i] :
( $true
!= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) )
& ( ! [X1: $i,X0: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ( setadjoinIL != $true ) ) ),
inference(nnf_transformation,[],[f6]) ).
thf(f15,plain,
( ( ( setadjoinIL = $true )
| ? [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X2 @ X3 ) )
= $true )
| ( setadjoinIL != $true ) ) ),
inference(rectify,[],[f14]) ).
thf(f16,plain,
( ( ( setadjoinIL = $true )
| ( ( in @ sK0 @ ( setadjoin @ sK0 @ sK1 ) )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X2 @ X3 ) )
= $true )
| ( setadjoinIL != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f15]) ).
thf(f17,plain,
( ( setadjoinIL = $true )
& ( uniqinunit = $true )
& ? [X0: $i,X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
= ( setadjoin @ X0 @ emptyset ) )
& ( X0 != X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f18,plain,
( ( setadjoinIL = $true )
& ( uniqinunit = $true )
& ( ( setadjoin @ sK3 @ emptyset )
= ( setadjoin @ sK2 @ emptyset ) )
& ( sK3 != sK2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f17]) ).
thf(f19,plain,
( ( ( uniqinunit = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true )
& ( X0 != X1 ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
| ( uniqinunit != $true ) ) ),
inference(nnf_transformation,[],[f13]) ).
thf(f20,plain,
( ( ( uniqinunit = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true )
& ( X0 != X1 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
| ( X2 = X3 ) )
| ( uniqinunit != $true ) ) ),
inference(rectify,[],[f19]) ).
thf(f21,plain,
( ( ( uniqinunit = $true )
| ( ( ( in @ sK4 @ ( setadjoin @ sK5 @ emptyset ) )
= $true )
& ( sK5 != sK4 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
| ( X2 = X3 ) )
| ( uniqinunit != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f20]) ).
thf(f22,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( setadjoin @ X2 @ X3 ) )
= $true )
| ( setadjoinIL != $true ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f24,plain,
sK3 != sK2,
inference(cnf_transformation,[],[f18]) ).
thf(f25,plain,
( ( setadjoin @ sK3 @ emptyset )
= ( setadjoin @ sK2 @ emptyset ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f26,plain,
uniqinunit = $true,
inference(cnf_transformation,[],[f18]) ).
thf(f27,plain,
setadjoinIL = $true,
inference(cnf_transformation,[],[f18]) ).
thf(f28,plain,
! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
| ( X2 = X3 )
| ( uniqinunit != $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f34,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( setadjoin @ X2 @ X3 ) )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[],[f22,f27]) ).
thf(f37,plain,
! [X2: $i,X3: $i] :
( ( X2 = X3 )
| ( $true != $true )
| ( $true
!= ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
inference(definition_unfolding,[],[f28,f26]) ).
thf(f38,plain,
! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X2 @ X3 ) )
= $true ),
inference(trivial_inequality_removal,[],[f34]) ).
thf(f39,plain,
! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
| ( X2 = X3 ) ),
inference(trivial_inequality_removal,[],[f37]) ).
thf(f40,plain,
( ( in @ sK2 @ ( setadjoin @ sK3 @ emptyset ) )
= $true ),
inference(constrained_superposition,[],[f38,f25]) ).
thf(f42,plain,
( ( $true != $true )
| ( sK3 = sK2 ) ),
inference(constrained_superposition,[],[f39,f40]) ).
thf(f43,plain,
sK3 = sK2,
inference(trivial_inequality_removal,[],[f42]) ).
thf(f44,plain,
$false,
inference(forward_subsumption_resolution,[],[f43,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU641^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.19 % Computer : n001.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Tue Sep 29 14:07:21 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.23 Running higher-order theorem proving
% 0.12/0.24 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 % (1293830)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.29 % (1293837)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1417418322:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.29 % (1293837)Refutation not found, incomplete strategy
% 0.23/0.29 % (1293837)------------------------------
% 0.23/0.29 % (1293837)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (1293837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (1293837)CaDiCaL version: 2.1.3
% 0.23/0.29 % (1293837)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.29 % (1293837)Time elapsed: 0.001 s
% 0.23/0.29 % (1293837)Peak memory usage: 12 MB
% 0.23/0.29 % (1293837)Instructions burned: 1 (million)
% 0.23/0.29 % (1293837)------------------------------
% 0.23/0.29 % (1293837)------------------------------
% 0.23/0.29 % (1293841)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 % (1293841)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 % (1293835)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3486426969:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.29 % (1293836)lrs+10_16_si=on:nwc=1.5:random_seed=2637669183:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.29 % (1293839)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1969618484:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.29 % (1293841)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=910614657:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.29 % (1293835) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1293830-1293835"...
% 0.23/0.29 % (1293836) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1293830-1293836"...
% 0.23/0.29 % (1293839) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1293830-1293839"...
% 0.23/0.29 % (1293838)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=3047927961: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)
% 0.23/0.29 % (1293835)...printing done.
% 0.23/0.29 % (1293836)...printing done.
% 0.23/0.29 % (1293839)...printing done.
% 0.23/0.29 % (1293835)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 % (1293835)------------------------------
% 0.23/0.29 % (1293835)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (1293835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (1293835)CaDiCaL version: 2.1.3
% 0.23/0.29 % (1293835)Termination reason: Refutation
% 0.23/0.29 % (1293835)Time elapsed: 0.003 s
% 0.23/0.29 % (1293835)Peak memory usage: 12 MB
% 0.23/0.29 % (1293835)Instructions burned: 3 (million)
% 0.23/0.29 % (1293830)Success in time 0.036 s
% 0.23/0.29 % Vampire exiting
%------------------------------------------------------------------------------