%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP010^2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:07:42 AM UTC 2026
% Result : Theorem 0.28s 0.26s
% Output : Refutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 161 ( 42 equ; 0 cnn)
% Maximal formula atoms : 6 ( 10 avg)
% Number of connectives : 385 ( 27 ~; 10 |; 14 &; 318 @)
% ( 5 <=>; 10 =>; 0 <=; 1 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 8 con; 0-3 aty)
% Number of variables : 36 ( 0 ^; 20 !; 16 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
del: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
bool: del ).
thf(func_def_1,type,
ind: del ).
thf(func_def_2,type,
arr: del > del > del ).
thf(func_def_3,type,
mem: $i > del > $o ).
thf(func_def_4,type,
ap: $i > $i > $i ).
thf(func_def_5,type,
lam: del > ( $i > $i ) > $i ).
thf(func_def_6,type,
p: $i > $o ).
thf(func_def_7,type,
inj__o: $o > $i ).
thf(func_def_10,type,
c_2Ecardinal_2Ecardleq: del > del > $i ).
thf(func_def_16,type,
c_2Emin_2E_3D: del > $i ).
thf(func_def_17,type,
c_2Ebool_2E_21: del > $i ).
thf(func_def_20,type,
sP0: $i > $i > $i > $o ).
thf(func_def_21,type,
sP1: $i > $i > $i > $o ).
thf(func_def_22,type,
sP2: $i > $i > $i > $o ).
thf(func_def_23,type,
sP3: $i > $i > $i > $o ).
thf(func_def_24,type,
sP4: $i > $i > $i > $o ).
thf(func_def_25,type,
sP5: $i > $i > $o ).
thf(func_def_26,type,
sP6: $i > $i > $o ).
thf(func_def_27,type,
sK7: $i > del > $i > $i ).
thf(func_def_28,type,
sK8: $i > del > $i ).
thf(func_def_29,type,
sK9: $i > del > $i ).
thf(func_def_30,type,
sK10: del > del > ( $i > $i ) > $i ).
thf(func_def_32,type,
sK12: del ).
thf(func_def_33,type,
sK13: del ).
thf(func_def_35,type,
vNOT: $o > $o ).
thf(f40,conjecture,
! [X2: $i,X0: del,X1: del] :
( ( mem @ X2 @ ( arr @ X0 @ bool ) )
=> ! [X3: $i] :
( ( mem @ X3 @ ( arr @ X1 @ bool ) )
=> ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 ) @ X2 ) @ X3 ) )
<=> ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 ) @ X2 ) @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ecardinal_2ECARD__NOT__LE) ).
thf(f41,negated_conjecture,
~ ! [X2: $i,X0: del,X1: del] :
( ( mem @ X2 @ ( arr @ X0 @ bool ) )
=> ! [X3: $i] :
( ( mem @ X3 @ ( arr @ X1 @ bool ) )
=> ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 ) @ X2 ) @ X3 ) )
<=> ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 ) @ X2 ) @ X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
thf(f68,plain,
~ ! [X0: $i,X1: del,X2: del] :
( ( mem @ X0 @ ( arr @ X1 @ bool ) )
=> ! [X3: $i] :
( ( mem @ X3 @ ( arr @ X2 @ bool ) )
=> ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X0 ) @ X3 ) )
<=> ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X0 ) @ X3 ) ) ) ) ),
inference(rectify,[],[f41]) ).
thf(f69,plain,
~ ! [X0: $i,X1: del,X2: del] :
( ( $true
= ( mem @ X0 @ ( arr @ X1 @ bool ) ) )
=> ! [X3: $i] :
( ( $true
= ( mem @ X3 @ ( arr @ X2 @ bool ) ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X0 ) @ X3 ) )
!= $true )
<=> ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X0 ) @ X3 ) )
!= $true ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f126,plain,
~ ! [X2: del,X0: $i,X1: del] :
( ( $true
= ( mem @ X0 @ ( arr @ X1 @ bool ) ) )
=> ! [X3: $i] :
( ( $true
= ( mem @ X3 @ ( arr @ X2 @ bool ) ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X0 ) @ X3 ) )
!= $true )
<=> ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X0 ) @ X3 ) )
!= $true ) ) ) ),
inference(flattening,[],[f69]) ).
thf(f147,plain,
? [X0: $i,X2: del,X1: del] :
( ( $true
= ( mem @ X0 @ ( arr @ X1 @ bool ) ) )
& ? [X3: $i] :
( ( ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X0 ) @ X3 ) )
!= $true )
<~> ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X0 ) @ X3 ) )
!= $true ) )
& ( $true
= ( mem @ X3 @ ( arr @ X2 @ bool ) ) ) ) ),
inference(ennf_transformation,[],[f126]) ).
thf(f226,plain,
? [X0: $i,X2: del,X1: del] :
( ( $true
= ( mem @ X0 @ ( arr @ X1 @ bool ) ) )
& ? [X3: $i] :
( ( ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X0 ) @ X3 ) )
= $true )
| ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X0 ) @ X3 ) )
= $true ) )
& ( ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X0 ) @ X3 ) )
!= $true )
| ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X0 ) @ X3 ) )
!= $true ) )
& ( $true
= ( mem @ X3 @ ( arr @ X2 @ bool ) ) ) ) ),
inference(nnf_transformation,[],[f147]) ).
thf(f227,plain,
? [X0: $i,X2: del,X1: del] :
( ( $true
= ( mem @ X0 @ ( arr @ X1 @ bool ) ) )
& ? [X3: $i] :
( ( ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X0 ) @ X3 ) )
= $true )
| ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X0 ) @ X3 ) )
= $true ) )
& ( ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X0 ) @ X3 ) )
!= $true )
| ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X0 ) @ X3 ) )
!= $true ) )
& ( $true
= ( mem @ X3 @ ( arr @ X2 @ bool ) ) ) ) ),
inference(flattening,[],[f226]) ).
thf(f228,plain,
? [X0: $i,X1: del,X2: del] :
( ( ( mem @ X0 @ ( arr @ X2 @ bool ) )
= $true )
& ? [X3: $i] :
( ( ( $true
= ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X2 @ X1 ) @ X0 ) @ X3 ) ) )
| ( $true
= ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X2 @ X1 ) @ X0 ) @ X3 ) ) ) )
& ( ( $true
!= ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X2 @ X1 ) @ X0 ) @ X3 ) ) )
| ( $true
!= ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X2 @ X1 ) @ X0 ) @ X3 ) ) ) )
& ( ( mem @ X3 @ ( arr @ X1 @ bool ) )
= $true ) ) ),
inference(rectify,[],[f227]) ).
thf(f229,plain,
( ( $true
= ( mem @ sK11 @ ( arr @ sK13 @ bool ) ) )
& ( ( $true
= ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ sK13 @ sK12 ) @ sK11 ) @ sK14 ) ) )
| ( $true
= ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ sK13 @ sK12 ) @ sK11 ) @ sK14 ) ) ) )
& ( ( $true
!= ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ sK13 @ sK12 ) @ sK11 ) @ sK14 ) ) )
| ( $true
!= ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ sK13 @ sK12 ) @ sK11 ) @ sK14 ) ) ) )
& ( ( mem @ sK14 @ ( arr @ sK12 @ bool ) )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13),skolemize(X3,sK14)],[f228]) ).
thf(f330,plain,
( ( $true
!= ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ sK13 @ sK12 ) @ sK11 ) @ sK14 ) ) )
| ( $true
!= ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ sK13 @ sK12 ) @ sK11 ) @ sK14 ) ) ) ),
inference(cnf_transformation,[],[f229]) ).
thf(f331,plain,
( ( $true
= ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ sK13 @ sK12 ) @ sK11 ) @ sK14 ) ) )
| ( $true
= ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ sK13 @ sK12 ) @ sK11 ) @ sK14 ) ) ) ),
inference(cnf_transformation,[],[f229]) ).
thf(f345,plain,
( $true
= ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ sK13 @ sK12 ) @ sK11 ) @ sK14 ) ) ),
inference(duplicate_literal_removal,[],[f331]) ).
thf(f353,plain,
( $true
!= ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ sK13 @ sK12 ) @ sK11 ) @ sK14 ) ) ),
inference(duplicate_literal_removal,[],[f330]) ).
thf(f355,plain,
$false,
inference(forward_subsumption_resolution,[],[f353,f345]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP010^2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n008.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 19:26:24 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.22 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
% 0.28/0.26 % (3611901)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.28/0.26 % (3611906)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2007999546:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.28/0.26 % (3611906) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3611901-3611906"...
% 0.28/0.26 % (3611907)lrs+10_16_si=on:nwc=1.5:random_seed=2427980257:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.28/0.26 % (3611908)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3888194829:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.28/0.26 % (3611906)...printing done.
% 0.28/0.26 % (3611906)Refutation found. Thanks to Tanya!
% 0.28/0.26 % SZS status Theorem for theBenchmark
% 0.28/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.28/0.26 % (3611906)------------------------------
% 0.28/0.26 % (3611906)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.26 % (3611906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.26 % (3611906)CaDiCaL version: 2.1.3
% 0.28/0.26 % (3611906)Termination reason: Refutation
% 0.28/0.26 % (3611906)Time elapsed: 0.007 s
% 0.28/0.26 % (3611906)Peak memory usage: 12 MB
% 0.28/0.26 % (3611906)Instructions burned: 27 (million)
% 0.28/0.26 % (3611901)Success in time 0.035 s
% 0.28/0.26 % Vampire exiting
%------------------------------------------------------------------------------