%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET086^1 : TPTP v9.3.1. Released v3.6.0.
% 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 08:23:14 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 40 ( 16 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 26 ( 10 ~; 0 |; 0 &; 16 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 3 con; 0-4 aty)
% Number of variables : 23 ( 8 ^; 10 !; 5 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > ( $i > $o ) > $o ).
thf(func_def_2,type,
is_a: $i > ( $i > $o ) > $o ).
thf(func_def_3,type,
emptyset: $i > $o ).
thf(func_def_4,type,
unord_pair: $i > $i > $i > $o ).
thf(func_def_5,type,
singleton: $i > $i > $o ).
thf(func_def_6,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
excl_union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
complement: ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
disjoint: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_12,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_13,type,
meets: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_14,type,
misses: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_17,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_20,type,
vAND: $o > $o > $o ).
thf(func_def_21,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vNOT: $o > $o ).
thf(func_def_23,type,
vOR: $o > $o > $o ).
thf(func_def_24,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_25,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_27,type,
vIMP: $o > $o > $o ).
thf(f5,axiom,
( ( ^ [X0: $i,X1: $i] : ( X1 = X0 ) )
= singleton ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^0.ax',singleton) ).
thf(f15,conjecture,
! [X0: $i] :
? [X1: $i] : ( singleton @ X0 @ X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f16,negated_conjecture,
~ ! [X0: $i] :
? [X1: $i] : ( singleton @ X0 @ X1 ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f17,plain,
~ ! [X0: $i] :
? [X1: $i] : ( singleton @ X0 @ X1 ),
inference(rectify,[],[f16]) ).
thf(f18,plain,
~ ! [X0: $i] :
? [X1: $i] :
( ( singleton @ X0 @ X1 )
= $true ),
inference(fool_elimination,[],[f17]) ).
thf(f29,plain,
( singleton
= ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f41,plain,
? [X0: $i] :
! [X1: $i] :
( ( singleton @ X0 @ X1 )
!= $true ),
inference(ennf_transformation,[],[f18]) ).
thf(f42,plain,
! [X1: $i] :
( $true
!= ( singleton @ sK0 @ X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f41]) ).
thf(f52,plain,
( singleton
= ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f57,plain,
! [X1: $i] :
( $true
!= ( singleton @ sK0 @ X1 ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f61,plain,
! [X1: $i] :
( $true
!= ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 )
@ sK0
@ X1 ) ),
inference(definition_unfolding,[],[f57,f52]) ).
thf(f62,plain,
! [X1: $i] :
( ( sK0 = X1 )
!= $true ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f63,plain,
! [X1: $i] : ( sK0 != X1 ),
inference(equality_proxy_clausification,[],[f62]) ).
thf(f64,plain,
sK0 != sK0,
inference(imitation,[],[f63]) ).
thf(f66,plain,
$false,
inference(trivial_inequality_removal,[],[f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET086^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n014.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:36:45 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.21/0.28 % (2660830)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (2660849)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4201036929:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (2660849) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2660830-2660849"...
% 0.21/0.28 % (2660849)...printing done.
% 0.21/0.28 % (2660849)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (2660849)------------------------------
% 0.21/0.28 % (2660849)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (2660849)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (2660849)CaDiCaL version: 2.1.3
% 0.21/0.28 % (2660849)Termination reason: Refutation
% 0.21/0.28 % (2660849)Time elapsed: 0.001 s
% 0.21/0.28 % (2660849)Peak memory usage: 12 MB
% 0.21/0.28 % (2660849)Instructions burned: 3 (million)
% 0.21/0.28 % (2660830)Success in time 0.028 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------