%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET017^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:23:10 AM UTC 2026
% Result : Theorem 0.23s 0.30s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 2
% Syntax : Number of formulae : 34 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 246 ( 116 equ; 0 cnn)
% Maximal formula atoms : 3 ( 7 avg)
% Number of connectives : 99 ( 14 ~; 46 |; 3 &; 34 @)
% ( 0 <=>; 2 =>; 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 : 32 ( 29 usr; 5 con; 0-4 aty)
% Number of variables : 50 ( 23 ^; 21 !; 6 ?; 50 :)
% 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_15,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_18,type,
vNOT: $o > $o ).
thf(func_def_19,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_20,type,
vOR: $o > $o > $o ).
thf(func_def_21,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
vAND: $o > $o > $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(f4,axiom,
( ( ^ [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 = X1 ) ) )
= unord_pair ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',unord_pair) ).
thf(f15,conjecture,
! [X2: $i,X0: $i,X1: $i] :
( ( ( unord_pair @ X0 @ X1 )
= ( unord_pair @ X0 @ X2 ) )
=> ( X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f16,negated_conjecture,
~ ! [X2: $i,X0: $i,X1: $i] :
( ( ( unord_pair @ X0 @ X1 )
= ( unord_pair @ X0 @ X2 ) )
=> ( X1 = X2 ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f36,plain,
( unord_pair
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y2 ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f39,plain,
? [X2: $i,X1: $i,X0: $i] :
( ( X1 != X2 )
& ( ( unord_pair @ X0 @ X1 )
= ( unord_pair @ X0 @ X2 ) ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f40,plain,
? [X0: $i,X1: $i,X2: $i] :
( ( X0 != X1 )
& ( ( unord_pair @ X2 @ X1 )
= ( unord_pair @ X2 @ X0 ) ) ),
inference(rectify,[],[f39]) ).
thf(f41,plain,
( ( sK1 != sK0 )
& ( ( unord_pair @ sK2 @ sK0 )
= ( unord_pair @ sK2 @ sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f40]) ).
thf(f48,plain,
( ( unord_pair @ sK2 @ sK0 )
= ( unord_pair @ sK2 @ sK1 ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f49,plain,
sK1 != sK0,
inference(cnf_transformation,[],[f41]) ).
thf(f50,plain,
( unord_pair
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y2 ) ) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f61,plain,
( ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y2 ) )
@ sK2
@ sK1 )
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y2 ) )
@ sK2
@ sK0 ) ),
inference(definition_unfolding,[],[f48,f50,f50]) ).
thf(f62,plain,
( ( ^ [Y0: $i] :
( ( sK0 = Y0 )
| ( sK2 = Y0 ) ) )
= ( ^ [Y0: $i] :
( ( sK1 = Y0 )
| ( sK2 = Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f63,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( sK1 = Y0 )
| ( sK2 = Y0 ) )
@ X1 )
= ( ^ [Y0: $i] :
( ( sK0 = Y0 )
| ( sK2 = Y0 ) )
@ X1 ) ),
inference(argument_congruence,[],[f62]) ).
thf(f64,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 = Y0 )
| ( sK2 = Y0 ) )
@ X1 ) )
| ( ( ^ [Y0: $i] :
( ( sK1 = Y0 )
| ( sK2 = Y0 ) )
@ X1 )
= $true ) ),
inference(iff_proxy_clausification,[],[f63]) ).
thf(f65,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK1 = Y0 )
| ( sK2 = Y0 ) )
@ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK0 = Y0 )
| ( sK2 = Y0 ) )
@ X1 )
= $true ) ),
inference(iff_proxy_clausification,[],[f63]) ).
thf(f66,plain,
! [X1: $i] :
( ( $false
= ( ( sK1 = X1 )
| ( sK2 = X1 ) ) )
| ( ( ( sK0 = X1 )
| ( sK2 = X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f65]) ).
thf(f68,plain,
! [X1: $i] :
( ( $false
= ( sK1 = X1 ) )
| ( ( ( sK0 = X1 )
| ( sK2 = X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f66]) ).
thf(f69,plain,
! [X1: $i] :
( ( ( ( sK0 = X1 )
| ( sK2 = X1 ) )
= $true )
| ( sK1 != X1 ) ),
inference(equality_proxy_clausification,[],[f68]) ).
thf(f70,plain,
! [X1: $i] :
( ( sK1 != X1 )
| ( ( sK0 = X1 )
= $true )
| ( ( sK2 = X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f69]) ).
thf(f71,plain,
! [X1: $i] :
( ( sK0 = X1 )
| ( ( sK2 = X1 )
= $true )
| ( sK1 != X1 ) ),
inference(equality_proxy_clausification,[],[f70]) ).
thf(f72,plain,
! [X1: $i] :
( ( sK1 != X1 )
| ( sK0 = X1 )
| ( sK2 = X1 ) ),
inference(equality_proxy_clausification,[],[f71]) ).
thf(f77,plain,
! [X1: $i] :
( ( ( ( sK1 = X1 )
| ( sK2 = X1 ) )
= $true )
| ( ( ( sK0 = X1 )
| ( sK2 = X1 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f78,plain,
! [X1: $i] :
( ( ( ( sK0 = X1 )
| ( sK2 = X1 ) )
= $false )
| ( ( sK1 = X1 )
= $true )
| ( ( sK2 = X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f77]) ).
thf(f80,plain,
! [X1: $i] :
( ( $false
= ( sK0 = X1 ) )
| ( ( sK1 = X1 )
= $true )
| ( ( sK2 = X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f78]) ).
thf(f81,plain,
! [X1: $i] :
( ( sK0 != X1 )
| ( ( sK2 = X1 )
= $true )
| ( ( sK1 = X1 )
= $true ) ),
inference(equality_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X1: $i] :
( ( sK2 = X1 )
| ( sK0 != X1 )
| ( ( sK1 = X1 )
= $true ) ),
inference(equality_proxy_clausification,[],[f81]) ).
thf(f83,plain,
! [X1: $i] :
( ( sK0 != X1 )
| ( sK2 = X1 )
| ( sK1 = X1 ) ),
inference(equality_proxy_clausification,[],[f82]) ).
thf(f88,plain,
( ( sK1 = sK0 )
| ( sK1 = sK2 ) ),
inference(equality_resolution,[],[f72]) ).
thf(f90,plain,
sK1 = sK2,
inference(forward_subsumption_resolution,[],[f88,f49]) ).
thf(f93,plain,
( ( sK2 = sK0 )
| ( sK1 = sK0 )
| ( sK0 != sK0 ) ),
inference(imitation,[],[f83]) ).
thf(f95,plain,
( ( sK2 = sK0 )
| ( sK1 = sK0 ) ),
inference(trivial_inequality_removal,[],[f93]) ).
thf(f96,plain,
sK2 = sK0,
inference(forward_subsumption_resolution,[],[f95,f49]) ).
thf(f99,plain,
sK1 != sK2,
inference(constrained_superposition,[],[f49,f96]) ).
thf(f100,plain,
$false,
inference(forward_subsumption_resolution,[],[f99,f90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET017^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n002.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
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 13:38:07 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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
% 0.23/0.30 % (1284324)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.30 % (1284333)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=1183673545: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)
% 0.23/0.30 % (1284330)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2440078754:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.30 % (1284334)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=939455667:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.30 % (1284332)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=852265936:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.30 % (1284330) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1284324-1284330"...
% 0.23/0.30 % (1284332)Refutation not found, incomplete strategy
% 0.23/0.30 % (1284332)------------------------------
% 0.23/0.30 % (1284332)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (1284332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (1284332)CaDiCaL version: 2.1.3
% 0.23/0.30 % (1284332)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.30 % (1284332)Time elapsed: 0.003 s
% 0.23/0.30 % (1284332)Peak memory usage: 12 MB
% 0.23/0.30 % (1284332)Instructions burned: 3 (million)
% 0.23/0.30 % (1284332)------------------------------
% 0.23/0.30 % (1284332)------------------------------
% 0.23/0.30 % (1284330)...printing done.
% 0.23/0.30 % (1284330)Refutation found. Thanks to Tanya!
% 0.23/0.30 % SZS status Theorem for theBenchmark
% 0.23/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.31 % (1284330)------------------------------
% 0.23/0.31 % (1284330)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (1284330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (1284330)CaDiCaL version: 2.1.3
% 0.23/0.31 % (1284330)Termination reason: Refutation
% 0.23/0.31 % (1284330)Time elapsed: 0.004 s
% 0.23/0.31 % (1284330)Peak memory usage: 12 MB
% 0.23/0.31 % (1284330)Instructions burned: 5 (million)
% 0.23/0.31 % (1284324)Success in time 0.047 s
% 0.23/0.31 % Vampire exiting
%------------------------------------------------------------------------------