%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n011.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 08:23:32 AM UTC 2026
% Result : Theorem 0.32s 0.42s
% Output : Refutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 2
% Syntax : Number of formulae : 32 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 233 ( 111 equ; 0 cnn)
% Maximal formula atoms : 3 ( 7 avg)
% Number of connectives : 90 ( 11 ~; 45 |; 2 &; 30 @)
% ( 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 : 47 ( 23 ^; 21 !; 3 ?; 47 :)
% 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_20,type,
vOR: $o > $o > $o ).
thf(func_def_21,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_23,type,
vAND: $o > $o > $o ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(func_def_25,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vIMP: $o > $o > $o ).
thf(func_def_27,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(f4,axiom,
( unord_pair
= ( ^ [X0: $i,X1: $i,X2: $i] :
( ( X2 = X1 )
| ( X2 = X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',unord_pair) ).
thf(f15,conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( ( unord_pair @ X0 @ X1 )
= ( unord_pair @ X0 @ X2 ) )
=> ( X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f16,negated_conjecture,
~ ! [X0: $i,X1: $i,X2: $i] :
( ( ( unord_pair @ X0 @ X1 )
= ( unord_pair @ X0 @ X2 ) )
=> ( X1 = X2 ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f20,plain,
( unord_pair
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( Y0 = Y2 )
| ( Y1 = Y2 ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f39,plain,
? [X0: $i,X1: $i,X2: $i] :
( ( X1 != X2 )
& ( ( unord_pair @ X0 @ X1 )
= ( unord_pair @ X0 @ X2 ) ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f40,plain,
( ( sK1 != sK2 )
& ( ( unord_pair @ sK0 @ sK1 )
= ( unord_pair @ sK0 @ sK2 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f39]) ).
thf(f44,plain,
( unord_pair
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( Y0 = Y2 )
| ( Y1 = Y2 ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f55,plain,
( ( unord_pair @ sK0 @ sK1 )
= ( unord_pair @ sK0 @ sK2 ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f56,plain,
sK1 != sK2,
inference(cnf_transformation,[],[f40]) ).
thf(f60,plain,
( ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( Y0 = Y2 )
| ( Y1 = Y2 ) )
@ sK0
@ sK1 )
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( Y0 = Y2 )
| ( Y1 = Y2 ) )
@ sK0
@ sK2 ) ),
inference(definition_unfolding,[],[f55,f44,f44]) ).
thf(f61,plain,
( ( ^ [Y0: $i] :
( ( sK0 = Y0 )
| ( sK1 = Y0 ) ) )
= ( ^ [Y0: $i] :
( ( sK0 = Y0 )
| ( sK2 = Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f60]) ).
thf(f69,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( sK0 = Y0 )
| ( sK1 = Y0 ) )
@ X1 )
= ( ^ [Y0: $i] :
( ( sK0 = Y0 )
| ( sK2 = Y0 ) )
@ X1 ) ),
inference(argument_congruence,[],[f61]) ).
thf(f70,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 = Y0 )
| ( sK1 = Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 = Y0 )
| ( sK2 = Y0 ) )
@ X1 ) ) ),
inference(iff_proxy_clausification,[],[f69]) ).
thf(f71,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 = Y0 )
| ( sK1 = Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 = Y0 )
| ( sK2 = Y0 ) )
@ X1 ) ) ),
inference(iff_proxy_clausification,[],[f69]) ).
thf(f72,plain,
! [X1: $i] :
( ( $false
= ( ( sK0 = X1 )
| ( sK1 = X1 ) ) )
| ( $true
= ( ( sK0 = X1 )
| ( sK2 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f71]) ).
thf(f73,plain,
! [X1: $i] :
( ( $false
= ( sK1 = X1 ) )
| ( $true
= ( ( sK0 = X1 )
| ( sK2 = X1 ) ) ) ),
inference(or_proxy_clausification,[],[f72]) ).
thf(f79,plain,
! [X1: $i] :
( ( sK1 != X1 )
| ( $true
= ( ( sK0 = X1 )
| ( sK2 = X1 ) ) ) ),
inference(equality_proxy_clausification,[],[f73]) ).
thf(f80,plain,
! [X1: $i] :
( ( sK1 != X1 )
| ( $true
= ( sK2 = X1 ) )
| ( $true
= ( sK0 = X1 ) ) ),
inference(or_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X1: $i] :
( ( sK1 != X1 )
| ( sK2 = X1 )
| ( $true
= ( sK0 = X1 ) ) ),
inference(equality_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X1: $i] :
( ( sK1 != X1 )
| ( sK2 = X1 )
| ( sK0 = X1 ) ),
inference(equality_proxy_clausification,[],[f81]) ).
thf(f83,plain,
! [X1: $i] :
( ( $true
= ( ( sK0 = X1 )
| ( sK1 = X1 ) ) )
| ( $false
= ( ( sK0 = X1 )
| ( sK2 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f70]) ).
thf(f84,plain,
! [X1: $i] :
( ( $true
= ( sK1 = X1 ) )
| ( $false
= ( ( sK0 = X1 )
| ( sK2 = X1 ) ) )
| ( $true
= ( sK0 = X1 ) ) ),
inference(or_proxy_clausification,[],[f83]) ).
thf(f85,plain,
! [X1: $i] :
( ( sK1 = X1 )
| ( $false
= ( ( sK0 = X1 )
| ( sK2 = X1 ) ) )
| ( $true
= ( sK0 = X1 ) ) ),
inference(equality_proxy_clausification,[],[f84]) ).
thf(f86,plain,
! [X1: $i] :
( ( sK1 = X1 )
| ( $false
= ( sK2 = X1 ) )
| ( $true
= ( sK0 = X1 ) ) ),
inference(or_proxy_clausification,[],[f85]) ).
thf(f90,plain,
! [X1: $i] :
( ( sK1 = X1 )
| ( sK2 != X1 )
| ( $true
= ( sK0 = X1 ) ) ),
inference(equality_proxy_clausification,[],[f86]) ).
thf(f91,plain,
! [X1: $i] :
( ( sK2 != X1 )
| ( sK1 = X1 )
| ( sK0 = X1 ) ),
inference(equality_proxy_clausification,[],[f90]) ).
thf(f92,plain,
( ( sK1 = sK2 )
| ( sK0 = sK1 ) ),
inference(equality_resolution,[],[f82]) ).
thf(f93,plain,
sK0 = sK1,
inference(forward_subsumption_resolution,[],[f92,f56]) ).
thf(f94,plain,
( ( sK1 = sK2 )
| ( sK0 = sK2 ) ),
inference(equality_resolution,[],[f91]) ).
thf(f95,plain,
sK0 = sK2,
inference(forward_subsumption_resolution,[],[f94,f56]) ).
thf(f98,plain,
sK0 != sK1,
inference(constrained_superposition,[],[f56,f95]) ).
thf(f99,plain,
$false,
inference(forward_subsumption_resolution,[],[f98,f93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET017^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.25/0.28 % Computer : n011.cluster.edu
% 0.25/0.28 % Model : x86_64 x86_64
% 0.25/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.28 % Memory : 8046.5625MB
% 0.25/0.28 % OS : Linux 6.8.0-71-generic
% 0.25/0.29 % CPULimit : 300
% 0.25/0.29 % WCLimit : 300
% 0.25/0.29 % DateTime : Tue Sep 29 13:35:31 UTC 2026
% 0.25/0.29 % CPUTime :
% 0.25/0.29 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.25/0.34 Running first-order model finding
% 0.25/0.34 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.32/0.42 % (94661)Will run a generic schedule for satisfiability detection.
% 0.32/0.42 % (94667)% WARNING: option uhcvi not known.
% 0.32/0.42 % (94667)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2207399739:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.32/0.42 % (94671)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3560052798:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.32/0.42 % (94669)dis+10_1_sil=32000:sp=arity:random_seed=4136601039:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.32/0.42 % (94672)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1532016862:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.32/0.42 % (94667)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.32/0.42 % (94667)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.32/0.42 % (94667) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-94661-94667"...
% 0.32/0.42 % (94671) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-94661-94671"...
% 0.32/0.42 % (94669) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-94661-94669"...
% 0.32/0.42 % (94667)...printing done.
% 0.32/0.42 % (94672) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-94661-94672"...
% 0.32/0.42 % (94667)Refutation found. Thanks to Tanya!
% 0.32/0.42 % SZS status Theorem for theBenchmark
% 0.32/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.32/0.42 % (94667)------------------------------
% 0.32/0.42 % (94667)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.42 % (94667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.42 % (94667)CaDiCaL version: 2.1.3
% 0.32/0.42 % (94667)Termination reason: Refutation
% 0.32/0.42 % (94667)Time elapsed: 0.004 s
% 0.32/0.42 % (94667)Peak memory usage: 12 MB
% 0.32/0.42 % (94667)Instructions burned: 5 (million)
% 0.32/0.42 % (94661)Success in time 0.063 s
% 0.32/0.42 % Vampire exiting
%------------------------------------------------------------------------------