%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL952^12 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 08:14:55 AM UTC 2026
% Result : Theorem 0.21s 0.31s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 11 unt; 0 typ; 1 def)
% Number of atoms : 140 ( 6 equ; 0 cnn)
% Maximal formula atoms : 11 ( 8 avg)
% Number of connectives : 206 ( 7 ~; 0 |; 0 &; 198 @)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 32 usr; 4 con; 0-4 aty)
% Number of variables : 22 ( 0 sgn 0 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
mrel: mworld > mworld > $o ).
thf(func_def_1,type,
mactual: mworld ).
thf(func_def_2,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_4,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_5,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
eiw_di: $i > mworld > $o ).
thf(func_def_12,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_14,type,
qmltpeq: $i > $i > mworld > $o ).
thf(func_def_15,type,
in: $i > $i > mworld > $o ).
thf(func_def_16,type,
empty: $i > mworld > $o ).
thf(func_def_17,type,
set_intersection2: $i > $i > $i ).
thf(func_def_18,type,
singleton: $i > $i ).
thf(func_def_19,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_25,type,
vOR: $o > $o > $o ).
thf(func_def_26,type,
vNOT: $o > $o ).
thf(func_def_27,type,
vIFF: $o > $o > $o ).
thf(func_def_28,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_29,type,
vIMP: $o > $o > $o ).
thf(func_def_30,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
vAND: $o > $o > $o ).
thf(func_def_32,type,
sK0: mworld > $i ).
thf(f27,conjecture,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mbox
@ ( mforall_di
@ ^ [X1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ X0 @ ( singleton @ X1 ) ) @ ( singleton @ X1 ) ) ) @ ( mbox @ ( in @ X1 @ X0 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_zfmisc_1) ).
thf(f28,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mbox
@ ( mforall_di
@ ^ [X1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ X0 @ ( singleton @ X1 ) ) @ ( singleton @ X1 ) ) ) @ ( mbox @ ( in @ X1 @ X0 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
thf(f29,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mbox
@ ( mforall_di
@ ^ [X1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ X0 @ ( singleton @ X1 ) ) @ ( singleton @ X1 ) ) ) @ ( mbox @ ( in @ X1 @ X0 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l30_zfmisc_1) ).
thf(f63,plain,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mbox
@ ( mforall_di
@ ^ [X1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ X0 @ ( singleton @ X1 ) ) @ ( singleton @ X1 ) ) ) @ ( mbox @ ( in @ X1 @ X0 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f29]) ).
thf(f64,plain,
( ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mbox
@ ( mforall_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ Y0 @ ( singleton @ Y1 ) ) @ ( singleton @ Y1 ) ) ) @ ( mbox @ ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f63]) ).
thf(f83,plain,
~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mbox
@ ( mforall_di
@ ^ [X1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ X0 @ ( singleton @ X1 ) ) @ ( singleton @ X1 ) ) ) @ ( mbox @ ( in @ X1 @ X0 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f28]) ).
thf(f84,plain,
( ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mbox
@ ( mforall_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ Y0 @ ( singleton @ Y1 ) ) @ ( singleton @ Y1 ) ) ) @ ( mbox @ ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f83]) ).
thf(f85,plain,
( ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mbox
@ ( mforall_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ Y0 @ ( singleton @ Y1 ) ) @ ( singleton @ Y1 ) ) ) @ ( mbox @ ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f84]) ).
thf(f105,plain,
( ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mbox
@ ( mforall_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ Y0 @ ( singleton @ Y1 ) ) @ ( singleton @ Y1 ) ) ) @ ( mbox @ ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f64]) ).
thf(f107,plain,
( ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mbox
@ ( mforall_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ Y0 @ ( singleton @ Y1 ) ) @ ( singleton @ Y1 ) ) ) @ ( mbox @ ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f85]) ).
thf(f177,definition,
( spl1_13
<=> ( ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mbox
@ ( mforall_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ Y0 @ ( singleton @ Y1 ) ) @ ( singleton @ Y1 ) ) ) @ ( mbox @ ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition]) ).
thf(f180,plain,
~ spl1_13,
inference(avatar_split_clause,[],[f107,f177]) ).
thf(f211,plain,
spl1_13,
inference(avatar_split_clause,[],[f105,f177]) ).
cnf(s13,plain,
~ spl1_13,
inference(sat_conversion,[],[f180]) ).
cnf(s20,plain,
spl1_13,
inference(sat_conversion,[],[f211]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s13,s20]) ).
thf(f242,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL952^12 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n010.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 10:51:18 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
% 0.08/0.24 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
% 0.21/0.31 % (2697474)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.31 % (2697480)lrs+10_16_si=on:nwc=1.5:random_seed=3884210637:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.31 % (2697480)Instruction limit reached!
% 0.21/0.31 % (2697480)------------------------------
% 0.21/0.31 % (2697480)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (2697480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (2697480)CaDiCaL version: 2.1.3
% 0.21/0.31 % (2697480)Termination reason: Instruction limit
% 0.21/0.31 % (2697480)Termination phase: Saturation
% 0.21/0.31 % (2697480)Time elapsed: 0.005 s
% 0.21/0.31 % (2697480)Peak memory usage: 11 MB
% 0.21/0.31 % (2697480)Instructions burned: 20 (million)
% 0.21/0.31 % (2697479)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=804161321:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.31 % (2697481)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1743038773:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.31 % (2697481)Instruction limit reached!
% 0.21/0.31 % (2697481)------------------------------
% 0.21/0.31 % (2697481)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (2697481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (2697481)CaDiCaL version: 2.1.3
% 0.21/0.31 % (2697481)Termination reason: Instruction limit
% 0.21/0.31 % (2697481)Termination phase: Property scanning
% 0.21/0.31 % (2697481)Time elapsed: 0.002 s
% 0.21/0.31 % (2697481)Peak memory usage: 9 MB
% 0.21/0.31 % (2697481)Instructions burned: 4 (million)
% 0.21/0.31 % (2697487)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1639969105:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.31 % (2697482)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=1570586821: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)
% 0.21/0.31 % (2697487)Instruction limit reached!
% 0.21/0.31 % (2697487)------------------------------
% 0.21/0.31 % (2697487)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (2697487)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (2697487)CaDiCaL version: 2.1.3
% 0.21/0.31 % (2697487)Termination reason: Instruction limit
% 0.21/0.31 % (2697487)Termination phase: Property scanning
% 0.21/0.31 % (2697487)Time elapsed: 0.001 s
% 0.21/0.31 % (2697487)Peak memory usage: 10 MB
% 0.21/0.31 % (2697487)Instructions burned: 5 (million)
% 0.21/0.31 % (2697493)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.31 % (2697482) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2697474-2697482"...
% 0.21/0.31 % (2697490)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3509841239:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.31 % (2697493)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2448457579:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.31 % (2697482)...printing done.
% 0.21/0.31 % (2697493)Instruction limit reached!
% 0.21/0.31 % (2697493)------------------------------
% 0.21/0.31 % (2697493)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (2697493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (2697493)CaDiCaL version: 2.1.3
% 0.21/0.31 % (2697493)Termination reason: Instruction limit
% 0.21/0.31 % (2697493)Termination phase: Property scanning
% 0.21/0.31 % (2697493)Time elapsed: 0.002 s
% 0.21/0.31 % (2697493)Peak memory usage: 10 MB
% 0.21/0.31 % (2697493)Instructions burned: 9 (million)
% 0.21/0.31 % (2697482)Refutation found. Thanks to Tanya!
% 0.21/0.31 % SZS status Theorem for theBenchmark
% 0.21/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.31 % (2697482)------------------------------
% 0.21/0.31 % (2697482)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (2697482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (2697482)CaDiCaL version: 2.1.3
% 0.21/0.31 % (2697482)Termination reason: Refutation
% 0.21/0.31 % (2697482)Time elapsed: 0.012 s
% 0.21/0.31 % (2697482)Peak memory usage: 12 MB
% 0.21/0.31 % (2697482)Instructions burned: 15 (million)
% 0.21/0.31 % (2697474)Success in time 0.056 s
% 0.21/0.31 % Vampire exiting
%------------------------------------------------------------------------------