%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU697^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 08:33:01 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 24 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 139 ( 9 ~; 2 |; 2 &; 118 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 4 con; 0-4 aty)
% Number of variables : 67 ( 46 ^; 18 !; 3 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_2,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_4,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
sK2: $i > $i ).
thf(func_def_14,type,
vNOT: $o > $o ).
thf(f1,axiom,
( lam
= ( ^ [X0: $i,X1: $i,X2: $i > $i] :
( dpsetconstr @ X0 @ X1
@ ^ [X3: $i,X4: $i] :
( ( X2 @ X3 )
= X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam) ).
thf(f2,conjecture,
! [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X2 @ X3 ) @ X1 ) )
=> ( ( lam @ X0 @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) )
= ( lam @ X0 @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2lamEq) ).
thf(f3,negated_conjecture,
~ ! [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X2 @ X3 ) @ X1 ) )
=> ( ( lam @ X0 @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) )
= ( lam @ X0 @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( lam
= ( ^ [X0: $i,X1: $i,X2: $i > $i] :
( dpsetconstr @ X0 @ X1
@ ^ [X3: $i,X4: $i] :
( ( X2 @ X3 )
= X4 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( lam
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i] :
( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i,Y4: $i] :
( ( Y2 @ Y3 )
= Y4 ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ! [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X2 @ X3 ) @ X1 ) )
=> ( ( lam @ X0 @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) )
= ( lam @ X0 @ X1
@ ^ [X5: $i] : ( X2 @ X5 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ! [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( in @ ( X2 @ X3 ) @ X1 )
= $true ) )
=> ( ( lam @ X0 @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
= ( lam @ X0 @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X0: $i,X1: $i,X2: $i > $i] :
( ( ( lam @ X0 @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
!= ( lam @ X0 @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
& ! [X3: $i] :
( ( ( in @ ( X2 @ X3 ) @ X1 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ( ( lam @ sK0 @ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) )
!= ( lam @ sK0 @ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) )
& ! [X3: $i] :
( ( $true
= ( in @ ( sK2 @ X3 ) @ sK1 ) )
| ( $true
!= ( in @ X3 @ sK0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f8]) ).
thf(f10,plain,
( lam
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i] :
( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i,Y4: $i] :
( ( Y2 @ Y3 )
= Y4 ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f12,plain,
( ( lam @ sK0 @ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) )
!= ( lam @ sK0 @ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f15,plain,
( ( ^ [Y0: $i,Y1: $i,Y2: $i > $i] :
( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i,Y4: $i] :
( ( Y2 @ Y3 )
= Y4 ) )
@ sK0
@ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i] :
( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i,Y4: $i] :
( ( Y2 @ Y3 )
= Y4 ) )
@ sK0
@ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) ),
inference(definition_unfolding,[],[f12,f10,f10]) ).
thf(f16,plain,
$false,
inference(trivial_inequality_removal,[],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU697^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n005.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:11:31 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.19/0.28 % (1725404)Will run a generic schedule for satisfiability detection.
% 0.19/0.28 % (1725409)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1018158124_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.28 % Exception at run slice level
% 0.19/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.28 % (1725410)% WARNING: option uhcvi not known.
% 0.19/0.28 % (1725413)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3353300649:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.28 % (1725410)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=793415825:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.28 % (1725411)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2747023536:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.28 % (1725412)dis+10_1_sil=32000:sp=arity:random_seed=3680780908:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.28 % (1725410)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.28 % (1725413)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.28 % (1725410)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.28 % (1725413) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1725404-1725413"...
% 0.19/0.28 % (1725410) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1725404-1725410"...
% 0.19/0.28 % (1725412) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1725404-1725412"...
% 0.19/0.28 % (1725411) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1725404-1725411"...
% 0.19/0.28 % (1725413)...printing done.
% 0.19/0.28 % (1725411)...printing done.
% 0.19/0.28 % (1725410)...printing done.
% 0.19/0.28 % (1725412)...printing done.
% 0.19/0.28 % (1725410)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.28 % (1725410)------------------------------
% 0.19/0.28 % (1725410)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (1725410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (1725410)CaDiCaL version: 2.1.3
% 0.19/0.28 % (1725410)Termination reason: Refutation
% 0.19/0.28 % (1725410)Time elapsed: 0.002 s
% 0.19/0.28 % (1725410)Peak memory usage: 11 MB
% 0.19/0.28 % (1725410)Instructions burned: 2 (million)
% 0.19/0.28 % (1725404)Success in time 0.044 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------