%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV169^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:37:57 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 22 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 50 ( 49 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 171 ( 9 ~; 0 |; 24 &; 134 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 86 ( 86 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 1 con; 0-4 aty)
% Number of variables : 189 ( 170 ^; 15 !; 4 ?; 189 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_2,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_3,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_4,type,
sK0: ( a > a > a ) > a ).
thf(func_def_5,type,
sK1: ( a > a > a ) > a ).
thf(func_def_6,type,
sK2: a > a > a ).
thf(f1,conjecture,
! [X1: ( a > a > a ) > a,X0: ( a > a > a ) > a] :
( ( ( ( X1
@ ^ [X3: a,X4: a] : X3 )
= ( X0
@ ^ [X3: a,X4: a] : X3 ) )
& ( X0
= ( ^ [X2: a > a > a] :
( X2
@ ( X0
@ ^ [X3: a,X4: a] : X3 )
@ ( X0
@ ^ [X3: a,X4: a] : X4 ) ) ) )
& ( ( X1
@ ^ [X3: a,X4: a] : X4 )
= ( X0
@ ^ [X3: a,X4: a] : X4 ) )
& ( X1
= ( ^ [X2: a > a > a] :
( X2
@ ( X1
@ ^ [X3: a,X4: a] : X3 )
@ ( X1
@ ^ [X3: a,X4: a] : X4 ) ) ) ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM188_pme) ).
thf(f2,negated_conjecture,
~ ! [X1: ( a > a > a ) > a,X0: ( a > a > a ) > a] :
( ( ( ( X1
@ ^ [X3: a,X4: a] : X3 )
= ( X0
@ ^ [X3: a,X4: a] : X3 ) )
& ( X0
= ( ^ [X2: a > a > a] :
( X2
@ ( X0
@ ^ [X3: a,X4: a] : X3 )
@ ( X0
@ ^ [X3: a,X4: a] : X4 ) ) ) )
& ( ( X1
@ ^ [X3: a,X4: a] : X4 )
= ( X0
@ ^ [X3: a,X4: a] : X4 ) )
& ( X1
= ( ^ [X2: a > a > a] :
( X2
@ ( X1
@ ^ [X3: a,X4: a] : X3 )
@ ( X1
@ ^ [X3: a,X4: a] : X4 ) ) ) ) )
=> ( X0 = X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: ( a > a > a ) > a,X1: ( a > a > a ) > a] :
( ( ( ( X0
@ ^ [X2: a,X3: a] : X2 )
= ( X1
@ ^ [X4: a,X5: a] : X4 ) )
& ( X1
= ( ^ [X6: a > a > a] :
( X6
@ ( X1
@ ^ [X7: a,X8: a] : X7 )
@ ( X1
@ ^ [X9: a,X10: a] : X10 ) ) ) )
& ( ( X0
@ ^ [X11: a,X12: a] : X12 )
= ( X1
@ ^ [X13: a,X14: a] : X14 ) )
& ( X0
= ( ^ [X15: a > a > a] :
( X15
@ ( X0
@ ^ [X16: a,X17: a] : X16 )
@ ( X0
@ ^ [X18: a,X19: a] : X19 ) ) ) ) )
=> ( X0 = X1 ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X1: ( a > a > a ) > a,X0: ( a > a > a ) > a] :
( ( ( ( ^ [Y0: a > a > a] :
( Y0
@ ( X1
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( X1
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= X1 )
& ( ( X0
@ ^ [Y0: a,Y1: a] : Y1 )
= ( X1
@ ^ [Y0: a,Y1: a] : Y1 ) )
& ( ( ^ [Y0: a > a > a] :
( Y0
@ ( X0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( X0
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= X0 )
& ( ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
= ( X0
@ ^ [Y0: a,Y1: a] : Y0 ) ) )
=> ( X0 = X1 ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X1: ( a > a > a ) > a,X0: ( a > a > a ) > a] :
( ( X0 != X1 )
& ( ( ^ [Y0: a > a > a] :
( Y0
@ ( X1
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( X1
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= X1 )
& ( ( X0
@ ^ [Y0: a,Y1: a] : Y1 )
= ( X1
@ ^ [Y0: a,Y1: a] : Y1 ) )
& ( ( ^ [Y0: a > a > a] :
( Y0
@ ( X0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( X0
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= X0 )
& ( ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
= ( X0
@ ^ [Y0: a,Y1: a] : Y0 ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: ( a > a > a ) > a,X1: ( a > a > a ) > a] :
( ( ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
= ( X0
@ ^ [Y0: a,Y1: a] : Y0 ) )
& ( ( ^ [Y0: a > a > a] :
( Y0
@ ( X0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( X0
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= X0 )
& ( X0 != X1 )
& ( ( ^ [Y0: a > a > a] :
( Y0
@ ( X1
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( X1
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= X1 )
& ( ( X0
@ ^ [Y0: a,Y1: a] : Y1 )
= ( X1
@ ^ [Y0: a,Y1: a] : Y1 ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ( ( sK0
@ ^ [Y0: a,Y1: a] : Y0 )
= ( sK1
@ ^ [Y0: a,Y1: a] : Y0 ) )
& ( ( ^ [Y0: a > a > a] :
( Y0
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= sK0 )
& ( sK1 != sK0 )
& ( sK1
= ( ^ [Y0: a > a > a] :
( Y0
@ ( sK1
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( sK1
@ ^ [Y1: a,Y2: a] : Y2 ) ) ) )
& ( ( sK0
@ ^ [Y0: a,Y1: a] : Y1 )
= ( sK1
@ ^ [Y0: a,Y1: a] : Y1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f6]) ).
thf(f8,plain,
( ( sK0
@ ^ [Y0: a,Y1: a] : Y1 )
= ( sK1
@ ^ [Y0: a,Y1: a] : Y1 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
( sK1
= ( ^ [Y0: a > a > a] :
( Y0
@ ( sK1
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( sK1
@ ^ [Y1: a,Y2: a] : Y2 ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
sK1 != sK0,
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
( ( ^ [Y0: a > a > a] :
( Y0
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= sK0 ),
inference(cnf_transformation,[],[f7]) ).
thf(f12,plain,
( ( sK0
@ ^ [Y0: a,Y1: a] : Y0 )
= ( sK1
@ ^ [Y0: a,Y1: a] : Y0 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,plain,
( ( sK1 @ sK2 )
!= ( sK0 @ sK2 ) ),
inference(negative_extensionality,[],[f10]) ).
thf(f14,plain,
! [X1: a > a > a] :
( ( ^ [Y0: a > a > a] :
( Y0
@ ( sK1
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( sK1
@ ^ [Y1: a,Y2: a] : Y2 ) )
@ X1 )
= ( sK1 @ X1 ) ),
inference(argument_congruence,[],[f9]) ).
thf(f15,plain,
! [X1: a > a > a] :
( ( X1
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y1 ) )
= ( sK1 @ X1 ) ),
inference(beta-eta_normalization,[],[f14]) ).
thf(f16,plain,
! [X1: a > a > a] :
( ( X1
@ ( sK0
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y1 ) )
= ( sK1 @ X1 ) ),
inference(forward_demodulation,[],[f15,f12]) ).
thf(f17,plain,
! [X1: a > a > a] :
( ( X1
@ ( sK0
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( sK0
@ ^ [Y0: a,Y1: a] : Y1 ) )
= ( sK1 @ X1 ) ),
inference(forward_demodulation,[],[f16,f8]) ).
thf(f18,plain,
! [X1: a > a > a] :
( ( ^ [Y0: a > a > a] :
( Y0
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y2 ) )
@ X1 )
= ( sK0 @ X1 ) ),
inference(argument_congruence,[],[f11]) ).
thf(f19,plain,
! [X1: a > a > a] :
( ( sK0 @ X1 )
= ( X1
@ ( sK0
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( sK0
@ ^ [Y0: a,Y1: a] : Y1 ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f20,plain,
! [X0: a > a > a] :
( ( sK1 @ X0 )
= ( sK0 @ X0 ) ),
inference(constrained_superposition,[],[f19,f17]) ).
thf(f22,plain,
( ( sK0 @ sK2 )
!= ( sK0 @ sK2 ) ),
inference(constrained_superposition,[],[f13,f20]) ).
thf(f23,plain,
$false,
inference(trivial_inequality_removal,[],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV169^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n018.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 15:20:26 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.22/0.29 % (211175)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (211182)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1723659521:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.29 % (211182) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-211175-211182"...
% 0.22/0.29 % (211182)...printing done.
% 0.22/0.29 % (211182)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (211182)------------------------------
% 0.22/0.29 % (211182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (211182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (211182)CaDiCaL version: 2.1.3
% 0.22/0.29 % (211182)Termination reason: Refutation
% 0.22/0.29 % (211182)Time elapsed: 0.002 s
% 0.22/0.29 % (211182)Peak memory usage: 12 MB
% 0.22/0.29 % (211182)Instructions burned: 4 (million)
% 0.22/0.29 % (211175)Success in time 0.033 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------