%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV169^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 08:39:05 AM UTC 2026
% Result : Theorem 0.07s 0.24s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 21 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 48 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 172 ( 9 ~; 0 |; 24 &; 135 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 84 ( 84 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 1 con; 0-4 aty)
% Number of variables : 192 ( 174 ^; 14 !; 4 ?; 192 :)
% 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(func_def_7,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db3:
!>[X0: $tType] : X0 ).
thf(f1,conjecture,
! [X0: ( a > a > a ) > a,X1: ( a > a > a ) > a] :
( ( ( ( X0
@ ^ [X3: a,X4: a] : X4 )
= ( X1
@ ^ [X3: a,X4: a] : X4 ) )
& ( ( X0
@ ^ [X3: a,X4: a] : X3 )
= ( X1
@ ^ [X3: a,X4: a] : X3 ) )
& ( X1
= ( ^ [X2: a > a > a] :
( X2
@ ( X1
@ ^ [X3: a,X4: a] : X3 )
@ ( X1
@ ^ [X3: a,X4: a] : X4 ) ) ) )
& ( X0
= ( ^ [X2: a > a > a] :
( X2
@ ( X0
@ ^ [X3: a,X4: a] : X3 )
@ ( X0
@ ^ [X3: a,X4: a] : X4 ) ) ) ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM188_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: ( a > a > a ) > a,X1: ( a > a > a ) > a] :
( ( ( ( X0
@ ^ [X3: a,X4: a] : X4 )
= ( X1
@ ^ [X3: a,X4: a] : X4 ) )
& ( ( X0
@ ^ [X3: a,X4: a] : X3 )
= ( X1
@ ^ [X3: a,X4: a] : X3 ) )
& ( X1
= ( ^ [X2: a > a > a] :
( X2
@ ( X1
@ ^ [X3: a,X4: a] : X3 )
@ ( X1
@ ^ [X3: a,X4: a] : X4 ) ) ) )
& ( X0
= ( ^ [X2: a > a > a] :
( X2
@ ( X0
@ ^ [X3: a,X4: a] : X3 )
@ ( X0
@ ^ [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] : X3 )
= ( X1
@ ^ [X4: a,X5: a] : X5 ) )
& ( ( X0
@ ^ [X6: a,X7: a] : X6 )
= ( X1
@ ^ [X8: a,X9: a] : X8 ) )
& ( X1
= ( ^ [X10: a > a > a] :
( X10
@ ( X1
@ ^ [X11: a,X12: a] : X11 )
@ ( 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,
~ ! [X0: ( a > a > a ) > a,X1: ( a > a > a ) > a] :
( ( ( ( X0
@ ^ [Y0: a,Y1: a] : Y1 )
= ( X1
@ ^ [Y0: a,Y1: a] : Y1 ) )
& ( ( X0
@ ^ [Y0: a,Y1: a] : Y0 )
= ( X1
@ ^ [Y0: a,Y1: a] : Y0 ) )
& ( ( ^ [Y0: a > a > a] :
( Y0
@ ( X1
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( X1
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= X1 )
& ( ( ^ [Y0: a > a > a] :
( Y0
@ ( X0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( X0
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= X0 ) )
=> ( X0 = X1 ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: ( a > a > a ) > a,X1: ( a > a > a ) > a] :
( ( X0 != X1 )
& ( ( X0
@ ^ [Y0: a,Y1: a] : Y1 )
= ( X1
@ ^ [Y0: a,Y1: a] : Y1 ) )
& ( ( X0
@ ^ [Y0: a,Y1: a] : Y0 )
= ( X1
@ ^ [Y0: a,Y1: a] : Y0 ) )
& ( ( ^ [Y0: a > a > a] :
( Y0
@ ( X1
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( X1
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= X1 )
& ( ( ^ [Y0: a > a > a] :
( Y0
@ ( X0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( X0
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= X0 ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: ( a > a > a ) > a,X1: ( a > a > a ) > a] :
( ( X0 != X1 )
& ( ( X0
@ ^ [Y0: a,Y1: a] : Y1 )
= ( X1
@ ^ [Y0: a,Y1: a] : Y1 ) )
& ( ( X0
@ ^ [Y0: a,Y1: a] : Y0 )
= ( X1
@ ^ [Y0: a,Y1: a] : Y0 ) )
& ( ( ^ [Y0: a > a > a] :
( Y0
@ ( X1
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( X1
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= X1 )
& ( ( ^ [Y0: a > a > a] :
( Y0
@ ( X0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( X0
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= X0 ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ( sK0 != sK1 )
& ( ( sK0
@ ^ [Y0: a,Y1: a] : Y1 )
= ( sK1
@ ^ [Y0: a,Y1: a] : Y1 ) )
& ( ( sK0
@ ^ [Y0: a,Y1: a] : Y0 )
= ( sK1
@ ^ [Y0: a,Y1: a] : Y0 ) )
& ( sK1
= ( ^ [Y0: a > a > a] :
( Y0
@ ( sK1
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( sK1
@ ^ [Y1: a,Y2: a] : Y2 ) ) ) )
& ( sK0
= ( ^ [Y0: a > a > a] :
( Y0
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y2 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f6]) ).
thf(f8,plain,
( sK0
= ( ^ [Y0: a > a > a] :
( Y0
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y2 ) ) ) ),
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,
( ( sK0
@ ^ [Y0: a,Y1: a] : Y0 )
= ( sK1
@ ^ [Y0: a,Y1: a] : Y0 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
( ( sK0
@ ^ [Y0: a,Y1: a] : Y1 )
= ( sK1
@ ^ [Y0: a,Y1: a] : Y1 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f12,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f7]) ).
thf(f13,plain,
( ( sK0 @ sK2 )
!= ( sK1 @ sK2 ) ),
inference(negative_extensionality,[],[f12]) ).
thf(f14,plain,
! [X1: a > a > a] :
( ( sK0 @ X1 )
= ( ^ [Y0: a > a > a] :
( Y0
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y2 ) )
@ X1 ) ),
inference(argument_congruence,[],[f8]) ).
thf(f15,plain,
! [X1: a > a > a] :
( ( sK0 @ X1 )
= ( X1
@ ( sK0
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( sK0
@ ^ [Y0: a,Y1: a] : Y1 ) ) ),
inference(beta-eta_normalization,[],[f14]) ).
thf(f16,plain,
! [X1: a > a > a] :
( ( sK1 @ X1 )
= ( ^ [Y0: a > a > a] :
( Y0
@ ( sK1
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( sK1
@ ^ [Y1: a,Y2: a] : Y2 ) )
@ X1 ) ),
inference(argument_congruence,[],[f9]) ).
thf(f17,plain,
! [X1: a > a > a] :
( ( sK1 @ X1 )
= ( X1
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y1 ) ) ),
inference(beta-eta_normalization,[],[f16]) ).
thf(f18,plain,
! [X1: a > a > a] :
( ( sK1 @ X1 )
= ( X1
@ ( sK0
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y1 ) ) ),
inference(forward_demodulation,[],[f17,f10]) ).
thf(f19,plain,
! [X1: a > a > a] :
( ( X1
@ ( sK0
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( sK0
@ ^ [Y0: a,Y1: a] : Y1 ) )
= ( sK1 @ X1 ) ),
inference(forward_demodulation,[],[f18,f11]) ).
thf(f30,plain,
( ( sK0 @ sK2 )
!= ( sK2
@ ( sK0
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( sK0
@ ^ [Y0: a,Y1: a] : Y1 ) ) ),
inference(constrained_superposition,[],[f13,f19]) ).
thf(f35,plain,
$false,
inference(forward_subsumption_resolution,[],[f30,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV169^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n001.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 15:24:06 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.24 % (1378016)Will run a generic schedule for satisfiability detection.
% 0.07/0.24 % (1378026)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=351574735:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.24 % (1378026) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1378016-1378026"...
% 0.07/0.24 % (1378026)...printing done.
% 0.07/0.24 % (1378026)Refutation found. Thanks to Tanya!
% 0.07/0.24 % SZS status Theorem for theBenchmark
% 0.07/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.24 % (1378026)------------------------------
% 0.07/0.24 % (1378026)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.24 % (1378026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.24 % (1378026)CaDiCaL version: 2.1.3
% 0.07/0.24 % (1378026)Termination reason: Refutation
% 0.07/0.24 % (1378026)Time elapsed: 0.003 s
% 0.07/0.24 % (1378026)Peak memory usage: 12 MB
% 0.07/0.24 % (1378026)Instructions burned: 8 (million)
% 0.07/0.24 % (1378016)Success in time 0.025 s
% 0.07/0.24 % Vampire exiting
%------------------------------------------------------------------------------