%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO218^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 08:49:33 AM UTC 2026
% Result : Theorem 0.11s 0.26s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 64 ( 42 equ; 3 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 44 ( 10 ~; 4 |; 2 &; 20 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 33 ( 15 ^; 16 !; 2 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_2,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_3,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,conjecture,
! [X0: $i,X1: $i] :
( ! [X2: ( $i > $o ) > $i] :
( ( X0
= ( X2
@ ^ [X3: $i] : ( X0 = X3 ) ) )
=> ( X1
= ( X2
@ ^ [X3: $i] : ( X1 = X3 ) ) ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM7B_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: $i,X1: $i] :
( ! [X2: ( $i > $o ) > $i] :
( ( X0
= ( X2
@ ^ [X3: $i] : ( X0 = X3 ) ) )
=> ( X1
= ( X2
@ ^ [X3: $i] : ( X1 = X3 ) ) ) )
=> ( X0 = X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: $i,X1: $i] :
( ! [X2: ( $i > $o ) > $i] :
( ( X0
= ( X2
@ ^ [X3: $i] : ( X0 = X3 ) ) )
=> ( X1
= ( X2
@ ^ [X4: $i] : ( X1 = X4 ) ) ) )
=> ( X0 = X1 ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i] :
( ! [X2: ( $i > $o ) > $i] :
( ( ( X2
@ ^ [Y0: $i] : ( X0 = Y0 ) )
= X0 )
=> ( ( X2
@ ^ [Y0: $i] : ( X1 = Y0 ) )
= X1 ) )
=> ( X0 = X1 ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ! [X2: ( $i > $o ) > $i] :
( ( ( X2
@ ^ [Y0: $i] : ( X1 = Y0 ) )
= X1 )
| ( ( X2
@ ^ [Y0: $i] : ( X0 = Y0 ) )
!= X0 ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( sK0 != sK1 )
& ! [X2: ( $i > $o ) > $i] :
( ( sK1
= ( X2
@ ^ [Y0: $i] : ( sK1 = Y0 ) ) )
| ( sK0
!= ( X2
@ ^ [Y0: $i] : ( sK0 = Y0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f5]) ).
thf(f7,plain,
! [X2: ( $i > $o ) > $i] :
( ( sK1
= ( X2
@ ^ [Y0: $i] : ( sK1 = Y0 ) ) )
| ( sK0
!= ( X2
@ ^ [Y0: $i] : ( sK0 = Y0 ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f6]) ).
thf(f11,plain,
! [X2: ( $i > $o ) > $i] :
( ( sK0
!= ( X2 @ ( (=) @ sK0 ) ) )
| ( sK1
= ( X2 @ ( (=) @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f7]) ).
thf(f12,plain,
( sK1
= ( ^ [Y0: $i > $o] : sK0
@ ( (=) @ sK1 ) ) ),
inference(equality_resolution,[],[f11]) ).
thf(f13,plain,
sK0 = sK1,
inference(beta-eta_normalization,[],[f12]) ).
thf(f14,plain,
$false,
inference(forward_subsumption_resolution,[],[f13,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO218^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.18 % Computer : n019.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Sep 29 16:39:48 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.21 Running first-order model finding
% 0.11/0.21 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
% 0.11/0.26 % (1026211)Will run a generic schedule for satisfiability detection.
% 0.11/0.26 % (1026219)dis+10_1_sil=32000:sp=arity:random_seed=1409723866:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.26 % (1026219) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1026211-1026219"...
% 0.11/0.26 % (1026219)...printing done.
% 0.11/0.26 % (1026219)Refutation found. Thanks to Tanya!
% 0.11/0.26 % SZS status Theorem for theBenchmark
% 0.11/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.26 % (1026219)------------------------------
% 0.11/0.26 % (1026219)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.26 % (1026219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.26 % (1026219)CaDiCaL version: 2.1.3
% 0.11/0.26 % (1026219)Termination reason: Refutation
% 0.11/0.26 % (1026219)Time elapsed: 0.001 s
% 0.11/0.26 % (1026219)Peak memory usage: 12 MB
% 0.11/0.26 % (1026219)Instructions burned: 1 (million)
% 0.11/0.26 % (1026211)Success in time 0.036 s
% 0.11/0.26 % Vampire exiting
%------------------------------------------------------------------------------