%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO125^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 08:46:39 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 8 unt; 0 typ; 1 def)
% Number of atoms : 67 ( 15 equ)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 30 ( 8 ~; 0 |; 8 &)
% ( 10 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 36 ( 30 fml; 6 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 3 ( 3 !; 0 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
cR: $o ).
tff(func_def_1,type,
cP: $o ).
tff(func_def_2,type,
cQ: $o ).
tff(pred_def_1,type,
sQ0_eqProxy: ( $o * $o ) > $o ).
tff(f1,conjecture,
( ( ( cQ
<=> cR )
& ( cP
<=> cQ ) )
=> ( cP
<=> cR ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTRIV4) ).
tff(f2,negated_conjecture,
~ ( ( ( cQ
<=> cR )
& ( cP
<=> cQ ) )
=> ( cP
<=> cR ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ( ( cQ
<=> cR )
& ( cP
<=> cQ ) )
=> ( cP
<=> cR ) ),
inference(rectify,[],[f2]) ).
tff(f4,plain,
~ ( ( ( cQ = cR )
& ( cP = cQ ) )
=> ( cP = cR ) ),
inference(fool_elimination,[],[f3]) ).
tff(f5,plain,
( ( cP != cR )
& ( cQ = cR )
& ( cP = cQ ) ),
inference(ennf_transformation,[],[f4]) ).
tff(f6,plain,
( ( cP != cR )
& ( cQ = cR )
& ( cP = cQ ) ),
inference(flattening,[],[f5]) ).
tff(f7,plain,
cP = cQ,
inference(cnf_transformation,[],[f6]) ).
tff(f8,plain,
cQ = cR,
inference(cnf_transformation,[],[f6]) ).
tff(f9,plain,
cP != cR,
inference(cnf_transformation,[],[f6]) ).
tff(f12,plain,
cP = cR,
inference(definition_unfolding,[],[f7,f8]) ).
tff(f13,plain,
cR != cR,
inference(definition_unfolding,[],[f9,f12]) ).
tff(f14,definition,
! [X0: $o,X1: $o] :
( sQ0_eqProxy((X0),(X1))
<=> ( (X0) = (X1) ) ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
tff(f17,plain,
~ sQ0_eqProxy(cR,cR),
inference(equality_proxy_replacement,[],[f13,f14]) ).
tff(f18,plain,
! [X0: $o] : sQ0_eqProxy((X0),(X0)),
inference(equality_proxy_axiom,[],[f14]) ).
tff(f20,plain,
$false,
inference(resolution,[],[f18,f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO125^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n015.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 16:37:48 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.28 % (3755685)Detected formulas, will run a generic FOF schedule.
% 0.21/0.28 % (3755696)dis+1011_1_slsqr=8,1:sil=2000:spb=units:fd=off:kmz=on:flr=on:sac=on:slsq=on:random_seed=2251060999:st=2:i=121:sd=30:aac=none:ep=RS:ss=axioms:sgt=10_2999 on theBenchmark for (2999ds/121Mi)
% 0.21/0.28 % (3755696) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3755685-3755696"...
% 0.21/0.28 % (3755696)...printing done.
% 0.21/0.28 % (3755696)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (3755696)------------------------------
% 0.21/0.29 % (3755696)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (3755696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (3755696)CaDiCaL version: 2.1.3
% 0.21/0.29 % (3755696)Termination reason: Refutation
% 0.21/0.29 % (3755696)Time elapsed: 0.001 s
% 0.21/0.29 % (3755696)Peak memory usage: 12 MB
% 0.21/0.29 % (3755685)Success in time 0.036 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------