%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO076^5 : 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 : 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 08:46:34 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 6 unt; 0 typ; 1 def)
% Number of atoms : 82 ( 19 equ)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 35 ( 13 ~; 5 |; 8 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 50 ( 44 fml; 6 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 3 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,
cQ: $o ).
tff(func_def_1,type,
cP: $o ).
tff(pred_def_1,type,
sQ0_eqProxy: ( $o * $o ) > $o ).
tff(f1,conjecture,
( ( ( cP
=> cQ )
& cP )
=> cQ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM114) ).
tff(f2,negated_conjecture,
~ ( ( ( cP
=> cQ )
& cP )
=> cQ ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ( ( cP
=> cQ )
& cP )
=> cQ ),
inference(rectify,[],[f2]) ).
tff(f4,plain,
~ ( ( ( ( cP = $true )
=> ( cQ = $true ) )
& ( cP = $true ) )
=> ( cQ = $true ) ),
inference(fool_elimination,[],[f3]) ).
tff(f5,plain,
( ( cQ != $true )
& ( ( cQ = $true )
| ( cP != $true ) )
& ( cP = $true ) ),
inference(ennf_transformation,[],[f4]) ).
tff(f6,plain,
( ( cQ != $true )
& ( ( cQ = $true )
| ( cP != $true ) )
& ( cP = $true ) ),
inference(flattening,[],[f5]) ).
tff(f7,plain,
cP = $true,
inference(cnf_transformation,[],[f6]) ).
tff(f8,plain,
( ( cQ = $true )
| ( cP != $true ) ),
inference(cnf_transformation,[],[f6]) ).
tff(f9,plain,
cQ != $true,
inference(cnf_transformation,[],[f6]) ).
tff(f12,plain,
( ( cQ = $true )
| ( $true != $true ) ),
inference(definition_unfolding,[],[f8,f7]) ).
tff(f13,definition,
! [X0: $o,X1: $o] :
( sQ0_eqProxy((X0),(X1))
<=> ( (X0) = (X1) ) ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
tff(f16,plain,
~ sQ0_eqProxy(cQ,$true),
inference(equality_proxy_replacement,[],[f9,f13]) ).
tff(f17,plain,
( sQ0_eqProxy(cQ,$true)
| ~ sQ0_eqProxy($true,$true) ),
inference(equality_proxy_replacement,[],[f12,f13,f13]) ).
tff(f18,plain,
! [X0: $o] : sQ0_eqProxy((X0),(X0)),
inference(equality_proxy_axiom,[],[f13]) ).
tff(f20,plain,
~ sQ0_eqProxy($true,$true),
inference(forward_subsumption_resolution,[],[f17,f16]) ).
tff(f21,plain,
$false,
inference(resolution,[],[f18,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO076^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n015.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 16:36:03 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 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
% 0.08/0.26 % (3749460)Detected formulas, will run a generic FOF schedule.
% 0.08/0.26 % (3749471)dis+1011_1_slsqr=8,1:sil=2000:spb=units:fd=off:kmz=on:flr=on:sac=on:slsq=on:random_seed=4279462732:st=2:i=121:sd=30:aac=none:ep=RS:ss=axioms:sgt=10_2999 on theBenchmark for (2999ds/121Mi)
% 0.08/0.26 % (3749471) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3749460-3749471"...
% 0.08/0.26 % (3749471)...printing done.
% 0.08/0.26 % (3749471)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.26 % (3749471)------------------------------
% 0.08/0.26 % (3749471)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (3749471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (3749471)CaDiCaL version: 2.1.3
% 0.08/0.26 % (3749471)Termination reason: Refutation
% 0.08/0.26 % (3749471)Time elapsed: 0.001 s
% 0.08/0.26 % (3749471)Peak memory usage: 12 MB
% 0.08/0.26 % (3749460)Success in time 0.033 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------