%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG287^5 : 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 : n008.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 07:45:21 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 94 ( 79 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 229 ( 26 ~; 13 |; 41 &; 136 @)
% ( 7 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 39 !; 0 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
v: a ).
thf(func_def_1,type,
u: a ).
thf(func_def_2,type,
y: a ).
thf(func_def_3,type,
x: a ).
thf(func_def_4,type,
cP: a > a > a ).
thf(func_def_5,type,
cR: a > a ).
thf(func_def_6,type,
cL: a > a ).
thf(func_def_7,type,
cZ: a ).
thf(f1,conjecture,
( ( ! [X1: a,X0: a] :
( ( cR @ ( cP @ X0 @ X1 ) )
= X1 )
& ! [X1: a,X0: a] :
( ( cL @ ( cP @ X0 @ X1 ) )
= X0 )
& ! [X2: a] :
( ( X2 != cZ )
<=> ( X2
= ( cP @ ( cL @ X2 ) @ ( cR @ X2 ) ) ) )
& ( ( cR @ cZ )
= cZ )
& ( ( cL @ cZ )
= cZ ) )
=> ( ( ( cP @ x @ u )
= ( cP @ y @ v ) )
=> ( ( u = v )
& ( x = y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPU_P_INJ_pme) ).
thf(f2,negated_conjecture,
~ ( ( ! [X1: a,X0: a] :
( ( cR @ ( cP @ X0 @ X1 ) )
= X1 )
& ! [X1: a,X0: a] :
( ( cL @ ( cP @ X0 @ X1 ) )
= X0 )
& ! [X2: a] :
( ( X2 != cZ )
<=> ( X2
= ( cP @ ( cL @ X2 ) @ ( cR @ X2 ) ) ) )
& ( ( cR @ cZ )
= cZ )
& ( ( cL @ cZ )
= cZ ) )
=> ( ( ( cP @ x @ u )
= ( cP @ y @ v ) )
=> ( ( u = v )
& ( x = y ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X4: a] :
( ( cZ != X4 )
<=> ( ( cP @ ( cL @ X4 ) @ ( cR @ X4 ) )
= X4 ) )
& ( ( cR @ cZ )
= cZ )
& ! [X1: a,X0: a] :
( ( cR @ ( cP @ X0 @ X1 ) )
= X1 )
& ( ( cL @ cZ )
= cZ )
& ! [X3: a,X2: a] :
( ( cL @ ( cP @ X3 @ X2 ) )
= X3 ) )
=> ( ( ( cP @ x @ u )
= ( cP @ y @ v ) )
=> ( ( u = v )
& ( x = y ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( ( ( u != v )
| ( x != y ) )
& ( ( cP @ x @ u )
= ( cP @ y @ v ) )
& ! [X4: a] :
( ( cZ != X4 )
<=> ( ( cP @ ( cL @ X4 ) @ ( cR @ X4 ) )
= X4 ) )
& ( ( cR @ cZ )
= cZ )
& ! [X1: a,X0: a] :
( ( cR @ ( cP @ X0 @ X1 ) )
= X1 )
& ( ( cL @ cZ )
= cZ )
& ! [X3: a,X2: a] :
( ( cL @ ( cP @ X3 @ X2 ) )
= X3 ) ),
inference(ennf_transformation,[],[f3]) ).
thf(f5,plain,
( ! [X4: a] :
( ( cZ != X4 )
<=> ( ( cP @ ( cL @ X4 ) @ ( cR @ X4 ) )
= X4 ) )
& ! [X1: a,X0: a] :
( ( cR @ ( cP @ X0 @ X1 ) )
= X1 )
& ( ( cP @ x @ u )
= ( cP @ y @ v ) )
& ( ( cR @ cZ )
= cZ )
& ( ( u != v )
| ( x != y ) )
& ! [X3: a,X2: a] :
( ( cL @ ( cP @ X3 @ X2 ) )
= X3 )
& ( ( cL @ cZ )
= cZ ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ! [X4: a] :
( ( ( cZ != X4 )
| ( ( cP @ ( cL @ X4 ) @ ( cR @ X4 ) )
!= X4 ) )
& ( ( ( cP @ ( cL @ X4 ) @ ( cR @ X4 ) )
= X4 )
| ( cZ = X4 ) ) )
& ! [X1: a,X0: a] :
( ( cR @ ( cP @ X0 @ X1 ) )
= X1 )
& ( ( cP @ x @ u )
= ( cP @ y @ v ) )
& ( ( cR @ cZ )
= cZ )
& ( ( u != v )
| ( x != y ) )
& ! [X3: a,X2: a] :
( ( cL @ ( cP @ X3 @ X2 ) )
= X3 )
& ( ( cL @ cZ )
= cZ ) ),
inference(nnf_transformation,[],[f5]) ).
thf(f7,plain,
( ! [X0: a] :
( ( ( cZ != X0 )
| ( ( cP @ ( cL @ X0 ) @ ( cR @ X0 ) )
!= X0 ) )
& ( ( ( cP @ ( cL @ X0 ) @ ( cR @ X0 ) )
= X0 )
| ( cZ = X0 ) ) )
& ! [X1: a,X2: a] :
( ( cR @ ( cP @ X2 @ X1 ) )
= X1 )
& ( ( cP @ x @ u )
= ( cP @ y @ v ) )
& ( ( cR @ cZ )
= cZ )
& ( ( u != v )
| ( x != y ) )
& ! [X3: a,X4: a] :
( ( cL @ ( cP @ X3 @ X4 ) )
= X3 )
& ( ( cL @ cZ )
= cZ ) ),
inference(rectify,[],[f6]) ).
thf(f9,plain,
! [X3: a,X4: a] :
( ( cL @ ( cP @ X3 @ X4 ) )
= X3 ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
( ( x != y )
| ( u != v ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f12,plain,
( ( cP @ x @ u )
= ( cP @ y @ v ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,plain,
! [X2: a,X1: a] :
( ( cR @ ( cP @ X2 @ X1 ) )
= X1 ),
inference(cnf_transformation,[],[f7]) ).
thf(f19,definition,
( spl0_1
<=> ( u = v ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f21,plain,
( ( u != v )
| spl0_1 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f23,definition,
( spl0_2
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f26,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f10,f23,f19]) ).
thf(f28,plain,
( v
= ( cR @ ( cP @ x @ u ) ) ),
inference(constrained_superposition,[],[f13,f12]) ).
thf(f29,plain,
( y
= ( cL @ ( cP @ x @ u ) ) ),
inference(constrained_superposition,[],[f9,f12]) ).
thf(f30,plain,
u = v,
inference(forward_demodulation,[],[f28,f13]) ).
thf(f31,plain,
x = y,
inference(forward_demodulation,[],[f29,f9]) ).
thf(f32,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f30,f21]) ).
thf(f33,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f32]) ).
thf(f34,plain,
spl0_2,
inference(avatar_split_clause,[],[f31,f23]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f26]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f33]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f34]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
thf(f35,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG287^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n008.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 17:38:24 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.24 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
% 0.22/0.29 % (3479507)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (3479524)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=330187956:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.29 % (3479524) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3479507-3479524"...
% 0.22/0.29 % (3479524)...printing done.
% 0.22/0.29 % (3479524)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 % (3479524)------------------------------
% 0.22/0.29 % (3479524)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (3479524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (3479524)CaDiCaL version: 2.1.3
% 0.22/0.29 % (3479524)Termination reason: Refutation
% 0.22/0.29 % (3479524)Time elapsed: 0.002 s
% 0.22/0.29 % (3479524)Peak memory usage: 13 MB
% 0.22/0.29 % (3479524)Instructions burned: 3 (million)
% 0.22/0.29 % (3479507)Success in time 0.036 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------