%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP065^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:08:11 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 17 unt; 0 typ; 2 def)
% Number of atoms : 76 ( 26 equ; 3 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 49 ( 19 ~; 14 |; 0 &; 14 @)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 23 usr; 6 con; 0-4 aty)
% Number of variables : 6 ( 0 sgn 3 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
tree_b: $tType ).
thf(type_def_6,type,
b: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
heapIm229596387mpty_b: tree_b > $o ).
thf(func_def_1,type,
heapIm1140443834left_b: tree_b > tree_b ).
thf(func_def_2,type,
heapIm1257206335ight_b: tree_b > tree_b ).
thf(func_def_3,type,
e_b: tree_b ).
thf(func_def_4,type,
t_b: b > tree_b > tree_b > tree_b ).
thf(func_def_5,type,
pred_Tree_b: ( b > $o ) > tree_b > $o ).
thf(func_def_6,type,
in_tree_b: b > tree_b > $o ).
thf(func_def_7,type,
val_b: tree_b > b ).
thf(func_def_8,type,
ord_less_eq_Tree_b_o: ( tree_b > $o ) > ( tree_b > $o ) > $o ).
thf(func_def_9,type,
ord_less_eq_b_o: ( b > $o ) > ( b > $o ) > $o ).
thf(func_def_13,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_15,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_16,type,
sK0: tree_b > tree_b ).
thf(func_def_17,type,
sK1: tree_b > tree_b ).
thf(func_def_18,type,
sK2: tree_b > b ).
thf(func_def_19,type,
sK3: ( tree_b > $o ) > b ).
thf(func_def_20,type,
sK4: ( tree_b > $o ) > tree_b ).
thf(func_def_21,type,
sK5: ( tree_b > $o ) > tree_b ).
thf(func_def_22,type,
vNOT: $o > $o ).
thf(f1,axiom,
( heapIm229596387mpty_b
= ( ^ [X0: tree_b] : ( X0 = e_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_hs__is__empty__def) ).
thf(f14,conjecture,
heapIm229596387mpty_b @ e_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f15,negated_conjecture,
~ ( heapIm229596387mpty_b @ e_b ),
inference(negated_conjecture,[status(cth)],[f14]) ).
thf(f18,plain,
( heapIm229596387mpty_b
= ( ^ [Y0: tree_b] : ( e_b = Y0 ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f21,plain,
~ ( heapIm229596387mpty_b @ e_b ),
inference(rectify,[],[f15]) ).
thf(f22,plain,
( ( heapIm229596387mpty_b @ e_b )
!= $true ),
inference(fool_elimination,[],[f21]) ).
thf(f37,plain,
( ( heapIm229596387mpty_b @ e_b )
!= $true ),
inference(flattening,[],[f22]) ).
thf(f60,plain,
( heapIm229596387mpty_b
= ( ^ [Y0: tree_b] : ( e_b = Y0 ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f61,plain,
( ( heapIm229596387mpty_b @ e_b )
!= $true ),
inference(cnf_transformation,[],[f37]) ).
thf(f90,plain,
( heapIm229596387mpty_b
= ( (=) @ e_b ) ),
inference(beta-eta_normalization,[],[f60]) ).
thf(f92,definition,
( spl6_1
<=> ( ( heapIm229596387mpty_b @ e_b )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f94,plain,
( ( ( heapIm229596387mpty_b @ e_b )
!= $true )
| spl6_1 ),
inference(avatar_component_clause,[],[f92]) ).
thf(f95,plain,
~ spl6_1,
inference(avatar_split_clause,[],[f61,f92]) ).
thf(f97,definition,
( spl6_2
<=> ( heapIm229596387mpty_b
= ( (=) @ e_b ) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f99,plain,
( ( heapIm229596387mpty_b
= ( (=) @ e_b ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f97]) ).
thf(f100,plain,
spl6_2,
inference(avatar_split_clause,[],[f90,f97]) ).
thf(f101,plain,
( ! [X1: tree_b] :
( ( e_b = X1 )
= ( heapIm229596387mpty_b @ X1 ) )
| ~ spl6_2 ),
inference(argument_congruence,[],[f99]) ).
thf(f103,plain,
( ! [X1: tree_b] :
( ( $false
= ( e_b = X1 ) )
| ( $true
= ( heapIm229596387mpty_b @ X1 ) ) )
| ~ spl6_2 ),
inference(iff_proxy_clausification,[],[f101]) ).
thf(f104,plain,
( ! [X1: tree_b] :
( ( $true
= ( heapIm229596387mpty_b @ X1 ) )
| ( e_b != X1 ) )
| ~ spl6_2 ),
inference(equality_proxy_clausification,[],[f103]) ).
thf(f121,plain,
( ( $true != $true )
| ( e_b != e_b )
| spl6_1
| ~ spl6_2 ),
inference(superposition,[],[f94,f104]) ).
thf(f122,plain,
( $false
| spl6_1
| ~ spl6_2 ),
inference(trivial_inequality_removal,[],[f121]) ).
thf(f123,plain,
( spl6_1
| ~ spl6_2 ),
inference(avatar_contradiction_clause,[],[f122]) ).
cnf(s1,plain,
~ spl6_1,
inference(sat_conversion,[],[f95]) ).
cnf(s2,plain,
spl6_2,
inference(sat_conversion,[],[f100]) ).
cnf(s3,plain,
( spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f123]) ).
cnf(s4,plain,
spl6_1,
inference(rat,[],[s3,s2]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4]) ).
thf(f124,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP065^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n004.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 19:45:37 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.22/0.28 % (1743960)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (1743968)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2367477649:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.28 % (1743968) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1743960-1743968"...
% 0.22/0.28 % (1743968)...printing done.
% 0.22/0.28 % (1743968)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.28 % (1743968)------------------------------
% 0.22/0.28 % (1743968)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (1743968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (1743968)CaDiCaL version: 2.1.3
% 0.22/0.28 % (1743968)Termination reason: Refutation
% 0.22/0.28 % (1743968)Time elapsed: 0.004 s
% 0.22/0.28 % (1743968)Peak memory usage: 13 MB
% 0.22/0.28 % (1743968)Instructions burned: 9 (million)
% 0.22/0.28 % (1743960)Success in time 0.035 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------