%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n005.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 08:10:34 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 14 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 15 ( 8 ~; 0 |; 0 &; 7 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 3 con; 0-4 aty)
% Number of variables : 4 ( 4 ^; 0 !; 0 ?; 4 :)
% 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_11,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_13,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_16,type,
vAND: $o > $o > $o ).
thf(func_def_17,type,
vOR: $o > $o > $o ).
thf(func_def_18,type,
sK0: tree_b > b ).
thf(func_def_19,type,
sK1: tree_b > tree_b ).
thf(func_def_20,type,
sK2: tree_b > tree_b ).
thf(func_def_21,type,
sK3: ( tree_b > $o ) > b ).
thf(func_def_22,type,
sK4: ( tree_b > $o ) > tree_b ).
thf(func_def_23,type,
sK5: ( tree_b > $o ) > tree_b ).
thf(func_def_24,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(f16,plain,
( heapIm229596387mpty_b
= ( ^ [Y0: tree_b] : ( e_b = Y0 ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f30,plain,
~ ( heapIm229596387mpty_b @ e_b ),
inference(rectify,[],[f15]) ).
thf(f31,plain,
( ( heapIm229596387mpty_b @ e_b )
!= $true ),
inference(fool_elimination,[],[f30]) ).
thf(f33,plain,
( ( heapIm229596387mpty_b @ e_b )
!= $true ),
inference(flattening,[],[f31]) ).
thf(f40,plain,
( heapIm229596387mpty_b
= ( ^ [Y0: tree_b] : ( e_b = Y0 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f55,plain,
( ( heapIm229596387mpty_b @ e_b )
!= $true ),
inference(cnf_transformation,[],[f33]) ).
thf(f58,plain,
( $true
!= ( ^ [Y0: tree_b] : ( e_b = Y0 )
@ e_b ) ),
inference(definition_unfolding,[],[f55,f40]) ).
thf(f59,plain,
( $true
!= ( e_b = e_b ) ),
inference(beta-eta_normalization,[],[f58]) ).
thf(f60,plain,
e_b != e_b,
inference(equality_proxy_clausification,[],[f59]) ).
thf(f61,plain,
$false,
inference(trivial_inequality_removal,[],[f60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP065^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n005.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 19:45:32 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 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
% 0.22/0.29 % (2119837)Will run a generic schedule for satisfiability detection.
% 0.22/0.29 % (2119844)% WARNING: option uhcvi not known.
% 0.22/0.29 % (2119844)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2421997766:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.29 % (2119844)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.29 % (2119844)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.22/0.29 % (2119844) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2119837-2119844"...
% 0.22/0.29 % (2119843)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3310690195_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.29 % (2119844)...printing done.
% 0.22/0.29 % (2119844)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 % (2119844)------------------------------
% 0.22/0.29 % (2119844)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (2119844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (2119844)CaDiCaL version: 2.1.3
% 0.22/0.29 % (2119844)Termination reason: Refutation
% 0.22/0.29 % (2119844)Time elapsed: 0.002 s
% 0.22/0.29 % (2119844)Peak memory usage: 11 MB
% 0.22/0.29 % (2119844)Instructions burned: 3 (million)
% 0.22/0.29 % (2119837)Success in time 0.036 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------