%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP001^7 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:07:34 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 14 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 15 ( 8 ~; 3 |; 1 &; 0 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 38 usr; 5 con; 0-4 aty)
% Number of variables : 12 ( 12 ^; 0 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
tyop_2Emin_2Ebool: $tType ).
thf(type_def_6,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_8,type,
tyop_2Emin_2Eind: $tType ).
thf(func_def_0,type,
c_2Ebool_2E_21:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_1,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(func_def_2,type,
c_2Emin_2E_3D:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_3,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(func_def_4,type,
c_2Ebool_2E_3F:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(func_def_6,type,
c_2Ebool_2E_7E: $o > $o ).
thf(func_def_8,type,
vNOT: $o > $o ).
thf(func_def_9,type,
c_2Ebool_2E_3F_21:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_10,type,
c_2Emin_2E_40:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_11,type,
c_2Ebool_2EBOUNDED: $o > $o ).
thf(func_def_12,type,
c_2Ebool_2ECOND:
!>[X0: $tType] : ( $o > X0 > X0 > X0 ) ).
thf(func_def_13,type,
c_2Ebool_2EDATATYPE:
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_14,type,
c_2Ebool_2EF: $o ).
thf(func_def_15,type,
c_2Ebool_2EIN:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_16,type,
c_2Ebool_2ELET:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 > X1 ) ).
thf(func_def_17,type,
c_2Ebool_2EONE__ONE:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > $o ) ).
thf(func_def_18,type,
c_2Ebool_2EONTO:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > $o ) ).
thf(func_def_19,type,
c_2Ebool_2ERES__EXISTS:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_20,type,
c_2Ebool_2ERES__EXISTS__UNIQUE:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_21,type,
c_2Ebool_2ERES__FORALL:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_22,type,
c_2Ebool_2ERES__SELECT:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_23,type,
c_2Ebool_2ET: $o ).
thf(func_def_24,type,
c_2Ebool_2ETYPE__DEFINITION:
!>[X0: $tType,X1: $tType] : ( ( X0 > $o ) > ( X1 > X0 ) > $o ) ).
thf(func_def_25,type,
c_2Ebool_2Eliteral__case:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 > X1 ) ).
thf(func_def_26,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_27,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_30,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_31,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
sK0:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_34,type,
sK1: $o ).
thf(func_def_35,type,
sK2:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_36,type,
sK3:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_37,type,
sK4:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_38,type,
sK5: tyop_2Emin_2Eind > tyop_2Emin_2Eind ).
thf(f19,axiom,
( c_2Ebool_2ET
<=> ( ( ^ [X0: $o] : X0 )
= ( ^ [X1: $o] : X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ET__DEF) ).
thf(f40,conjecture,
c_2Ebool_2ET,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(f41,negated_conjecture,
~ c_2Ebool_2ET,
inference(negated_conjecture,[status(cth)],[f40]) ).
thf(f62,plain,
( c_2Ebool_2ET
<=> ( ( ^ [X0: $o] : X0 )
= ( ^ [X1: $o] : X1 ) ) ),
inference(rectify,[],[f19]) ).
thf(f63,plain,
( ( ( ^ [Y0: $o] : Y0 )
= ( ^ [Y0: $o] : Y0 ) )
<=> ( c_2Ebool_2ET = $true ) ),
inference(fool_elimination,[],[f62]) ).
thf(f110,plain,
~ c_2Ebool_2ET,
inference(rectify,[],[f41]) ).
thf(f111,plain,
c_2Ebool_2ET != $true,
inference(fool_elimination,[],[f110]) ).
thf(f112,plain,
c_2Ebool_2ET != $true,
inference(flattening,[],[f111]) ).
thf(f152,plain,
( ( ( ( ^ [Y0: $o] : Y0 )
= ( ^ [Y0: $o] : Y0 ) )
| ( c_2Ebool_2ET != $true ) )
& ( ( c_2Ebool_2ET = $true )
| ( ( ^ [Y0: $o] : Y0 )
!= ( ^ [Y0: $o] : Y0 ) ) ) ),
inference(nnf_transformation,[],[f63]) ).
thf(f161,plain,
c_2Ebool_2ET != $true,
inference(cnf_transformation,[],[f112]) ).
thf(f206,plain,
( ( ( ^ [Y0: $o] : Y0 )
!= ( ^ [Y0: $o] : Y0 ) )
| ( c_2Ebool_2ET = $true ) ),
inference(cnf_transformation,[],[f152]) ).
thf(f249,plain,
c_2Ebool_2ET = $true,
inference(trivial_inequality_removal,[],[f206]) ).
thf(f254,plain,
$false,
inference(forward_subsumption_resolution,[],[f249,f161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP001^7 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n014.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 19:18:05 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.23 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
% 0.20/0.28 % (3087186)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (3087195)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1730373154:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.28 % (3087195) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3087186-3087195"...
% 0.20/0.28 % (3087195)...printing done.
% 0.20/0.28 % (3087197)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.28 % (3087197)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.28 % (3087195)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (3087195)------------------------------
% 0.20/0.28 % (3087195)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3087195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3087195)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3087195)Termination reason: Refutation
% 0.20/0.28 % (3087195)Time elapsed: 0.003 s
% 0.20/0.28 % (3087195)Peak memory usage: 12 MB
% 0.20/0.28 % (3087195)Instructions burned: 9 (million)
% 0.20/0.28 % (3087186)Success in time 0.043 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------